Exploring macroeconomic models in the water, energy, food, and ecosystem (WEFE) field: a comprehensive review

This study conducts a comprehensive review of macroeconomic models within the Water, Energy, Food, and Ecosystem (WEFE) nexus, considering four different approaches: computable general equilibrium (CGE) models, integrated assessment models (IAMs), agent-based models (ABMs), and dynamic stochastic general equilibrium (DSGE) models. Specifically, we examine how macroeconomic models represent not only the WEFE nexus as a whole but also its individual components and their combinations. Spanning a collection of 77 papers published in the last 20 years, this review underscores the prevalence of CGE models and IAMs, followed by ABMs, as dominant avenues of research within this field. CGE models frequently investigate interconnections between pairs of WEFE


Introduction
The Water, Energy, and Food (WEF) nexus introduced at the 2011 Bonn conference represents the complex interplay between those natural resources within societal and economic contexts (Simpson andJewitt 2019, Daher andMohtar 2021).In recent years, this topic has garnered increasing attention from researchers and decision-makers, propelled by the looming challenges of climate change and population growth5 .The nexus's central position in these contemporary issues has led to the formal expansion of its scope to include the Ecosystem, giving rise to the WEFE nexus.
The imperative for a review of the macroeconomic models examining WEFE single components and their combinations becomes apparent as one considers the intricate network of interactions and interdependencies within them as well as with economic and social dimensions.The WEFE conceptual framework acknowledges these nonlinear relationships, characterized by feedback loops and externalities, that govern the utilization and distribution of natural resources.In particular, the external pressure and adaptive behavior of individuals in response to evolving environmental conditions constitute the basis of the analysis (Heckbert et al 2010, An 2012).Moreover, the entwined connections of the nexus components represent a challenge for the economists involved in the modeling activity since such complexity requires the combination of economic principles with physical models 6 .Different research skills, perspectives, and dedicated tools must be structured coherently to provide a correct interpretation of the general WEFE framework while also delivering effective and scalable policy recommendations.
To date, the exploration of the WEFE nexus and its components has encompassed various dimensions, including economic analysis and sustainable development.Several studies examined the efforts made in the modeling activity, highlighting strengths, weaknesses, and knowledge gaps.Among others, McCarl et al (2017a) review the models used in the field of the WEF nexus by focusing on the related challenges.Their research underscores the importance of prioritizing multi-sector and nexus-wide decisionmaking models over fragmented, domain-specific frameworks.Moreover, they accentuate the need to promote the active participation and acceptance of WEF analysis among decision-makers, advocating for the development of an entirely new family of models, defined as integrated WEF nexus modeling frameworks.In a subsequent work, McCarl et al (2017b) examine the issue of data availability in this field, recommending the creation of innovative protocols for data collection, storage, and inference.
At the same time, Albrecht et al (2018) conduct a systematic review encompassing 245 journal articles and book chapters.Their findings highlight a concerning trend of low reproducibility in the revised works and limited participation of social sciences in the WEF field.Furthermore, their study reveals a widespread preference for quantitative methods and a lack of interdisciplinary analyses, with most studies confined within their respective disciplines.
The literature review of de Andrade Guerra et al (2020) examines the scientific publications focusing on the WEF nexus, sustainable development, and the impact of climate change in developing countries.According to their findings, improving the management of natural resources requires extending the existing modeling frameworks to encompass decision-making amidst uncertainty, stochastic optimization, and comprehensive cost assessment.Further, the focus of scientific research must also move from macro models to real case studies, which are highly underrepresented in this field.
Lastly, Endo et al (2020) perform a meta-analysis of WEF review articles and categorize them into five groups: comprehensive review articles, targeted review articles, synthesis articles, articles that assessed the interlinkages, trade-offs and synergies, and nexus case studies.While it may be susceptible to limits in its implementation (e.g.due to different scales in the analysis), they suggest creating a holistic nexus methodology, developed by integrating diverse approaches and tools, encompassing both qualitative and quantitative methods, as well as a combination of natural and social sciences.
Our study contributes to this literature by providing a comprehensive assessment of this subject from a macroeconomic perspective.To broaden the scope of the review and offer a more extensive understanding of this topic, we examine how economic models represent not only the WEFE nexus but also its individual components and their combinations.Moreover, given the different strengths and criticalities of the diverse approaches, we distinguish them into four main areas, namely: computable general equilibrium (CGE) models, integrated assessment models (IAMs), agent-based models (ABMs), and dynamic stochastic general equilibrium (DSGE) models.
