Green productivity and undesirable outputs in agriculture: a systematic review of DEA approach and policy recommendations

Abstract Measuring efficiency in the presence of undesirable outputs could be difficult depending on how to treat these outputs; thus, undesirable outputs modelling has been an exciting subject of several studies in the Data envelopment analysis (DEA) literature in the last two decades. The present study aims to illustrate a thorough overlook of studies in which DEA has applied for measuring efficiency with undesirable outputs. Fifty-eight articles were published from 2000 to 2020 have been systematically reviewed through PRISMA protocol. The results indicated that "Journal of Cleaner Production" ranked first with six published articles, and Chinese scholars have the most contributions to this field, with twenty-third articles. Also, almost a quarter of the published articles' scope was related to agricultural pollution, and thirteen articles were published in 2016, the highest number of published articles annually. Taken together, the theoretical and empirical implications of research in the field of Green Productivity are discussed, and some policies were recommended.


Introduction
The agriculture sector plays a crucial role in debates on green, circular, and bioeconomy mainstreamed global sustainability concepts (Tsangas et al., 2020). It is characterised by several feedstocks appropriate to be improved in terms of material and energy; thus, new opportunities are provided by the circular economy for investors (D'Adamo et al., 2019). The circular economy has two primary goals: improving waste management (or reutilizing), reducing energy consumption (or boosting green energy) (Kapsalis et al., 2019). It is believed that by transforming the agri-sector into circular, apart from the technological sector, circular economy goals could be more achievable; since the agri-sector is one of the most sectors in which a high percentage of biomass has been produced (Jimenez-Lopez et al., 2020). On top of that, renewable biological resources (biomass) and circularity are the critical aspects of the bioeconomy (D'Adamo et al., 2020a); thus, materials recycling, fossil fuel use reduction, and waste management lead the bioeconomy to obtain biofuel, bioenergy, etc., which are vital for achieving sustainable development goals (SDGs) (Duque-Acevedo et al., 2020, Morone & D'Amato, 2019. SDGs could provide a framework of measurable goals and targets and goals, linked directly or indirectly with circular economy principles, to harmonise sustainable development and world economies (Loizia et al., 2021, D'Adamo et al., 2020b. Economic development and industrialisation rely on high resource input, while the capacities of the environment and resources are neglected, which caused undesirable outputs and ecological crises . Undesirable outputs comprise wastewater, CO 2 emission, air pollution, etc., which are dangerous for the environment (Tohidi et al., 2014). Undesirable outputs are produced unwillingly in the agricultural sector; thus, policy-makers need to utilise scientific approaches to cope with the undesirable outputs' of production and reduce them (Halkos & Petrou, 2019b, Tohidi et al., 2014. Both undesirable and desirable outputs produce jointly; however, undesirable outputs affect efficiency scores' evaluation of decision-making units (DMUs). Over the last decade, for instance, energy consumption and CO 2 emissions have risen considerably in China, emitting almost 8200 million tons of CO 2 in 2012, produced by industries and agricultural sectors (Sun et al., 2016). Also, waste, an environmental issue having strong relationships whit economic and social dimensions, has increased dramatically over the years (Doula et al., 2019. Zorpas (2020) mentioned various reasons for producing waste in which undesirable outputs, such as CO 2 emissions, were ranked as the most influential reason; also, D' Adamo et al. (2021) mentioned that biomethane could be used as fuel which is an excellent potential for EU leading them towards a green economy; therefore, assessing the environmental productivity in the presence of the undesirable outputs is vital (Dakpo et al., 2014).
There are three popular methods for measuring productivity within a broad context, including index measurement, linear programming, and econometric models (Singh et al., 2000). Index measurement comprises the employing of five ratios for measuring productivity: "single-factor productivity," "multiple factor productivity," "total productivity," "managerial control ratio," and "productivity costing." The most prevalent ratio is the total productivity, in which the productivity is measured as a ratio of various inputs. Linear programming, in which Data envelopment analysis (DEA) is the most prevalent, creates a production frontier and assesses the inputs' contribution to the productivity considering the past performance data . DEA models and econometric models are applicable when large data series are available. In econometric models, statistical models are applied to the data series to estimate productivity. The leaner programming and econometrics models are usually integrated to deal with productivity measurement issues (Singh et al., 2000). The DEA models' main advantages over the other methods are: DEA models could maximise multiple outputs simultaneously, while total productivity index could only maximise one output. DEA is a non-parametric mathematical model; thus, a specific functional form is not required making DEA more flexible and applicable compared to others (Liu et al., 2017). DEA could trace less-productive inputs by employing separate and specific optimisation routines for each input, making DEA more robust than the others.
