A metafrontier network DEA approach for water usage efficiency assessment in the light of SDG target 6.4

A metafrontier network DEA approach for water usage efficiency assessment in the light of SDG target 6.4 Sebasti´ an Lozano a , * , María M. Borrego-Marín b , c a Department of Industrial Management, University of Seville, Spain b Department of Applied Economics III, University of Seville, Spain c WEARE –Water, Environmental and Agricultural Resources Economics Research Group, University of C´ ordoba, Spain ARTICLE INFO Keywords: SDG 6 Water usage efficiency AQUASTAT Network DEA Non-radial DDF Metafrontier analysis ABSTRACT The efficient use of water must be enhanced and promoted to achieve the Sustainable Development Goal (SDG) 6. Thus, to contribute to the achievement of SDG Target 6.4 and close a research gap in SDGs’progress, this paper carries out a water usage efficiency analysis of 126 countries leveraging the AQUASTAT database maintained by the Food and Agriculture Organization of the United Nations (FAO), providing information that can help assess and promote the sustainable use and management of water. The methodology uses a conceptual model that considers a Water Withdrawal (WW) stage and a Water Productivity (WP) stage, each one with its own set of variables, designing a customised non-parametric frontier analysis solution that identifies the countries with the best practices and uses them as benchmarks for global efficient water usage. In particular, the proposed approach uses a non-radial Directional Distance Function (DDF) that estimates the inefficiency along the different dimensions, both desirable and undesirable, quantifying potential improvement and computing an efficiency score for each stage and for the whole system. Due to the heterogeneity of the sample, a metafrontier analysis has been carried out. The results indicate that there are significant differences between countries and regions in terms of water usage efficiency. The regions with highest efficiency include Australia, Western and Central Europe and Southern and Eastern Asia, while Central Asia has the lowest. Most of the inefficiency corresponds to the Gross Value Added dimension and the WW stage efficiency is generally higher than that of the WP stage. 1. Introduction At the midpoint of the implementation of the 2030 Agenda for Sustainable Development (2030 Agenda), the latest data indicate that most of the SDG targets are still far from being achieved. The lingering effects of the COVID-19 pandemic, along with other crises such as climate change and armed conflicts, are having widespread impacts on all dimensions, including poverty, food security and nutrition, health and the environment. In addition, to ensure progress across the social, economic and environmental dimensions required by the 2030 Agenda it is crucial to improve data capabilities. Despite extensive efforts towards building stronger data and statistical systems for Sustainable Development Goal monitoring, significant data gaps still exist. (FAO, 2023a). The research reported in this paper has applied the Design Science Research Methodology (DSRM). DSRM has been previously applied in efficiency assessment problems (e.g., Charles et al., 2019,Tsolas et al., 2020). According to DSRM, a research project should include six steps: 1) Problem identification and motivation, 2) Definition of the objectives of a solution, 3) Solution design and development, 4) Solution demonstration, 5) Solution evaluation, and 6) Communication (De Sordi, 2021). The problem addressed needs to be precisely formulated and have real importance and the solution generally takes the form of an artefact. Before designing the artefact, its requirements, i.e., its objectives, need to be defined and, once the artefact has been developed its ability to solve a specific instance of the problem needs to be demonstrated. Further evaluation is generally required to assess to what extent the artefact fulfils the stated requirements and achieves the ultimate goal of solving the practical problem addressed. The final step of communicating the development of the artefact and its validity should be aimed to both practitioners and other researchers, thus entering into the knowledge space of the field. Table 1 shows the DSRM steps applied to the current study. Thus, the problem identified is the lack of suitable indicators of water use efficiency worldwide. Given the scarcity of this natural resource, both at the * Correspondence to: Escuela Superior de Ingenieros, Camino de los Descubrimientos, s/n, Sevilla 41092, Spain. E-mail address: [email protected] (S. Lozano). Contents lists available at ScienceDirect Environmental Science and Policy journal homepage: www.elsevier.com/locate/envsci https://doi.org/10.1016/j.envsci.2024.103857 Received 8 June 2023; Received in revised form 12 July 2024; Accepted 30 July 2024 Environmental Science and Policy 160 (2024) 103857 Available online 8 August 2024 1462-9011/© 2024 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC license ( http://creativecommons.org/licenses/bync/4.0/ ). local and global levels, the efficient use of water must be enhanced and promoted in order to achieve the Sustainable Development Goal (SDG) 6 of ensuring availability and sustainable management of water and sanitation for all. Although there are specific SDG indicators related to this problem, namely Indicator 6.4.1: Change in water-use efficiency over time and Indicator 6.4.2: Level of water stress, both are aggregated in character and its computation uses a limited amount of information. These indicators, together with the information are based on and many other water-related data, is publicly available through the AQUASTAT database maintained by the Food and Agriculture Organization of the United Nations (FAO). This background is provided in Section 2. The envisaged solution should assess the overall water efficiency of a country by relating its available renewable water resources, population (rural and urban) and agricultural needs to the water consumed by the different sectors of the economy (including domestic consumption) and the latter to the benefits of that water consumption, both economic and social, and all this without ignoring neither the existence of minimum Environmental Flow Requirements (EFR) nor the generation of undesirable outputs such as wastewater. Given the large number of variables involved and the complex non-linear relationships between them, it would be preferable that the artifact did not make ant functional assumptions as regards those dependencies. Moreover, the required tool should use the countries with the best