Our search refers to online repositories like Scopus, Science Direct, and Google Scholar for relevant articles, which we then classify by modeling type.The review covers a time horizon of two decades, between 2002 and 2021.Over this interval, we select 77 papers, half of which analyze only WEFE single components, with the prevalence of CGE models and IAMs.Moreover, while CGE models explore the interactions between pairs of WEF elements, IAMs focus more on the nexus as a whole.Conversely, ABMs spread from the analysis of WEFE single components to their aggregate without a clear pattern.Lastly, DSGE models mainly investigate individual elements with a focus on energy.The synthesis underscores the need for integrated WEFE nexus modeling frameworks and reveals an evolving landscape of methodologies.In particular, the development of DSGE models and ABMs is still at an early stage, with the former potentially allowing the analysis of uncertainty and risk in this field and the latter possibly offering new insights into the complex interactions between natural and human systems but still lacking a common framework.
Therefore, the novelty of our work lies in the specific focus on macroeconomic models examining nexus components and their interdependencies.Indeed, while being widely used by scholars and policymakers to assess the effectiveness of policies and forecast future economic paths, macroeconomic models have been underrepresented in the WEFE field (and vice versa).A detailed overview of this topic, intersecting social and natural sciences, can thus increase their diffusion among stakeholders and stimulate participation in the research.In this way, it can promote the required interdisciplinary nature of the analysis and constitute the basis for a common modeling framework.Moreover, this review sets the stage for new avenues in this field by identifying strengths, weaknesses, and knowledge gaps.In particular, by analyzing the landscape of macroeconomic models in the last two decades, it uncovers novel insights and methodologies that can enrich the understanding of nexus dynamics.Through our comprehensive analysis, we aim to establish a robust foundation for future research endeavors, policy formulation, and decision-making within the evolving context of the WEFE nexus and its components.
The paper is organized as follows: section 2 describes the review process, section 3 presents the selected papers, dividing them according to their thematic focus (i.e.WEFE individual components, their combinations, and the nexus) and the type of macroeconomic model, providing a brief description of each work.It also presents the strengths and weaknesses of the different approaches to offer a clear perspective on this topic.Section 4 concludes.
We conduct the research focusing on Englishlanguage scholarly articles and using web search engines on the online research repositories Scopus, Science Direct, and Google Scholar.We devise the identification of relevant studies through a combination of different keywords that characterize the WEFE nexus, its components, and their combinations (e.g.water alone, or water AND energy, or water AND energy AND food), coupled with the inclusion of the term macroeconomic models.Table 1 summarizes the keywords and the related combinations used for the search.
Subsequently, we collect all the search outcomes in a preliminary database to use as a reference for our analysis.To assess their relevance in our field of interest, we first review the abstract of articles and then classify them singularly according to the following different categories: • general information: title, year, authors, DOI, and journal name; • main information: type (modeling), keywords, methodology, unit of analysis (geographical scale), and time horizon; • thematic content: overview and main findings.
After inspecting each item in the list, we include additional publications among those cited in such works to complete our analysis and refine our search by removing redundant articles.In particular, given the extensive research on individual WEFE components (especially energy) within CGE models and IAMs, we focus only on key developments in those fields.Following this update, we categorize the collected research articles based on their type of macroeconomic model (i.e.CGE models, IAMs, DSGE models, and ABMs).

Results
This section reviews the selected papers, starting with a descriptive analysis of their distribution across different WEFE components and providing figures concerning their evolution over time.Subsequently, we present a general overview of our findings for the different modeling approaches (i.e.CGE, IAMs, ABMs, and DSGE), then focus on WEFE single components and combinations, and conclude by summarizing the strengths and criticalities of the various macroeconomic models.Appendix B briefly explains the general background of the four modeling approaches analyzed in this review.

Number of words
Note: W stands for water, E for energy, F for Food and EC for ecosystems.ME refers to Macroeconomic.All listed search were performed in all the mentioned online research repositories, where the searching operator between the words was always AND.

Figure 1.
Overtime evolution of research articles by model type.

Descriptive statistics
Following our search methodology, we selected 77 papers.Table A.1 in the appendix provides a comprehensive list showing their WEFE classification.We found 27 CGE models, 27 IAMs, 9 DSGE models, and 14 ABMs over twenty years between 2002 and 2021.Across all types of models, there is a notable surge in new articles beginning in 2015 (figure 1), underscoring the increasing attention toward the nexus and its related facets.