DEA is a mathematical method proposed by Charnes et al. (1978), and it utilises linear programming methods to turn inputs into outputs to evaluate the performance. Also, any DMUs can freely select any mixture of inputs and outputs to increase their relative efficiency (Kang et al., 2018). By dividing the total weighed output by the total weighted input, the efficiency score or relative efficiency is calculated. The relative efficiency is a non-negative value and calculated concerning linear interactions between the inputs and outputs of the DMUs (Mardani et al., 2018, Zare et al., 2019. Simply put, the relative efficiency shows the level of efficiency of a DMU in a determined level of output concerning the quantity of input, which consumes compared to similar DMUs (Zhou et al., 2019). Shen et al. (2017) mentioned that many researchers used DEA to assess agricultural performance, environmental efficiency, and productivity with undesirable outputs. For instance, Fei and Lin (2017b) utilised Meta-Frontier DEA to tackle the agricultural problems related to carbon dioxide emissions. Li et al. (2013) used constant returns-to-scale (CRS) and variable returnsto-scale (VRS)-DEA to allocate resources to reduce CO 2 emission effectively. Yaqubi et al. (2016) used Directional Distance Functions (DDF)-DEA to assess environmental practices' efficiency and shadow values.
There are three basic DEA models, including radial, additive, and slack-based measure (SBM) models. The radial model was proposed by Charnes et al. (1978) is considered the original DEA model, also called the CCR (Charnes, Cooper, and Rhodes) model (Yang & Wei, 2019). In this model, The DMU's efficiency score is measured based on the proportional or radial distance to the efficiency frontier. The radial models are divided into two models: CCR and BCC (Banker, Chames, and Cooper) models. In the BCC model, the production technology shows variable returns to scale (Paradi et al., 2018). Furthermore, the additive model is used if there are multiple inputs and multiple outputs; therefore, the additive model determines all potential of inefficiency through the summation of the total inputs and desirable outputs slacks. The value of variable data could be zeros or negative in the additive model, unlike the radial DEA model (Cooper et al., 2006). Moreover, the SBM model is considered an extension of the additive model developed by Tone (2001). In this model, like the additive model, a mix of multiple inputs and outputs could be considered; however, it could be a unit invariant and generate a standard efficiency score, unlike the additive model.
Measuring productivity is considered a crucial research avenue in economics since it explains how inputs transform into outputs through factors of changes (Bale zentis et al., 2021); however, measuring productivity in the presence of undesirable outputs could be difficult depending on how to treat these outputs. The various treatment methods with undesirable outputs in DEA have recently received more attention (Boussemart et al., 2020). Halkos and Petrou (2019b) did attend to present four possible way to cope with undesirable outputs in DEA, including (1) disregarding negative outputs from the production process, (2) regarding negative outputs as inputs, (3) regarding negative outputs as positive outputs, and (4) applying required modifications to take negative outputs into account. They also mentioned a new model named Zero-Sum Gains-DEA (ZSG-DEA) models utilised by Gomes and Lins (2008) to deal with undesirable outputs. Therefore, it is necessary to a clear and comprehensive review of the various treatment methods with undesirable outputs in DEA models be provided due to the effect of the treatment method on productivity; also, capabilities of various DEA models could be highlighted through a comprehensive review motivating scholars to apply them for measuring productivity with undesirable outputs and compare them with the previous research. On top of that, current research gaps in measuring productivity and methodological concerns are highlighted through a systematic literature review providing a clear pathway for future research.
State of the art in applying DEA models for measuring agricultural productivity with undesirable outputs through systematic literature review and recommending applicable policies, based on obtained results, to boost green, circular, and bioeconomy could be considered the present study's novelties. Simply put, providing a broad overview of DEA models' application in agriculture productivity with undesirable outputs is the ultimate aim of the present study; therefore, the ultimate aim can be divided into four research issues: (1) which area of agricultural productivity with undesirable outputs has utilised DEA more? (2) which nationality has conducted further research in this area? (3) in which year did scholars publish the most articles? (4) which journals have further published articles in this field? The present study will focus on the significance of DEA in agricultural productivity with undesirable outputs. The main contributions of this article are as follows: (1) improving the understanding of the current scientific knowledge on green productivity and undesirable outputs (2) highlighting why and how DEA models are widely used to measure productivity with undesirable outputs in the agri-sector (3) providing an overview of research limitations and gaps that hinder measuring productivity with undesirable outputs (4) investigating the current status of DEA application for measuring productivity with undesirable outputs concerning the years of publication, authors' nationality, articles' scope, and publication frequency (5) recommending policies and research avenues to provide a pathway for future empirical and theoretical research.
The article's structure is arranged as follows: Section 2 expresses four DEA models being popular in agricultural productivity with undesirable outputs. Section 3 presents the methodology of the present research and how the articles were classified is presented. Section 4 presents the results, including distribution of articles by publication time, author's nationality, and journals. The results were discussed in Section 5. Section 6 presents conclusions, limitations, policies, and future research recommendations.