practices as benchmarks, identifying these countries so that these best practices can be identified and promoted. In addition, to carrying out a global benchmarking, the artefact should benchmark the countries at the regional level. It would desirable also that the artefact distinguishes between the efficiency in terms of the amount of water consumed (with respect to its availability and the needs of the country), on one hand, and the efficiency in extracting benefits (economic and social) from the water actually consumed, on the other. A final requirement of the desired artefact is that, in addition to providing efficiency scores, estimations of improvement targets and potential improvements along the discretionary dimensions should be produced. Given the above requirements and looking at the available artefacts reviewed in Section 2, we were led to design our artefact using a wellknown non-parametric frontier analysis methodology, namely Data Envelopment Analysis (DEA), more specifically the variant that considers different stages or subsystems within the system under study and that is called Network DEA (NDEA, F¨ are and Grosskopf, 2000,Kao 2014a). The next step was the design of the artifact itself, including the topology of the network of processes, the inputs and output variables of each process and the intermediate flows between them, the non-discretionary or undesirable character of some of the variables, the returns to scale of the processes, and other technical details that are explained in Section 4. The solution developed in this research and that is presented in that section is the best artifact we have been able to design for the problem at hand based on the state of the art in NDEA, the available alternatives and our previous experience with the methodology. The demonstration of the proposed artifact is carried out in Section 5, in which the process and results of applying it to a sample of 126 countries (62 countries had to be left out of the analysis due to incomplete data) using data from the AQUASTAT database are presented and discussed. Since the process of collecting, cleaning, verifying and curating the data in that official UN-sponsored database is complex and lengthy, there is always a time lag as regards the availability of the data so that for this proof of concept we used the data corresponding to the latest available, i.e., year 2020. Pending a more thorough evaluation of the designed artefact, the main policy implications that can be derived from the case study are discussed in Section 6 and the summary and conclusions of the study are presented in Section 7. From the above, apart from the SDG Indicator 6.4.1., which is a simple ratio and has its own limitations, there are no available solutions to the identified problem, let alone a solution with the demanded characteristics. Moreover, although the overall methodology used, based on NDEA, has been used for other water usage efficiency problems, the proposed solution has been custom-made for this application. Therefore, the main contribution of this paper is the use of a specific NDEA approach tool to assess the water withdrawal and water productivity efficiencies of countries from an integral perspective that makes use of a large number of variables, all available from AQUASTAT. Thus, a country is labelled efficient if, given its renewable water resources, its land and population, and assuming that its EFR are satisfied, neither its water withdrawals nor the municipal wastewater can be reduced without decreasing the Gross Valued Added (GVA) of the different economic sectors or the percentage of its population with access to safe drinking water. In summary, this is mainly an application-oriented paper but that also has some innovative methodological aspects. Thus, apart from assessing water usage efficiency at the global level, something that has not been done before using DEA, we have developed a conceptual model that integrates multiple interrelated variables in a consistent way using a Water Withdrawal (WW) stage and a Water Productivity (WP) stage. This conceptual model is original and innovative as it is also the NDEA model that has been proposed to assess the efficiency of the different countries. Such NDEA model has some standard elements (like the nonoriented non-radial DDF metric, the weak disposability of the undesirable outputs or the convex metafrontier), some advanced features but that are not original (like the way the metafrontier model takes into account the within-group projection so as to guarantee that the technology gap ratios are less than or equal to unity) and then some innovations that have been introduced to take into account the specificity of the situation being modelled. Among the latter, we can count the way the non-discretionary inputs of the WW stage have been included in the model, the way the intermediate products (i.e., the water withdrawal variables) are handled and the way the efficiency of the stages and of the overall system are computed. 2. Background The 2030 Agenda for Sustainable Development (A/RES/70/1, 2015), with its 17 Sustainable Development Goals (SDGs) was adopted at the UN Sustainable Development Summit in New York in September 2015 (United Nations, 2023a). Two years later, in July 2017, the lists of Table 1 Design Science Research Methodology (DSRM) applied to the current study. DSRM activities Activity description Knowledge base Problem identification and motivation Lack of suitable indicators of water usage efficiency worldwide Literature review SDG Indicators 6.4.1 and 6.4.2 Define the objectives of a solution Design of a mathematical model for assessing relative water usage efficiency at the country level Literature review on water resources utilization efficiency Knowledge of DEA methodology Design and development Build a customized optimization model that considers the relevant variables, with its specific features, and aims at removing existing inefficiencies Conceptual model Network DEA Non-radial Directional Distance Function Metafrontier analysis Demonstration Apply the artefact using the latest data available and including as many countries as possible AQUASTAT database (FAO) Overall water usage efficiency scores Water withdrawal efficiency scores Water productivity efficiency scores Technology gap ratios Potential efficiency improvements Evaluation Analysis of the results and discussion Policy implications S. Lozano and M.M. Borrego-Marín Environmental Science and Policy 160 (2024) 103857 2 targets and indicators for each of the 17 SDGs was published in a UN resolution (A/RES/71/313, 2017). The lists of targets and indicators for