Figure 2 summarizes the distribution of models across WEFE elements, combinations, and the nexus as a whole (figure A.1 and table A.2 in the appendix provide alternative visualizations).Approximately half of the revised works (39 articles) address the single components of the WEFE nexus, namely water (W), energy (E), food (F), and ecosystems (EC).All four modeling approaches explore those elements, with IAMs and DSGE models mainly focusing on the first three, while ABMs and CGE models also tackle the EC dimension.Interestingly, energy represents the most studied component in our search, totaling 18 articles.Looking at WEFE combinations (22 articles), CGE-based papers are the most numerous, followed by IAMs and ABMs.Lastly, moving to WEF and WEFE nexuses (14 and 2 contributions, respectively), they are analyzed primarily by IAMs and ABMs, with the former providing the only two examples of works tackling all those elements together.Nevertheless, among all the possible combinations between WEFE components, the WEF nexus is the most studied, underscoring its increasing relevance in the literature.

General findings
Different modeling approaches can provide valuable insights into the interconnected dynamics of WEFE elements by examining them as standalone components, combined pairs, or aggregate nexus.When analyzing the relevance of this framework at the macroeconomic level, recent literature presents numerous solutions.Therefore, the challenge of determining an optimal configuration depends on the specific aim of the research focus.
Starting from CGE models, they have been traditionally used to study the macroeconomic effects of structural changes and policies on economic systems, focusing on the analysis of input-output linkages between industries and countries as well as factor allocation across economic sectors.This approach relies on a multi-sector and multi-factor view of the economy, in which all markets clear in each simulation period (Nechifor andWinning 2017, Bardazzi andBosello 2021).Accordingly, CGE models can assess the impact of different growth paths, demographic trends, as well as policy and economic shocks on a baseline scenario by tracking and forecasting the accumulation of capital stock, the evolution of labor supply and its productivity, and the price adjustments needed to balance markets under given resources, policy, or technological constraints (Ge et al 2014, Zhang et al 2019).Further, they can also include demand aspects of the economy by internalizing changes in the final demand of agents (e.g.households, government, and firms) according to their spending behavior.As a result, the multi-sector and multi-factor approach of CGE models explains their extensive use in examining WEFE single components and their combinations, totaling 27 articles investigating those topics.Nevertheless, their strong dependence on calibration data reduces their predictive power the more one moves away from the reference period, and their reliance on neoclassical assumptions does not consider agent heterogeneity, changes in factor allocation, and technological barriers, especially in the earliest studies of the CGE literature.
At the same time, by integrating economic and environmental processes in an intertemporal optimization setting, IAMs further extend the analysis of WEFE components and their nexus, with the capability to provide insights around specific trade-offs and optimal policies.While relying on neoclassical assumptions like CGE models, they overcome some of their limitations by offering a dynamic perspective of human and natural phenomena, albeit at the cost of a lower resolution.In light of this, Larkin et al (2020) raise concerns about their ability to represent the complex interconnections between single WEFE elements.In their view, IAMs may fail to capture the scale and the rate of shifting social, geographical, and political contexts that shape how innovations upscale.Nevertheless, other authors recognize IAMs as useful modeling tools for investigating the WEFE nexus (McCarl et al 2017a), thus explaining their vast diffusion in this area, with 17 articles included in the present review.Lastly, IAMs can assist long-term investment decisions in the WEFE field by quantifying related costs and benefits, even though it is fundamental to acknowledge the need for more research on integrating economic decisionmaking structures with biophysical models (Kling et al 2017).
Conversely, if the interest is in studying the (simultaneous) impacts of policies, stochastic shocks, and uncertainty on the macroeconomy in a dynamic setting, DSGE models represent a powerful instrument for assessing different WEFE dimensions.However, the use of such models in this field is still at an early stage, with few applications to environmental themes while none explicitly addressing ecosystem topics.At the theoretical level, DSGE models are valued for their solid microeconomic foundations and consistency with business cycle dynamics.Nevertheless, this strength constitutes a disadvantage when trying to extend them to a multi-sector and multi-factor context due to their inherent analytical and computational complexity.