DEA models for dealing with undesirable outputs
In 1978, Charnes et al. presented the first DEA model, namely CCR, to calculate the technical efficiency of DMUs in the form of a non-parametric model, while there are many inputs and outputs (Charnes et al., 1978). Researchers used CCR-DEA, BCC-DEA, SBM-DEA, and Range-Adjusted Measure (RAM)-DEA to calculate agricultural productivity with undesirable outputs. The four mentioned models, which are the most popular agriculture performance model with undesirable outputs, are presented.

CCR-DEA model
The overall efficiency for a DMU is calculated through the CCR-DEA model if both scale efficiency and pure technical efficiency are combined into a single value. On top of that, the CCR-DEA model never measures absolute efficiency as it is always measured relatively. Also, CCR-DEA is suitable for a situation in which all DMUs are operating at an optimal scale. Assume a manufacturing system with n DMUs, which has three elements, including inputs (X), desirable outputs (G), and undesirable outputs (B). The three matrices X, G, B, and the production possibility set (P) are defined through equation one and k is the intensity vector (Li et al., 2013).
The output-oriented DEA model coping with undesirable outputs for assessing DMU x 0 , g 0 , b 0 ð Þ is presented below, and r Ã is the inefficiency score of DMUs calculated by equation two (Li et al., 2013). It should be noted that efficiency score can be calculated by h ¼ 1 1þr :