each of the 17 SDGs (Global indicator framework, 2023) include 231 unique indicators (United Nations, 2023b). The Food and Agriculture Organization of the United Nations (FAO) is the custodian agency of 21 of the indicators, including the two that are concerned with in this study and that correspond to SDG 6: “Ensure availability and sustainable management of water and sanitation for all” (United Nations, 2023c). As a custodian agency, FAO is in charge of compiling and verifying country data and metadata, and of submitting the data, along with regional and global aggregates, to the United Nations Statistics Division (UNSD). SDG 6 has eight different targets, covering the main aspects linked to freshwater within the context of sustainable development. The two indicators related to this work measure the Target 6.4: “By 2030, substantially increase water-use efficiency across all sectors and ensure sustainable withdrawals and supply of freshwater to address water scarcity and substantially reduce the number of people suffering from water scarcity”. The two indicators are: •Indicator 6.4.1: Change in water-use efficiency over time (FAO, 2023b). •Indicator 6.4.2: Level of water stress: freshwater withdrawal as a proportion of available freshwater resources (FAO, 2023c). Indicator 6.4.1 measures water-use efficiency over time by all economic activities, focusing on agriculture (excluding the portion generated by rainfed agriculture), manufacturing, construction, mining, energy, services and water collection, treatment, and supply. Freshwater is used by all sectors of society, with agriculture being the biggest user in global terms (70 % of all water withdrawals globally). Water-use efficiency (WUE) is defined as the value added per water-used, expressed in USD/m 3 (value/volume) of a given sector or sub-sector of the economy. The formula for calculating water-use efficiency of a given economic sector (WUEx) is: WUEx=GVAx Vx where x:Economic sector (A=Agriculture, I=Industry, S=Services) GVAx:Gross Value Added by economic sector x [USD] Vx:Volume of water used by economic sector x [m 3 ] There is a small caveat as regards the Agriculture sector (A) and it is that the corresponding GVA does not include the fraction that corresponds to rainfed agriculture. Denoting this fraction as Cr, the water-use efficiency of the agriculture sector is computed as WUEA=GVAA⋅(1−Cr) VA Indicator 6.4.1 is calculated: 1. By computing individual WUE indicators for each of the three main economic sectors 2. Weighting them according to the proportion of water used by each sector (pA,pI,pS) 3. Aggregating them into a single figure WUE =pA⋅WUEA+pI⋅WUEI+pS⋅WUES Indicator 6.4.1 is an economic indicator, assessing to what extent a country’s economic growth is dependent on the use of water resources. If the trend in water-use efficiency growth is higher than that of the economy value added, than we can say that the indicator is on the right path. In this case, the increase of the indicator is caused by the fact that the volume of water used by the economy is relatively stable or decreasing while the economy grows, so indicating a lower risk of water becoming a limiting factor for economic growth. If the indicator follows the same trend as economic growth, it indicates that the risk of water becoming a limiting factor for economic growth is linked to the overall amount of water resources available in the country. Finally, if the trend in water-use efficiency growth is lower than that of the economy value added, it indicates a considerable risk of water becoming a limiting factor for economic growth on the medium or long term. Indicator 6.4.2 measures the level of water stress, by providing an estimate of the pressure exerted by all economic sectors on the country’s renewable freshwater resources. The level of water stress is the proportion of freshwater withdrawal from the available renewable freshwater resources. It indicates the degree to which water resources are being exploited to meet the country’s water demand. The formula for calculating water stress is: Water Stress (%)=TFWW TRWR −EFR⋅100 where TFWW:Total freshwater withdrawal is the volume of freshwater extracted from its source (rivers, lakes, aquifers) for the three main sectors: agriculture, industry, and services (including municipalities and domestic water withdrawal). TRWR:Total renewable freshwater resources refer to the maximum theoretical yearly amount of renewable freshwater available for a country. TRWR are computed as the sum of Internal (IRWR) and External Renewable Water Resources (ERWR). EFR:Environmental flow requirements refer to the quantity and timing of water flows required to maintain the components, functions, processes, and resilience of aquatic ecosystems that provide goods and services to people, where flows are regulated. A value of the indicator below 25 % indicates no stress; between 25 % and 50 % indicates low stress; between 50 % and 75 % indicates medium stress; between 75 % and 100 % indicates high stress; and more than 100 % indicates critical stress. Indicator 6.4.2 allows countries to track progress in regard to sustainable withdrawals and the supply of freshwater, and to address water scarcity. It therefore signals the importance of effective supply and demand management policies. Increased values of the indicator show an increase in water stress, which has potentially negative effects on the sustainability of natural resources and on economic development. On the other hand, low values of the indicator suggest that water does not represent a particular challenge or limiting factor for economic development and sustainability. All the information related to both indicators, water use efficiency (SDG 6.4.1) and the level of water stress (SDG 6.4.2), can be found in the AQUASTAT database (FAO, 2023d). AQUASTAT is the FAO global information system on water resources and agricultural water management. It collects, analyses, and provides free access to over 180 variables and indicators by country from 1960. 