Lastly, ABMs better address the heterogeneous and nonlinear nature of complex systems.Those models rely on a bottom-up approach where interactions at the local level impact aggregate dynamics, making them well-suited for capturing the different facets of WEFE components and their nexus.Their strength lies in the ability to represent individual decision-making and behavioral patterns (Smajgl et al 2011, Smajgl andWard 2013).Indeed, they uniquely model decisions at the level of single agents while also considering their heterogeneity and adaptive behavior (Balbi andGiupponi 2010, Heckbert et al 2010).That is especially important in the WEFE domain, characterized by heterogeneity, feedback through interactions, and adaptation.At the same time, ABMs can incorporate social and ecological processes, along with norms and institutional factors.Lastly, they provide the flexibility to integrate multiscale and multi-disciplinary knowledge, accommodating both qualitative and quantitative approaches to mobilize a simulated world (An 2012).However, the lack of a common modeling framework, together with their complex development and calibration, limits their diffusion in this topic.

W-water
Water is the lifeblood of ecosystems, as all living organisms need it to grow and survive.It plays a vital role in the creation and prosperity of life on Earth through its circulation in the atmosphere, lands, rivers, lakes, and oceans.While it is fundamental to recognize the inherent link between water and ecosystems, we believe it is necessary to initially analyze it as a separate element to capture its specific contribution and complexity discussed in the literature.
Most CGE models focus on the management of limited water resources, especially in the context of climate change.Gómez et al (2004) open a serious debate on which type of water management policy can better address water scarcity during severe periods of drought.Focusing on drinking water, they use a general equilibrium analysis for the Balearic Islands to assess the welfare gains from developing a market for the exchange of water rights between agricultural and urban users.Their results indicate that introducing a trading scheme between those sectors promotes the efficient allocation of water resources, with a consequent increase in agricultural income due to the ownership of water rights.This demand-regulating policy improves the allocation of water resources and is more effective than traditional water supply approaches, which require expensive infrastructures, such as dams and desalination plants, contributing to increase energy prices.Similarly, Roson and Damania (2017) confirm the importance of an economically efficient reallocation of scarce water resources in sectors where it has a higher value7 .This, together with a shift towards less water-intensive productions and an increase in imports of more water-consuming goods, can neutralize water-related climate risks in critical regions.
Moving away from water allocation policies, Bosello et al (2007) analyze the management of water resources due to the global sea level rise projected by 2050.Their results show that the optimal adaptation to this phenomenon lies between two policy extremes, i.e. complete and zero coastal protection.This intermediate solution stems from the fact that, in the case of full protection, GDP would grow mainly as consequence of investments in coastal infrastructures such as sea walls and dikes.However, such economic boost would come at the cost of reduced utility due to increased price on the international capital market.Conversely, in the scenario without coastal protection, economies heavily relying on agriculture would bear the brunt of damages.In these shrinking economies, overall energy consumption would fall, indirectly hurting energy exporters.
Moving to IAMs, Voisin et al (2013) analyze the interaction between the water cycle and human activities to assess how climate change will affect them in three regions of the Upper Midwest region of the US.They do so by coupling a global IAM with a land surface hydrology-routing-water resources management model.They perform a temporal and spatial disaggregation to downscale the annual regional water demand simulations into daily time steps and sub-basin levels.After implementing different emissions scenarios, they investigate future water supply, deficit, and management, demonstrating that natural flows, but not regulated ones, will suffer most of the changes in the entire region.
Using a scenario-based modeling paradigm, Letcher et al (2007) develop a conceptual framework for developing IAMs to consider water allocation issues.The framework outlines a generalized set of links between socioeconomic and biophysical measures based on two characteristics of the problem under consideration: the nature of interactions between production decisions and the hydrological cycle.They then assess water allocation issues in Thailand and Australia, focusing on long-run capital investment and related effects on high-value agriculture in Australia and subsistence production and income generation in small upland catchments in Thailand.Lastly, Corona et al (2020) discuss a model developed by the Environmental Protection Agency, consisting of an online water quantity and quality modeling system and a modeling platform for quantifying the economic benefits of changes in water quality, and apply it to the Republican River Basin.
Stochastic surface water flows and groundwater recharge are at the core of the DSGE model developed by Li and Swain (2016), who assess how uncertainty affects future water resilience, economic growth, and welfare in South Africa.The assumption of distinct water uses between productive and residential sectors allows the authors to derive the shadow (resilience) value of surface and groundwater stocks and investigate the connections between consumption and investments, water extraction and resilience services, and different water use.Their findings indicate that capital accumulation can promote long-term development despite the increased future water scarcity.Nevertheless, a high discount factor, reducing investments, is not sustainable in the long run.Lastly, an increase in precipitation variation negatively affects water resilience and the expected dynamic welfare.