Bcc-DEA model
Variable return to scale frontiers is assumed in the BCC model, while the CCR model assumes a constant return to scale frontiers. Also, overall technical efficiency is measured by the CCR model, while the BCC model measures the pure technical efficiency. Also, as mentioned, the CCR model is not appropriate if DMUs are not operating at an optimal scale; in contrast, the BCC model was developed to deal with situations in which technical efficiencies variables are measured while confounded to scale efficiencies. Assume a manufacturing system with n DMUs is considered, while it has three elements, including inputs (X), desirable outputs (G), and undesirable outputs (B). The three matrices X, G, B, and the production possibility set (P) are defined through equation three and k is the intensity vector (Li et al., 2013).
The output-oriented DEA model coping with negatives outputs for assessing DMU x 0 , g 0 , b 0 ð Þis presented below, and r Ã is the inefficiency score of DMUs calculated by equation four (Li et al., 2013). It should be noted that efficiency score can be calculated by h ¼ 1 1þr : Inputs (outputs) may not behave proportionally in reality, while radial DEA models, such as CCR and BCC, deal with proportional changes in inputs(outputs). Also, radial models neglect slacks in measuring efficiency, while non-radial slacks affect managerial efficiency. In contrast, the slack-based DEA model works directly with slacks and puts aside the proportional changes assumption; however, two primary conditions, including unit invariant and monotone, should be met. Let X ¼ x 1 , . . . , x I ð Þ 2 R I þ be an inputs' vector, G ¼ g 1 , . . . , g J ð Þ 2 R J þ be a desirable outputs' vector, and þ be an undesirable outputs' vector. Also, k k is an intensity vector, and k ¼ k 1 , . . . , K ð Þis the index of DMUs. Therefore, the SBM-DEA model accounting for any outputs is presented through equation five .
where 0 q t 1 with q t ¼ 1 shows total efficiency, while t ¼ 1, 2, … , K. it is presented that the t-th observation presented by input-output ðx t i , g t i , b t i Þ is showed in the production frontier at the point are the optimal value of s x i , s g j , and s b l , respectively .

RAM-DEA model
In the non-radial RAM-DEA, desirable and undesirable outputs could easily be incorporated into a unified model compared to the radial DEA models. Also, RAM-DEA is a linear non-radial model making it more applicable than the non-linear conventional DEA models. RAM-DEA model is specially proposed and applied by Sueyoshi and Goto (2012) and Sueyoshi and Goto (2011) to measure productivity in the presence of undesirable outputs. Let G j ¼ g 1j , . . . , g nj ð Þ T be a vector of desirable outputs, and B j ¼ b 1j , . . . , b nj À Á T be a vector of undesirable outputs, while for j ¼ 1, . . . , n, G > 0, and B > 0; therefore, in the following, the non-radial RAM-DEA proposed by Sueyoshi and Goto (2011) is presented through equation six.
where k g j and k b j are, respectively, intensity variables for desirable and undesirable outputs. Also, d g r is a surplus variable for r-th desirable output, d b r is a slack variable for f-th undesirable output, and R g r and R b f indicate the DEA model ranges for desirable and undesirable outputs, respectively, presented through equation seven, while s and h show the number of desirable and undesirable outputs.
where m represents the number of inputs utilised for yielding desirable and undesirable outputs; therefore, the unified efficiency score of the k-th DMU is calculated through equation eight, while d gÃ t , and d bÃ t are the optimal value of d g t , and d b t , respectively.

Research methodology
The present article used the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) protocol to conduct a systematic literature review (SLR). SLR maps and evaluates the current knowledge and gaps in research fields, developing the knowledge base further. SLR follows scientific, replicable, and transparent stages differing from conventional narrative reviews (Murschetz et al., 2020). All publications related to the specific issue could be collected concerning the pre-defined criteria to answer research questions. SLR avoids bias occurring throughout searching, identification, appraisal, synthesis, analysis, and summary of studies using the systematic and explicit procedure (Mengist et al., 2020). Therefore, SLR could provide reliable findings and conclusions due to its capabilities to deal with bias, helping scholars and decision-makers to act accordingly (Saraji & Sharifabadi, 2017). Moreover, apart from PRISMA, there are several methodologies to conduct SLR, such as Search, Appraisal, Synthesis, and Analysis (SALSA). However, PRISMA has some advantages over other methods, such as (1) it has a detailed, precise, and welldescribed checklist helping scholars in improving systematic review reporting and meta-analyses (2) it is an updated protocol due to its various versions were released time to time, which the newest one was released in 2020; therefore, the present study employed PRISMA protocol to conduct a systematic literature review.
Scrutinizing the current literature is the first step of SLR. In this stage, some substantial scientific databases named Google Scholar, Web of Science (WOS), and Scopus are nominated to find the published articles related to the topic. The search is conducted for grey literature; we search for critical journals and scan the references' lists. The second step, named the eligibility criteria stage, focuses on the study's different characteristics, including the population of interest, study design, time duration, publication year, publication status, and language. Next, the PRISMA focuses on the information sources. This stage explains all related information of resources, such as electronic databases, authors' information, trial registers, and coverage date.