3. Literature review 3.1. Network DEA The proposed approach uses the DEA methodology to assess the water usage efficiency at the country level. DEA is a well-known, datadriven, non-parametric methodology to assess the relative efficiency of a set of homogeneous organizational units generally called Decision Making Units (DMUs) (Petropoulos, Laporte et al., 2024). DMUs typically consume inputs and produce both desirable and undesirable outputs. DEA uses some basic axioms to derive, from the observed data, the production possibility set that contains all operating points that are deemed feasible. The non-dominated subset of the production possibility set is called the efficient frontier and represents the best practice. The DMUs are labelled as efficient or inefficient depending on whether or not S. Lozano and M.M. Borrego-Marín Environmental Science and Policy 160 (2024) 103857 3 they lie on this efficient frontier. Inefficient units are projected onto the efficient frontier giving as a result an efficient target operating point and an efficiency score that gauges the distance to the frontier, i.e., the magnitude of the inefficiency detected. The comparison between the target operating point and the observed DMU indicates the improvement potential for each of the variables. When the observations are heterogeneous, a metafrontier analysis can be carried out so that in addition to the within-group and metafrontier relative efficiency scores of the DMUs a Technology Gap Ratio (TGR) for each group of observations can be computed (O’Donnell et al., 2008). Although conventional DEA approaches consider that the production process is carried out by a single process, it is also possible to consider Network DEA (NDEA) scenarios in which the system under study is modelled using more than one process, each one with its own inputs and outputs and very often with intermediate products generated by one process and consumed by others (F¨ are and Grosskopf, 2000). There are many NDEA approaches, some of them assuming a specific network configuration (e.g., Kao and Hwang, 2008) and others considering a general network of processes (e.g., Lozano, 2011). The literature on NDEA is very large and a review of it is out of the scope of this paper. Kao (2014a) provides an introductory review of early NDEA approaches. Alves and Meza (2023) present a more recent review although covering only approaches using the popular slacks-based measure of efficiency. Cook and Zhu (2014) and Kao (2017) are also good references on the subject. As regards NDEA methodology relevant to this research, there are many NDEA approaches that consider metafrontier analysis (e.g., Lin et al., 2012,Yu et al., 2019,See et al., 2021) with some of them also considering undesirable outputs (e.g., Yin et al., 2018,Bansal et al., 2022,Kordrostami and Noveiri, 2022). Moreover, some metafrontier NDEA approaches use non-radial Directional Distance Function (DDF) (e.g., Yu and Chen, 2020,Nourani et al., 2022) and some of these consider also undesirable outputs (e.g., Chiu et al., 2016). The latter, therefore, is the most similar methodological approach. Specifically, Chiu et al. (2016) consider two stages with inputs in stage 1, intermediate products from stage 1 to stage 2 and desirable and undesirable outputs in stage 2. Therefore, stage 1 does not produce final outputs. Also, although the undesirable outputs are assumed weakly disposable, no abatement factors are used in spite of the model assuming Variable Returns to Scale (VRS). Another difference with the model proposed in this paper is the non-radial DDF approach considered, which is unweighted and involves the inputs on one hand and the outputs (desirable and undesirable) on the other. 3.2. Single-process DEA applications to water resources utilization efficiency There are many DEA applications in the water sector involving water utilities, urban water services and water distribution networks (e.g., lo Storto, 2020,Palomero-Gonz´ alez et al., 2021,Mocholi-Arce et al., 2022) or to Wastewater Treatment Plants (WWTP) (e.g., Molinos-Senante et al., 2016,Mocholi-Arce et al., 2020). But the type of studies that interests us more in this research are those that aim at assessing water usage and water resource utilization efficiency. Some of these studies consider a single process whose typical inputs are Capital (or Fixed asset investment), Employment level (or Population) and Water consumption (total, industrial or municipal, depending on the application). The single desirable output considered is local or regional gross domestic product (GDP) and an additional undesirable output is produced, namely wastewater discharged. Sometimes (e.g., Wang et al., 2015) separate Chemical Oxygen Demand (COD) and Ammonia Nitrogen (NH 4 -N, AN) discharges are considered. The DEA approach most commonly used is the non-oriented slacks-based measure of efficiency (SBM) (e.g., Deng et al., 2016) and the super-efficiency SBM (SE-SBM) (e.g., Ding et al., 2019, Liu et al., 2020, Bao et al., 2023) although some researchers used DDF (e.g., Song et al., 2018), non-radial DDF (e.g., Wang et al., 2018, Sheng and Qiu, 2023) or even radial input-oriented DEA models (e.g., Deng and Zhang, 2022). Xi et al. (2022) used cross-efficiency and a variable selection approach from an extended list of inputs and outputs. Some studies use metafrontier analysis (e.g., Shah et al., 2022,Sheng and Qiu, 2023). And Zhang et al. (2023) used separate single-process DEA models for agricultural, industrial, and domestic water utilizations, aggregating the corresponding efficiency scores into a water resources utilization efficiency index. Some researchers were interested in the coupling of regional water and energy efficiency. Thus, for example, Wang et al. (2022) used two separate SE-SBM models to compute Total factor water efficiency and Total factor energy efficiency. The latter included energy consumption in the life cycle of water as additional input and CO 2 and air pollutants emissions as additional undesirable outputs while the energy efficiency model considered water consumption for energy production as additional input and water pollutants discharge from energy-related sectors as an additional undesirable output. A different approach was proposed in Wang et al. (2019), which used a non-oriented SBM DEA model that considered capital stock, employment, energy consumption and water footprint as inputs, GDP as desirable output and CO 2 emissions and grey water ecological footprint as undesirable outputs. Yet a different approach was proposed in Ali et al. (2022), which used a radial, input-oriented VRS DEA model to study the water-energy-food nexus in 36 districts in Punjab, Pakistan. They considered water consumption, coal consumption and grain production as inputs and GDP per capita as desirable output. The undesirable output, namely waste gas emissions, was modelled as an additional input. 