E-energy
Energy plays a fundamental role in human development.Its critical role as a production input makes it a constant priority issue on the international political scene, as evidenced by the political impact of the energy crises of the 1970s and 2020s, and explains the extensive coverage of this topic in the scientific literature, making energy the most relevant single component in our review with 18 articles.
Given the extensive body of work in this research area (see Soytas and Sar 2021, for an in-depth review), we focus only on key developments in CGE models examining this field.Burniaux and Truong (2002) provide one of the earliest attempts to integrate energy as an input in both demand and production functions.In particular, they consider energy as a primary factor alongside labor and capital in the production process, and it also plays a role as a consumption commodity in both government and household expenditure.In the latter, a crucial parameter for the initial setup of the model is the determination of the elasticity of substitution, either between energy and other inputs or with other commodities.
Another important strand of the literature links energy to technical change, as Otto et al (2007) do in the context of endogenous growth models.The main novelty of their approach lies in recognizing that innovations are often biased towards a specific technology, which can be either energy or non-energy intensive, depending on its economic and regulatory characteristics, which determine its production, diffusion, and externalities with the rest of the economy.Focusing on the determinants of the energy bias, the study finds that cross-technology spillovers and substitutability between final goods are two key drivers, as the model predicts a stronger bias towards the production of non-energy intensive goods the more intense the feedback effects and elasticities are.
Finally, moving from endogenous technical progress to exogenous changes in productivity, Hanley et al (2006) consider the impact of energy efficiency on both economic and environmental outcomes.Estimating the economy-wide effects of an energy efficiency stimulus for a model calibrated to Scotland, the authors find that improvements in energy efficiency stimulate energy production and consumption but lead to a deterioration in environmental indicators.From the policymaking perspective, these results highlight the need to combine policies promoting energy efficiency with those aiming to reduce energy consumption.
Like CGE models, IAMs represent the majority of works dealing with energy issues.To assess market and non-market costs and benefits of climate change, Kemfert (2002) develop an IAM containing a detailed energy module representing the international markets of coal, gas, and oil.Energy stems from the combined consumption of fossil fuels in a CES production function, thus generating a comprehensive set of greenhouse gases (GHGs) and requiring different abatement technologies.Interestingly, this approach provides a realistic functioning of the oil market, with the OPEC regions exploiting their market power to influence wholesale prices.
Hübler et al (2012) study endogenous directed technical change in the energy sector by distinguishing between R&D and international technology spillovers, i.e. innovation and imitation, and considering the role of capital investment in creating and implementing new technologies.Their results indicate that a higher return on energy-specific innovation and imitation expenditures can overcompensate rising emissions thanks to increased economic growth and lower mitigation costs.However, the decarbonization process requires a switch from fossil to renewable inputs, and the timing of such a change can affect regional mitigation costs.
A better understanding of future energy scenarios to stabilize GHG concentrations and their links with climate policies requires the development of hybrid models, i.e. models that combine the technological details of bottom-up approaches and the long-run dynamics of top-down frameworks.Along this line, Bosetti et al (2006) introduce an IAM accounting for endogenous technological progress in energy production, either in the form of learning curves affecting the price of new capital vintages or through R&D investments.Their framework can address different issues, like the design of optimal policies to stabilize GHG concentration.Similarly, Luderer et al (2015) develop a global energy-economy-climate model, in which the macroeconomic core and the energy system module are hard-linked through final energy demand and energy production costs.Economic activity results in demand for final energy such as transport, electricity, and non-electric energy for stationary end uses and is modeled through a nested CES production function.The energy system module accounts for endowments of exhaustible primary energy resources as well as renewable energy potentials.More than 50 technologies are available for the conversion of primary energy into secondary energy carriers as well as for the distribution of secondary energy carriers into final energy.
Forecasting future energy demand and its composition is a fundamental key factor for developing effective and efficient alternative policies toward a low-carbon economy.Under this view, de Blas et al (2019) introduce a novel methodology to estimate energy demand in IAMs based on sectoral projections of final energy intensities.Those forecasts stem from three main factors: historical trends, expected variations in energy efficiency, and future changes in the type of final energy consumed.Their findings highlight the significant role of scarcity perception in shaping future energy dynamics and related to the uncertain responsiveness of production capacity to changes in relatively scarce inputs.