Searching method
According to the first step of PRISMA, some viable databases, e.g., WOS, Google Scholar, and Scopus, have been selected to comprehensively review the implementation of DEA in agricultural productivity with undesirable outputs. To find the related publications, we search in the selected databases with various keywords such as "DEA and energy efficiency in agricultural with undesirable outputs," "DEA and performance assessment in agricultural with undesirable outputs," "DEA and agricultural pollution with undesirable outputs," "DEA and sustainable agriculture with undesirable outputs," "DEA and agricultural economics with undesirable outputs," "DEA and agricultural industry," "DEA and crop production in agricultural with undesirable outputs," "DEA and resource efficiency," "DEA and agricultural production with undesirable outputs," etc. also, we attempt to involve the recently published articles, and therefore, our selection years are between 2000 and 2020. In the first attempt, based on the above keywords, in total, we identify 276 publication records. In the next stage, we screen the publications based on abstracts and titles to eliminate different items. After eliminating different items in this step, in total, 58 articles remained for the following stages. The PRISMA diagram is shown in Figure 1.

Publications' eligibility
In this step, the full text of the remaining articles has been reviewed one after another. We choose the articles that used an extension of DEA to compute agricultural productivity and efficiency with undesirable outputs. At this stage, we omit some documents such as essays, Ph.D. and master theses, book chapters, books, other published resources in other languages except English, and editor's notes. Finally, after the mentioned stages, we choose 58 articles related to the DEA applications in agricultural productivity with undesirable outputs from 36 international scholarly journals between 2000 and 2020.

Data extraction and summarizing
In this step, firstly, required information has been extracted from the remaining articles. Finally, the remaining articles were classified into different groups (see Table  1) according to the article's primary purpose. Furthermore, all fifty-eight publications are reviewed and summarised based on various views; and are grouped into five  classifications), including agricultural pollution, sustainable agriculture, agricultural economics, environmental performance, and resource efficiency.

Classification articles based on agricultural pollution
A wide variety of agricultural pollution, including air pollution, water pollution, wastewater, CO 2 emissions, etc. considered as significant challenges in countries (Chen et al., 2017). Agricultural activities increase pollutants affecting air quality, environmental performance, water quality, and other areas (Abbasi et al., 2014). Several studies have been conducted to measure productivity in which DEA was used to calculate efficiency of agricultural DMU, while agricultural pollutions were considered undesirable outputs. For instance, Falavigna et al. (2013) used Directional Output Distance Function (DODF)-DEA and Malmquist index to estimate the production possibility for each DMU, while they considered emission quantities of NHO 3 as undesirable outputs, and Kuhn et al. (2018) used SBM-DEA to carry out the difference between waste management in commercials and backyard hog farms, while CO 2 emission as an undesirable output. Table 2 indicates details extracting from the articles were related to agricultural pollution.

Classification articles based on sustainable agriculture
Sustainability has become attractive among practitioners, scholars, and strategists due to the growing environmental and social concerns (Boussemart et al., 2020). Sustainable agriculture relies on meeting human food, fibre, and biofuel expectations, and it improves the quality of the environment and resource base; the agronomists' living standards, farmworkers, and society to ensure the economic viability of the agricultural sector (Goła s et al., 2020). Also, sustainable agriculture looks for increasing profitable farm income and promoting environmental stewardship. Therefore, evaluating sustainable agriculture potentials has become attractive for scholars as various methods have been developed for this purpose (Ren et al., 2021). For example, Shen et al. (2018) integrated the by-production model and DEA to calculate the shadow price of CO 2 emission in china's agricultural sectors, since due to the high population of china, having sustainable agriculture is vital, and Vlontzos et al. (2017) developed a synthetic Eco-(in) efficiency index using DDF-DEA model to evaluate the sustainability of the EU agricultural sector over 13 years from 1999 to 2012 on a  country level. Table 3 indicates all details extracting from the articles were related to Sustainable agriculture.