3.3. NDEA applications to water resources utilization efficiency Apart from the single-process DEA approaches mentioned above, there are also a number of NDEA applications to water usage efficiency. Most of them consider two stages, namely Water utilization (WU) and Wastewater treatment (WWT). The WU stage uses the same inputs and outputs seen above for single-process DEA approaches. The difference is that now the wastewater discharge is considered not a final (undesirable) output but as an intermediate product that enters the WWT stage for processing. This WWT stage typically consumes exogenous inputs (e. g., capital, labour, operating costs) and produces both desirable outputs (i.e., wastewater recovered up to standard) and final undesirable output (i.e., wastewater discharge). Sometimes the wastewater produced is substituted by separate COD and AN emissions (e.g., Zhao et al., 2017) and sometimes, instead of considering the wastewater discharge as an undesirable output the corresponding COD and AN abated are considered as desirable output of the WWT stage (e.g. Hu et al., 2018). Interestingly, several studies consider the treated wastewater instead of as a final output of the WWT stage, an intermediate product (typically labelled Reused water) generated by that stage and consumed by the WU stage together with its exogenous inputs (e.g., Hu et al., 2018). Some researchers consider than not all wastewater produced is treated by the WWT stage but that some wastewater is directly discharged unprocessed as an undesirable output of the WU stage. As regards the NDEA model considered the most frequently used is the Network SBM (NSBM) (e.g., Zhao et al., 2017) although RAM NDEA (e.g., Shan and Ying, 2022), cost minimization (e.g., Hu et al., 2018), efficiency composition (e.g., Bian et al., 2014) or even game cross efficiency DEA models (e.g., Wang et al., 2021) have also been proposed. Also, some studies used a Dynamic NDEA (DNDEA) approach (e.g., Shi et al., 2022). Apart from the two-stage NDEA approaches reviewed above, some researchers have considered more than two stages. Thus, Nematizadeh et al. (2020) split the WU stage in two, one for industrial and agriculture water utilization and the other for household and environmental utilization. Each of these stages has its own water consumption input plus a shared capital input. Each of the two stages has its own wastewater produced which are consumed, together with a WWT investment input, by the WWT stage, which produces treated wastewater (desirable S. Lozano and M.M. Borrego-Marín Environmental Science and Policy 160 (2024) 103857 4 output) and wastewater discharge (undesirable output). The industry and agriculture water utilization stage has a final output (industry and agriculture GDP) while the household and environmental water utilization stage produces two final outputs (percentage of urban population and urban disposable income per capita). Le et al. (2022) also considered three stages to assess the water resource utilization efficiency of 29 sub-basins of the Dong Nai River Basin in Vietnam. Thus, the Economic and Social subsystems function in parallel and both feed the Social and economic development subsystem. The Economic and the Social subsystems have their corresponding water resources consumption input and produce, as intermediate products, Regional GDP, % of GDP produced by industry and service sectors, in one case and population and % urban dwellers, in the other. The final outputs produced by the Social and economic development subsystem considered were population growth rate, urban population growth rate, regional GDP growth rate and growth rate of the industry and service sector GDP. The DNDEA approach proposed by Shi et al. (2021) involved three stages in series. The inputs of the first stage, labelled Production, were Urban employment, Investment on fixed assets and Domestic and Urban water. The stage produced GDP and the intermediate product Wastewater produced, which entered the second WWT stage. This stage also consumed Completed investments in WWT projects and number of WWT plants and produced a final output (namely, Municipal sewage treatment capacity) plus two intermediate products (COD and Heavy metals pollutant equivalent concentrations). The latter then entered the last stage, labelled Health, which also consumed Number of health technicians and Medical and health expenditure to produce the Life expectancy (desirable output) and Carcinogenic risk (undesirable output). The carryovers in this DNDEA approach were Investment in fixed assets. Finally, we have the circular water economy approach of Bronner et al. (2022) which is a DNDEA with four stages in series. First stage is labelled Water provision and uses a Labour input and a Water supply connections carryover and produces Water supplied to end users, an intermediate product that feeds the second stage, labelled Water consumption, which produces a final output (namely, Water provision &wastewater joint GVA) and a Wastewater produced intermediate product, which in turn enters the WWT stage. The WWT stage consumes Labour (exogenous input) and Length of sewer network (carryover) and produces the intermediate product Treated wastewater released into nature that enters the fourth and last stage, labelled Natural water endowment. This stage has as inputs the Area made up of vegetation and water and the Precipitation and other water released into nature (non-discretionary input) and produces an intermediate product (Water abstracted from nature) that closes the circle by entering the Water production stage. 3.4. Research gap From the above literature review, it follows that most of the existing DEA and NDEA approaches study water resources utilization at the local or regional level, most often within China. A study at the country level and aligned with the indicators of SDG 6 target 6.4 on water stress and water use efficiency, is lacking. Moreover, despite the quality of the AQUASTAT database, no studies exploiting such wealth of information seem to exist. Also, from a modelling and methodology point of view, although there are many non-radial DDF NDEA approaches in the literature, some of them considering a convex metafrontier. these papers are either theoretical (i.e., general) or they address a certain problem, different from the one considered in this paper, and hence were not fit for the task. As a result, there is the need to adapt the general non-radial NDEA approach under convex metafrontier framework to the problem of assessing water efficiency of the countries in a holistic way, considering multiple interrelated variables, some of the non-discretionary, some of them undesirable, etc. That is the research gap that have we identified and tried to address in this paper. 