Focusing on market competition, Leibowicz (2015) develops a model in which producers of renewable technology are engaged in Cournot competition and apply this approach to evaluate how climate policy and learning spillovers interact with the market structure to influence technological, economic, and emissions outcomes.Their results show that prices are higher in concentrated markets, thus leading to a weaker adoption of renewable technologies and higher carbon emissions.Furthermore, widespread solar photovoltaics adoption is a key component for ambitious emissions reduction and can only diffuse strongly if the industry is highly competitive and with know-how spreading freely across firms.Their findings suggest that the standard IAM formulation of endogenous technological change, which does not account for markups, is valid only when markets are approximatively competitive but could be overly optimistic about the adoption of renewable technologies if market power is significant in those industries.
When looking at DSGE models, almost all of them focus on energy alone over the reference time horizon.That is due to their late application in the environmental field and to the central role of energy, both as a source of income for countries with fossil fuel reserves and as an input in the production process of goods.Specifically, DSGE models have been extensively applied in the energy field to investigate two main issues: evaluating the influence of the energy sector on the economy and understanding the impact of energy consumption on climate change.Bukowski and Kowal (2010) develop one of the first applications on this topic by focusing on the Polish economy, one of the most coal-based in the European Union (EU).In their work, they design a multisector DSGE model (eleven production sectors) to assess the macroeconomic impact of different GHG mitigation policies in the nation.Focusing on the relation and linkages between the origin and spending of the chosen environmental measures, they evaluate the associated macroeconomic effects on GDP, employment, and agents' welfare.Moreover, by considering different mitigation levers-ranging from investments in energy capacity (fuel switch) to energy or fuel efficiency improvements-they construct a macroeconomic version of the marginal abatement curves.Such outcomes allow the authors to assess the macroeconomic impact of policies in terms of abatement potential and compare them under alternative fiscal frameworks.
Similarly, Golosov et al (2014) design a DSGE model with a climate change externality resulting from the use of fossil energy.Final goods production requires an energy composite, depending on three imperfectly substitutable inputs, i.e. oil, coal, and green energy.Although their main focus is on the identification of the marginal damage function of emission externalities, they also compute the optimal tax on fossil fuels and the first-best market (dynamic) allocation of different energy sources, thus allowing a better study of the role of different energy sources in future climate and consumption paths.Punzi (2018) extends the baseline framework linking energy and emissions to the financial dimension, presenting the first example of an Environmental DSGE (E-DSGE) model.In this work, the production side of the economy is characterized by heterogeneous production sectors (intermediate and final goods) with different emission levels (green low-carbon and non-green high-carbon emissions firms) and relying on different financing sources (debt and equity).The key assumption of the model is that green firms' funds can only come from bank loans, while non-green companies can also issue equities.In this way, the author can study the effect of monetary, technological, and financial shocks on the economy, finding that the green sector benefits most from positive financial shocks because of the related easing in borrowing conditions.In contrast, productivity improvements combined with looser monetary policies do not affect green firms, which, conversely, experience losses in the long term.
Moving to the analysis of energy as a source of income, the following works focus on the optimal management of oil and gas revenues.Devarajan et al (2017) analyze the case of a small low-income but resource-rich country like Niger to derive optimal public budget rules in the face of volatile revenues from natural resources, i.e. driven by a stochastic world price of the resource.The model includes both domestic production and international trade, distinguishing between export flows of traditional goods and natural resources.Private and public capitals are treated separately to take account of the benefits arising from the exploitation of natural resources and assess the impact of these revenues on national consumption, through transfers to households, or the consequences of public investment in infrastructure.Under the assumption of unexpected shocks affecting the price of natural resources, they suggest saving windfall revenues in a sovereign fund and using the interest income to support national consumption.
Similarly, Blazquez et al (2019) provide an example of a DSGE model focusing on a small, open, and resource-rich economy like Saudi Arabia.They model energy at different levels by allowing firms to produce electricity and energy services (air conditioning, use of electrical appliances, lighting, and private transportation) while considering three different energy sources, i.e. oil, gas, and renewable energy.At the same time, export flows consist of final goods and fossil fuels, thus accounting for the global dynamics of energy prices.Overall, their goal is to study the impact of specific reforms on the national economy while also considering the macroeconomic effects of energy price shocks and energy policies, such as domestic energy price reforms and the deployment of renewables.Their energy framework is the most detailed among the DSGE models included in this review.
The authors design a model to assess the effects of oil shocks on economic fluctuations in an oil-exporting open country, Iran in this case, while also considering public finance choices.In their framework, the government owns the oil inventory, and domestic inputs are not essential for oil production, which is instead mainly exported.As in other DSGE models, the main aim of this work is to examine how different policies for the public management of financial flows from oil sales can affect long-term economic stability.Their findings suggest the accumulation of oil revenues in a specific financial fund, whose steady flow of income can substitute the unpredictable revenues coming from oil exports.