Classification articles based on agricultural economics
Agricultural economics looks for applying economic theories to optimise the production and distribution of agricultural production. Also, Agricultural economics is a branch of economics dealing with land usage, and it emphasises maximising agricultural production and maintaining a good soil ecosystem (Martin, 2019). For instance, the low-carbon economy, a part of agricultural economics, aims to reduce greenhouse gas emissions and save energy consumption to have sustainable agriculture (Streimikiene, 2021). Agricultural economics includes many areas and approaches, including DEA models; therefore, many studies have been carried out to compute energy efficiency and CO 2 emission efficiency concerning low carbon economics policies. For instance, Fei and Lin (2017b) used meta-frontier DEA to find an acceptable policy for agricultural energy saving and to carry out the sources of CO 2 emissions reduction, and Rebolledo-Leiva et al. (2017) integrated Life-cycle assessment (LCA) and VRS-DEA to maximise production and to decrease Carbon Footprint (CF) concerning the economics and ecological perspectives. Table 4 indicates details extracting from the articles were related to agricultural economics.

Classification articles based on environmental performance
Singh et al. (2020) mentioned that environmental performance is the organization's behaviour concerning the natural environment regarding how it goes about consuming resources to scan pollution emissions strictly. It is considered an introduction of biodegradable ingredients in products, reducing waste and pollution, reducing materials being harmful to the environment, enhancing energy efficiency, etc. (Singh et al., 2019). Due to the importance of environmental performance, several studies used different models, such as DEA, to measure environmental performance. For example, Guti errez et al. (2017) used a hybrid multi-stages DEA and regression analysis to calculate rain-fed cereals' efficiency based on actual management circumstances and environmental variables. Le et al. (2019) used the SBM-DEA model to determine the differences in productivity and agriculture efficiency among Asian countries. Table 5 indicates all details extracting from the articles were related to environmental performance.