4. Proposed NDEA approach 4.1. Methodology and Conceptual model The methodology used for designing the solution approach is based on DEA. This methodology has been selected because of its data-driven, non-parametric character, its ability to identify the best practice frontier and to benchmark the DMUs using this as reference. The usefulness of this methodology has been demonstrated in numerous practical applications in many different sectors, including water utilities, wastewater treatment plants and also, as seen in the literature review, water usage efficiency at the local and regional level. In addition, the methodology is well developed and rather flexible, allowing different stages/subprocess to be considered within the system with appropriate intermediate flows (what is called NDEA) as well as distinguishing between desirable and desirable variables, discretionary and non-discretionary variables, strongly and weakly disposable variables, etc. DEA (and NDEA) also provides different ways of measuring potential improvements along the different dimensions and of integrating them into meaningful efficiency scores. In some sense, the DEA methodology is so versatile and rich that it is often difficult to select, among the different variants and alternatives, which one is best suited for a particular situation. Fig. 1. Two-stage NDEA configuration considered. Table 2 Inputs, outputs, and intermediate products considered. Type Variable Symbol Unit of measurement Non-discretionary inputs (WW stage) Total renewable groundwater (TRGW) xij km 3 Total renewable surface water (TRSW) km 3 Cultivated area (CA) 10 3 ha Total harvested irrigated crop area (full control irrigation) (THICA) 10 3 ha Rural population (RP) Number Urban population (UP) Number Non-discretionary output (WW stage) Environmental Flow Requirements (EFR) fjkm 3 Intermediate products Agricultural water withdrawal (AWW) zrj km 3 Industrial water withdrawal (IWW) km 3 Municipal water withdrawal (MWW) km 3 Desirable outputs (WP stage) Agriculture, value added to GDP (GVAA) ykj current Mill. US$ Industry, value added to GDP (GVAI) current Mill. US$ Services, value added to GDP (GVAS) current Mill. US$ Rural population with access to safe drinking water (RPASW) Number Urban population with access to safe drinking water (UPASW) Number Undesirable outputs (WP stage) Produced municipal wastewater (PMWW) bjkm 3 S. Lozano and M.M. Borrego-Marín Environmental Science and Policy 160 (2024) 103857 5 In the case of the problem addressed in this paper, a simple two-stage NDEA approach, with definite inputs, outputs and intermediate products has been selected. The specific configuration considered is original and corresponds to the conceptual model presented below, which is based on a rationalization and abstraction (plus simplification) of the problem and also takes into account the data available. Basically, the problem of assessing the water usage efficiency of a country is structured in two interrelated parts which corresponds to the following questions: Are the current water withdrawals for different uses more than they should be given the water resources available, the basic needs of the country (e.g., land and population) and its EFR? And, are these water withdrawals productively and environmentally friendly employed or can the social and economic benefits obtained from them be increased or its environmental impact reduced? This way of approaching the problem is original. Recall that the only existing solution to the water usage efficiency of countries corresponds to the SDG 6.4.1 water-use efficiency indicator, which basically computes the ratio of the total GVA of the different economic sectors and the total water consumed by them. The proposed solution integrates these variables with those used by the SDG 6.4.2. water stress indicator plus additional variables related to wastewater production and to population size and access to safe drinking water. As a result, this solution design allows a more thorough and holistic assessment of the water usage efficiency of countries. Therefore, the conceptual model behind the proposed NDEA approach, shown in Fig. 1 and Table 2, considers two stages: Water Withdrawal (WW) and Water Productivity (WP). The first represents the process of water production for all types of uses, including the EFR. This stage uses as inputs the total renewable water resources, the cultivated and irrigated land, and the rural and urban population. A general rule in choosing inputs and outputs in DEA is that more inputs should lead to more outputs and that is the case here. Thus, presumably, the larger the total renewable water resources the larger the water withdrawals and the EFR. Similarly, the larger the cultivated and irrigated land and the population, the larger the water withdrawal needs. An important caveat must be mentioned here and it is that all the inputs as well as the EFR output are considered non-discretionary. This will prevent the model from trying to reduce these inputs, which does not make sense, or increasing the EFR, which being minimum requirements as they are, are supposedly fixed. Note also that while EFR is a final output of the WW stage the water withdrawal variables are intermediate products that are used by the second stage. The label of this WP stage conveys that this process aims at extracting the maximum benefits from water consumption. Some of the outputs of this process are economic, i.e., the GVA of the different sectors, while others are social, i.e., population access to safe drinking water. The WP stage also generates an undesirable output, i.e., Municipal wastewater produced. It must be noted that all the variables considered (and their labels shown in Table 2) come from the AQUASTAT database. 4.2. Non-radial DDF NDEA model The proposed non-radial DDF model assumes a directional vector g0=(gx 0,gf 0,gz 0,gy 0,gb 0)=(0,0,−z0,y0,−b0), which is consistent with the non-discretionary character of the inputs and the EFR output. Note that this directional vector implies means that the potential improvements are computed as a fraction of the observed values, thus making the proposed NDEA approach units-invariant. As regards returns to scale, since scale effects are likely to exist, VRS are assumed. As regards the non-discretionary variables of the WW stage, they are modelled as per Banker and Morey (1986). In the case of the EFR variable that means that the DMU is benchmarked against a target with larger EFR. The same happens in the case of the inputs, i.e., the DMU is benchmarked against a target with larger values of the inputs. The idea is that the WW stage is inefficient if, even having more population, more land, and more renewable water resources, it would be feasible to have smaller water withdrawals and still produce the same (or more) economic and social outputs and maintain the