Also macroeconomic ABMs explore the energy component, especially in the most recent literature.We identify three papers, all building on the work of Deissenberg et al (2008).Fadiran et al (2018) provide a first attempt in this research area by analyzing three distinct policies that have been implemented in advanced nations to achieve Sustainable Development Goals (SDGs)8 .Among these, one involves the introduction of an energy tax, modeled as a cost component in the production function of firms.By defining, among other economic actors, a single energy supplier that sets energy prices to meet the (constant) demand of manufacturing firms, they investigate the macroeconomic effects of different levels of an energy tax in a developing country.
In a more detailed framework, Ponta et al (2018) explore the economic implications of a feed-in tariff policy mechanism to encourage investments in renewable energy production capacity.They consider an energy sector composed of a fossil fuel and a renewable-energy power producer.The former imports fossil fuels from abroad at a given price and produces electricity with decreasing returns to scale, while the latter invests in renewable technology subject to government sustainability policy.Since the government's feed-in tariff influences the pricing and the capacity investment decisions of both power producers, the authors show that this policy can foster the transition of the energy sector while increasing the level of investments, with a positive impact on employment.
Finally, Raberto et al (2018) focus on the effects of shifting the banking sector from speculative to green lending on the adoption of more energy-efficient production technologies.By incorporating heterogeneous capital goods with varying energy efficiency in the production technology, they examine the introduction of differentiated capital requirements based on the lending purpose.In particular, banks engaged in speculative lending are subject to stricter conditions, thus encouraging financial institutions to finance firms' green investments.The model design implies that up-to-date capital goods exhibit higher energy efficiency, thus allowing for the production of consumption goods at a lower energy intensity.It follows that an accelerated pace of investments leads to positive environmental effects.

F-food
When analyzing the food component alone, most models examine this subject in the context of agricultural production, focusing on the impacts of trade policies liberalization and climate change.
By allowing the direct comparison between different scenarios, CGE models deal with the food element by studying the economic and distributional effects of agricultural trade policies.Keeney and Hertel (2005) develop a pioneering model in this literature by introducing a specific module describing the production of crops destined for animal feed and their potential substitutability with other alternative sources.On the demand side, consumer expenditure can vary between food and non-food commodities, while farm household income follows a detailed characterization.Within this framework, they test the welfare effects of trade policies affecting the agricultural sector, both from an aggregate point of view and at the level of farm households.By assessing the general equilibrium effects of full trade liberalization in agricultural and non-agricultural markets, the model provides detailed estimates of the related changes in the agricultural sector and farm incomes.In particular, farm households in the OECD countries are likely to be adversely affected by liberalization, and due to the relatively small size of the farm economy in these regions, the regional welfare results may be misleading in terms of political feasibility.Beckman et al (2019) analyze the impact of export taxes on food consumption and poverty, as they remain a popular policy tool in the era of globalization, while other trade barriers, such as tariffs and export subsidies, have been in steady decline since the creation of the World Trade Organisation.In particular, this study provides a detailed view of the linkages between export taxes, food prices, and poverty from a global perspective.Their results, which are robust to permutations in the Armington elasticity parameter 9 , show that the sustained wave of export taxes registered in 2008 positively impacted only the price of selected agricultural commodities and did not spill over to the entire international food sector, nor did it significantly reduce poverty.Moreover, the study of a hypothetical scenario in which export taxes are completely removed shows similar results in terms of changes in agricultural prices and poverty, with only countries reducing export taxes benefiting from this policy.
While most of the CGE models focus on agricultural trade policies, IAMs only investigate the impact of climate change on food production since the dynamics of international trade have not yet been taken into account in their settings Müller and Robertson (2013) integrate a standard economic framework with two climate modules and two biophysical crop growth models (representing two gridded global crop models) to examine the effects of global warming on land productivity and its spatial patterns.With the economic model describing the endogenous development of agricultural practices, they analyze the worst-case scenarios predicted by climate and crop growth modules, showing that the 9 Armington elasticity measures the degree of substitution in demand between similar goods produced in different countries.
global production of individual crops can decrease between 10% and 38%, with large differences in spatial patterns due to uncertainty in climate projections and expected damages.