Classification articles based on resource efficiency
It is challenging to develop indicators reflecting resource use and its impacts on the environment, economy, and security due to several natural resources characterised by different attributes. However, resource use is distinguished into four categories: usage of material, water, land, energy, and climate change. Modern agriculture faces significant challenges, including extreme water supply and fertiliser impacts (Zamparas et al., 2019a), deforestation (Tsiantikoudis et al., 2019), GHG emissions    (Kyriakopoulos & Chalikias, 2013, Kyriakopoulos et al., 2010, soil erosion, eutrophication (Zamparas et al., 2019b), and water pollution ( (Zamparas et al., 2020). Also, resource use efficiency means allocating and using various scarce resources to reach benefits. Due to the importance of agricultural economics, resource, consumption, and allocation efficiency are the main research stream in this branch of the economy; therefore, Resource consumption and allocative efficiency can be examined through the different approaches, including the DEA model. For instance, Yang and Li (2017) utilised SBM-DEA to evaluate the Total Factor Efficiency of Water resource (TFEW) and the Total Factor Efficiency of Energy (TFEE), and Deng et al. (2016) employed SBM-DEA to calculate the usage efficiency of water in china areas. Table 6 indicates all details extracting from the articles were related to resource efficiency. Table 7 provides information about the frequency of articles by journals' names. The articles linked to the agricultural performance assessment with undesirable outputs and the DEA models have been chosen through 36 a vast verity of journals from the WOS database, Scopus, Google Scholar. On the surface, "Journal of Cleaner Production" was ranked first with six articles, followed by "Sustainability," "Renewable and Sustainable Energy Reviews," "European Journal of Operational Research," "Agricultural Economics," and "Ecological Indicators" with three articles. The results indicated "Journal of Cleaner Production" made the most contribution in implementing DEA models in agricultural performance assessment with undesirable outputs. Table 8 indicates that authors from seventeen countries utilised DEA models in agricultural performance assessment with undesirable outputs, while the Chinese had the most contributions with39.66%. The figure for Australia accounting for the second country is 8.62%. Interestingly, the figure for Iran and Lithuania are the same, with 6.90%. On top of that, the results indicated that Chinese scholars utilised By-production technology and directional distance function (Shen et al., 2017, Fei & Lin, 2017a, the SBM DEA (Kuhn et al., 2018, Deng et al., 2016, Tao et al., 2016, Bian et al., 2014, Dong et al., 2018, Long et al., 2018, Song et al., 2014, Pang et al., 2016, Yang & Li, 2017, the Zero-Sum-Gains DEA (Sheng et al., 2016), meta-frontier DEA (Fei & Lin, 2017b, Fei & Lin, 2016, Malmquist index DEA (Wang et al., 2015, Zhang et al., 2011, Lin & Fei, 2015, DEA-Game (Wu et al., 2013), BCC-DEA (Li et al., 2013), DEA-Tobit (You & Zhang, 2016), centralised DEA (Sun et al., 2016). Australian scholars utilised the directional distance function (Hoang & Coelli, 2011, Azad & Ancev, 2014, CCR-DEA (Coelli et al., 2007, Hoang & Alauddin, 2012, BCC-DEA (Pagotto & Halog, 2016). Iranian scholars utilised the directional distance function (Yaqubi et al., 2016), non-radial DEA (Babazadeh et al., 2015, Zare-Haghighi et al., 2014, BCC-DEA (Khoshroo et al., 2018).   Figure 2 illustrates the frequency of the publication time. The number of articles written in applying the DEA model in agricultural performance assessment with undesirable outputs rose dramatically over the past two decades. The first article was published in 2000, while in 2019, the number of articles is 58, while more of them was published in 2016, with 13 articles. It is anticipated the number of articles in this field will be increased in the future.

Discussion
Results indicated that DEA models showed great promise to be an excellent assessment tool for further productivity measurement in the agricultural sector, especially when it is complicated to determine the production function represented the inputs and outputs relationships. The DEA models' superiority in dealing with multiple inputs and multiple outputs makes them an exciting research field for scholars interested in productivity measurement with undesirable outputs in agricultural sectors. Not only could DEA models be an alternative for index measurement or econometric models for productivity measurement, but also DEA models could be integrated with various methods, such as game theory (Wu et al., 2013), artificial neural network (ANN) , regression (Buckley & Carney, 2013), Tobit analysis (You & Zhang, 2016), LCA (Rebolledo-Leiva et al., 2017), goal programming (Andre et al., 2010) to deal with productivity measurement with undesirable outputs. Furthermore, the results indicated that there are different types of DEA models such as Meta-frontier DEA, Malmquist index (Fei & Lin, 2016), VRS-DEA (Zhang, 2008)  models can accommodate multiple inputs and outputs to calculate the relative efficiency of DMUs in agri-sectors, while it is not necessary to set the weights for DMUs since DEA models use a ratio of "weighted outputs sum" to "weighted inputs' sum;" therefore, DEA models could be applied for measuring agricultural productivity due to its superiority in dealing with undesirable outputs, which is consistent with previous studies, such as Bale zentis et al. (2016)