corresponding EFR. Hence the "greater than or equal to" character of these input constraints, which is not the usual way that inputs are modelled in NDEA (or in DEA for that matter). The underlying reason is that the inputs of the WW stage are not only discretionary but also desirable, which justifies treating them different to the way conventional inputs are treated. Recall that the inputs of the WW stage represent water, land and population resources while the outputs of that stage are EFR on one hand and water withdrawals on the other hand. Hence, given a certain country, this stage would be efficient if there is not an operating point within the corresponding DEA technology that, respecting the EFR (which are minimum requirements), has lower water withdrawals in spite of having more land, more population and more water available. Another way to put it is that a DMU is projected onto a target that dominates it, i.e., that operates more efficiently. This means, in this case, a target that with the same (or less) amount of water withdrawals is able to supply more Cultivated area (CA), more Total harvested irrigated crop area (full control irrigation) (THICA), more Rural and Urban Population, etc. That is why these input constraints are of ≥type. To put it bluntly, WW efficiency does not mean to consume less water because you have less population or less cultivated area. WW efficiency comes from being able to cultivate more land and to supply more population with less water. That is why the proposed NDEA model sees if there is such a feasible operating point, one with more cultivated land and more population and that, at the same time, consumes less water. For the inputs Total renewable groundwater (TRGW) and Total renewable surface water (TRSW) the reasoning is analogous, i.e., consuming less water when there are less water resources available is not a sign of WW efficiency but of water resources scarcity. WW efficiency does not mean consuming less water when there are less renewable water resources available but consuming less water when the same (or more) renewable water resources are available. In our case, the intermediate products are assumed undesirable, i.e., ceteris paribus, the lower the water withdrawals the better. Thus, given the rural and urban population, cultivated and irrigated area and renewable water resources of a country, the smaller the water withdrawals (i.e., the water consumed) by the population and by the agriculture and industrial sectors, the more efficient the WW stage is. Hence, removing inefficiency in the WW stage implies reducing these WW variables, which is what the proposed approach does. Also, since the desirable outputs can be clearly grouped into two categories (economic and social), a separate inefficiency variable for each is used and labelled βy1and βy2, respectively. The two subsets of outputs are labeled O1 and O2, respectively. The objective function is a weighted average of the four inefficiency variables of which, as said before, βy1and βy2correspond to the desirable outputs and the other two, βzand βb, correspond to the intermediate products and the undesirable output, respectively. Moreover, since the model looks for reductions in the two latter dimensions and for increases in the two desirable output dimensions, in order to maintain balance between them, the weights used in the objective function are assumed to be such that wz+wb=wy1+wy2=1. The undesirable output (Municipal wastewater produced) is considered weakly disposable and the corresponding technology of the WP stage is modelled using the non-uniform abatement factors approach of Kuosmanen (2005). This implies that, unlike those of the desirable outputs, the constraint that corresponds to the undesirable output should be an equality (F¨ are and Grosskopf, 2003). In regards to the undesirable output considered, it should be noted that, as one of the reviewers rightly pointed out, agricultural and industrial activities also produce wastewater and, as in the case of China, this may represent a significant amount. However, when one wishes to benchmark as many countries as possible one has to face choices and constraints in terms of data availability. As a result of these, and considering that, unlike the other economic activities, data on municipal wastewater is available for S. Lozano and M.M. Borrego-Marín Environmental Science and Policy 160 (2024) 103857 6 a large number of countries and that this represents, for most countries, the largest source of wastewater, we decided to use this variable as proxy for the overall wastewater produced in the country. Of course, this is an approximation but that can be revised and refined, provided appropriate data become available in the future. While it is clear how to model the weakly disposable undesirable outputs of the WP stage, it is less clear how to properly deal with the intermediate products. These water withdrawal variables are deemed undesirable, reverse intermediate products as Lewis and Sexton (2004) calls them, in the sense that in order to attain efficiency they need to be reduced, not increased. Although this reminds of undesirable outputs, they are not exactly the same, at least not in this case. Actually, even if we assimilated these intermediate products to undesirable outputs, note that undesirable outputs are not always modelled as weakly disposable. There are numerous DEA and NDEA applications that consider undesirable outputs as strongly disposable. In the case of the water withdrawal variables, we think that it is more correct to consider them “as-input”links in terminology of Tone and Tsutsui (2014) and, hence, strongly disposable. Thus, we do not think that reducing these variables would divert certain amounts of inputs (and hence reduce the amount of the desirable output of that stage), which is the rationale behind weak disposability. That is why, unlike the undesirable outputs of the WP stage, which are modelled as weakly disposable, the intermediate products of the WW stage are considered strongly disposable “as-input” links. As pointed out by one of the reviewers, it is worth noting that the intermediate products are undesirable from the point of view of the WW stage and also undesirable from the point of view of the WP. This is quite reasonable if you think about it. The undesirability of the water withdrawal variables from the point of view of the WW stage is clear: given the inputs (and non-discretionary EFR output) the less water is consumed by the population and by the economy (agriculture, industry, etc), the better. And from the point of view of the WP stage, given the outputs (i.e., GVA by the