Conclusion and policy recommendations
The present article's primary purpose is to provide a holistic overview of the DEA's implementation in assessing agricultural productivity with undesirable outputs. In this regard, a systematic review using PRISMA protocol has been conducted to find and review the published articles in agricultural production with undesirable outputs over 2000 to 2020. Primary databases, including Google Scholar, Scopus, and WOS, were searched. This study classified the found articles concerning application areas, including agricultural pollution, sustainable agriculture, agricultural economics, environmental performance, and resource efficiency. Agriculture pollution was ranked first. Also, the selected articles are categorised based on different indicators such as the name of journals, author(s) names, methods, area of implementation, study and DEA purposes, articles' contribution and gaps, outcomes and results, year of publication, and authors' nationalities. In this regard, there were 36 journals had contributed to this article which. The "Journal of Cleaner Production" was ranked the first journal with six publications, followed by "Sustainability," "Renewable and Sustainable Energy Reviews," "European Journal of Operational Research," "Agricultural Economics and Ecological Indicators" journals with three published articles. In terms of country nationality, China was ranked first with 39.66%, followed by Australia, Iran, and Lithuania with 8.62%. And 6.90% respectively. It could be concluded that DEA models could correctly measure agricultural productivity in the presence of undesirable outputs dut the following advantages: (1) DMUs could operate under various condition, and DEA avoid this assumption; (2) multiple inputs and multiple outputs could be analyzed simultaneously, and there is no necessity to assign weight by the users in DEA models due to Pareto efficiency used by DEA; (3) the overall efficiency could easily be interpreted, and the most productive units and successful factors could be identified simply due to superiority of DEA in dealing with productivity measurement issues. Also, it is noticeable that the SBM-DEA model was widely used more than other methods, according to table eight. SBM-DEA is appropriate for a situation in which Inputs (outputs) may not behave proportionally. Furthermore, the slack-based DEA model works directly with slacks and puts aside the proportional changes assumption, while radial models neglect slacks in measuring efficiency.

Policy recommendations
Countries should balance the opportunity cost for the farmers, which is the core principle of agriculture economics. The opportunity cost of farming enables farmers to grow crops, sell, and make money. Society could increase the production profit by decreasing the inefficiency through an undesirable output reduction so that compensation could pay to farmers, considering an opportunity cost for the farmers. Thus, it is unnecessary to produce more without paying a pollution emissions fee, which reduces pollution, a giant leap for sustainable development. Undesirable outputs, especially in the agri-sector, must be treated carefully. For instance, it is possible to turn nitrogen surpluses, considered an undesirable output, into a desirable input by stocking them into the soil to apply in the future production process. Therefore, setting a price to biomass as pollution or natural fertiliser requires more expertise as either a desirable input or undesirable output. Also, the same could be applied to GHG, such as livestock methane emission as biogas. Biogas is a green form of energy having great potential to use as an alternative to conventional fuel. It can be produced from various sources, such as agricultural waste, manure, and waste dumps.
Assessment of green agriculture productivity using DEA models allows policymakers to promote sustainable agriculture through highlighting various treatment methods with undesirable outputs; then, DEA models could analyze the effect of various subsidy policies concerning the treatment methods with undesirable outputs. Afterward, the empirical results based on DEA models can assess the appropriateness of incorporating subsidy policies and agriculture productivity evaluations.

Limitations and future research
Like other review articles, this review had some limitations that can be used as recommendations for future works. One of the article's limitations is about the sources of collected articles; this study only selected and collected the published articles from journals of popular databases; therefore, the present article did not consider the published articles from doctoral dissertations and textbooks. Therefore, future studies would consider the published articles of these sources. Another contribution of the article is about the selected journals; in this regard, this study only considered the published articles in English languages, and other published articles in other languages are excluded in this article. Therefore, future works can include the published articles in other languages in the future articles. Another limitation of this review article is related to the classification of the published articles; this study classified the published articles in agriculture into five different application areas; in this regard, it recommends the further works classify the articles in other application areas. Due to this review article's objective, only the implementation of DEA models in agriculture production performance is considered in this article; therefore, future studies can review DEA's application in other application areas, industries, organisations, sectors, and firms. Also of this limitation, the current review article only emphasised the implementation of DEA models in the assessment of agriculture production performance; in this regard, the future works can review the application of other methods like fuzzy sets, decision making, optimizations models, neural networks and econometrics approaches and methods in agriculture production performance assessment.

Disclosure statement
No potential conflict of interest was reported by the author(s).