different sectors of the economy and population with access to safe drinking water), the less water is consumed to generate those outputs the better. Hence, not only there is no inconsistency or contradiction in the above but, on the contrary, it makes perfect sense in this case. This contrasts with the fact that generally, in a twostage NDEA system, there is a conflict as regards the interests of the stages when their efficiency is assessed so that the first stage increases its efficiency by increasing the intermediate products while the second stage increases its efficiency by reducing the consumption of the intermediate products. That is so in general but not in this case in which, as argued above, the intermediate variables are “as-input”links and hence both stages aim at reducing them. Also, as it is inherent to NDEA, each stage has its own set of intensity variables, identified by the corresponding superscripts WW and WP as in λWW jand λWP j. Note, however, that because of the non-uniform abatement factors mentioned before, the WP stage has two sets of intensity variables λWP jand μ WP jand that the VRS constraint applies to the sum of both sets. The model below corresponds to projecting a given DMU 0. Although all the DMUs are projected, in turn, the DMUs that define the production possibility set are all of them in the case of the metafrontier projection but only the DMUs that belong to the same group as DMU 0 in the case of the group projection. The set labeled D0represents the DMUs in the same group as DMU 0 in contrast to the set D, which represents all the DMUs. Taking into account the above comments, the proposed group efficiency NDEA model is Max wzβz+wy1βy1+wy2βy2+wbβb s.t. ∑ j∈D0 λWW jxij ≥xi0∀i ∑ j∈D0 λWW jfj≥f0 ∑ j∈D0 λWW jzrj =∑ j(λWP j+ μ WP j)zrj ≤zr0⋅(1−βz) ∀r ∑ j∈D0 λWP jykj ≥yk0⋅(1+βy1)∀k∈O1 ∑ j∈D0 λWP jykj ≥yk0⋅(1+βy2)∀k∈O2 ∑ j∈D0 λWP jbj=b0⋅(1−βb) ∑ j∈D0 λWW j=1 ∑ j∈D0(λWP j+ μ WP j)=1 λWW j,λWP j, μ WP j≥0∀j∈D0βz ,βy1 ,βy2 ,βb≥0 (1) Note, first of all, that this model is always feasible. That is clear since the observed values for DMU 0 represent a feasible (with an objective function value of zero). More importantly, this model provides inefficiency scores for the different dimensions βz ,βy1 ,βy2 ,βb, from which the following overall efficiency and stage efficiency scores can be computed as ξS,G 0=wz⋅(1−βz∗) + wb⋅(1−βb∗) wy1⋅(1+βy1∗)+wy2⋅(1+βy2∗)=1−(wz⋅βz∗+wb⋅βb∗) 1+(wy1⋅βy1∗+wy2⋅βy2∗)(2) ξWW,G 0=1−βz∗(3) Table 3 Summary statistics of the different variables. Variable Min Avg. Max Std. dev. TRGW 0.0 67.5 1383.0 183.5 TRSW 0.0 355.8 8647.0 1003.9 CA 0.7 10,894.1 168,669.1 27,048.4 THICA 0.2 2815.7 95,486.0 12,100.3 RP 21.4 22,460.6 900,099.1 94,822.6 UP 39.3 31,531.3 902,077.8 95,934.9 EFR 0.0 204.8 4105.0 556.4 AWW 0.0 22.1 688.0 74.6 IWW 0.0 4.7 209.7 21.1 MWW 0.0 4.0 117.0 12.9 GVAA 19.9 26,833.8 1175,288.2 112,882.0 GVAI 101.4 155,332.0 5256,563.7 570,127.9 GVAS 732.3 443,880.4 17,369,300.0 1758,079.8 RPASW 34.6 86.5 100.0 18.5 UPASW 50.7 95.7 100.0 8.4 PMWW 0.0 2.5 60.41 7.4 Table 4 Regional groups: acronyms and number of countries. Region Acronym # World All 126 Northern America NAM 3 Central America and Caribbean CAM 10 Southern America SAM 10 Western and Central Europe WCE 30 Eastern Europe EE 7 Northern Africa NAF 5 Sub-Saharan Africa SSAF 20 Middle East–Western Asia MEWAS 18 Central Asia CAS 5 Southern and Eastern Asia SEAS 17 Australia A 1 Pacific Islands –0 S. Lozano and M.M. Borrego-Marín Environmental Science and Policy 160 (2024) 103857 7 ξWP,G 0=1−βb∗ wy1⋅(1+βy1∗)+wy2⋅(1+βy2∗)=1−βb∗ 1+(wy1βy1∗+wy2βy2∗)(4) Note, first of all, that the above efficiency scores are between 0 and 1. This is clear since the inefficiency scores βz ,βy1 ,βy2 ,βb≥0 and, also, those that correspond to water withdrawals and wastewater reductions are both βz≤1,βb≤1 (as the maximum reduction would be at most a 100 % reduction). The rationale behind these efficiency scores is that the potential reduction of the water withdrawals should be credited to the WW stage while the inefficiencies involving the desirable and the undesirable outputs should be credited to the WP stage. Of course, for the overall efficiency score all inefficiency sources should be accounted (in a weighted manner). This criterion is analogous to that used in other NDEA approaches like, for example, NSBM (e.g., Kao 2014b), in which the objective function corresponds to the overall system efficiency which can be decomposed ex post, i.e. once the optimal solution is obtained, into a weighted sum of the efficiency of the different stages. The proposed approach is more along the lines of other non-radial DDF approaches (e.g., Wang et al. 2016,Yu et al. 2022) that maximize a weighted sum of the inefficiencies along the different input and output dimensions and ex post compute an efficiency score using those inefficiencies. Fig. 2. Overall system efficiency ξ S,M 0(top) and TGRS 0(bottom). S. Lozano and M.M. Borrego-Marín Environmental Science and Policy 160 (2024) 103857 8 Therefore, the proposed water usage efficiency takes into account the potential improvements in all dimensions, integrating them into a single figure using weights that represent the relative importance of these dimensions. Since improvements in all these dimensions are desirable, the solution method requires guidance in order to weigh them. Hence, these weights should be determined ex ante by the Decision Maker, according with their preferences as regards water withdrawal reduction, GVA increase, access to safe drinking water increase and municipal wastewater reduction. The same weights are also used to compute the efficiency scores of the WW and WP stages. This method of computing an overall water usage efficiency as well as corresponding WW efficiency and WP efficiency components is consistent, reasonable and original and provides summary information about the water usage situation of each country and how this can be improved. We believe that these efficiency scorers, together with the detailed slacks along the different dimensions and the reference units that exhibit the best practices, provide useful and actionable information to the countries. Note that the proposed water efficiency index can be decomposed as: ξS,G 0=wz 1+(wy1⋅βy1∗+wy2⋅βy2∗)⋅ξWW,G 0+wb⋅ξWP,G 0(5) This decomposition cannot be interpreted as that the overall efficiency is a weighted average of the stage efficiencies. This is so because the weights of the two stage efficiencies do not necessarily add up to one. Fig. 3. WW stage efficiency ξ WW,M 0(top) and TGRWW 0(bottom). S. Lozano and M.M. Borrego-Marín Environmental Science and Policy 160 (2024) 103857 9