Alvi et al (2021) adopt a hybrid approach to analyze food security in South Asia under climate change.In particular, they exploit the historical link between temperature, precipitation, and cereal production to estimate the impact of climate change on crop yields.At the same time, they integrate a standard economic model with the external projections of temperatures and precipitations coming from the Coupled Model Inter-comparison Project Phase 5. Their results show a decrease in cereal production due to climate change by 2050, leading to an ex-post increase in grain prices and a consequent decline in income and welfare.
Lastly, the only DSGE model characterized by a direct focus on the food sector is that of Colla-De-Robertis et al (2019), who study the case of fisheries in the Spanish community of Galicia.The authors develop a counterfactual analysis of a less stringent EU policy on fisheries (Common Fisheries Policy-CFP) between 1986 and 2012.In particular, they model the regulation of fishing days as a technological constraint that affects the probability of fishing.Moreover, they assume that the size of the fishery stock has an impact on the total factor productivity of the economy and, on the biological side, evolves according to an age-structured population with unexpected shocks affecting the mortality rate of fish.After estimating the model on the Galician fleet, they found that a less stringent CFP would have increased the fishing activity and the working hours in the reference period.However, that would have reduced the sector's profitability, lowering wages and the return on capital.

EC-ecosystem
The CGE literature analyzes the ecosystem dimension by focusing directly on the impact of climate change on ecosystem services (especially in terms of carbon sequestration, as in Bosello et al 2011), or indirectly by considering the impact of climate change on other WEF elements, in particular water and food, through changes in the availability of certain ecosystem elements, such as soil salinity (Osman et al 2019), soil erosion (Sartori et al 2019), and agricultural production (Bosello et al 2011, Kahsay et al 2017, Khan et al 2020, Vatankhah et al 2020).
Starting from the direct linkages between climate change and ecosystem services, the study of Bosello et al (2011) represents a significant effort to delineate the role of ecosystem services in market transactions.That is achieved by estimating the value of carbon sequestration services provided by forest, cropland, and grassland ecosystems in the EU and by assessing how climate change could potentially affect them, using various indicators such as changes in land productivity, land loss due to sea-level rise and changes in energy consumption.The calibration of the model replicates the regional GDP growth paths associated with the A2 scenario in the Special Report on Emissions Scenarios (SRES) of the Intergovernmental Panel on Climate Change (IPCC)10 , which assumes constant population growth, no commitment to reduce GHG emissions, and regionalized economic development in all regions of the world.The economic impact of climate change is then tested for temperature increases of 1.2 • C and 3.1 • C between 2050 and 2100.Their results show that some regions of the EU would be disproportionately affected by climate change, with the Mediterranean area expected to suffer the most.That translates into a decrease in land productivity of −6% under the 3.1 • C temperature scenario and a loss of forest ecosystem services in the region.In addition, the total value of carbon sequestration in the EU, assessed by estimating the avoided environmental damage due to the cooling effect of forests, grasslands, and croplands, ranges between 0.55 and 1.7 billion US dollars per year.
Moving to mutations in the ecosystem due to climate change and their consequence on the other element of the nexus, the work of Sartori et al (2019) combines a biophysical model with a CGE framework to estimate the economic impact of soil erosion due to rising water levels on the world economy, with a total annual cost of 8 billion US dollars to global GDP.At the same time, Osman et al (2019) illustrate the importance of including water quality in the analysis of water systems and assess the impact of investments to improve water quality in Egypt.The findings underscore the significant economic benefits of addressing irrigation water quality issues, ranging from increased production of high-value crops such as fruits, vegetables, and rice to improved food security.
Considering the effects of climate change on agricultural production, Khan et al (2020) evaluate the long-term impact of climate-induced damages on crop production in Pakistan.The projected loss in wheat and rice production accounts for more than 19 billion US dollars in Pakistan's real GDP by 2050, followed by a consequent rise in commodity prices and a significant decrease in private domestic consumption due to the dominant role of agriculture in the economy.Vatankhah et al (2020) find similar results in another case study of Iran, where the authors highlight an increase in production factors' prices in response to an overall production decline due to unfavorable climatic conditions.
Extending a CGE framework at the meso level, Kahsay et al (2017) focus on the Nile River Basin and evaluate the combined effects of trade liberalization and climate change on economic growth and water resource availability.Following Calzadilla et al (2011), they examine both short and long-term effects of climate change by implementing a model that distinguishes between rainfed and irrigated agriculture and includes water as an input factor of irrigated lands.Their results show that although climate change will modestly improve water supply in the next decade, this increase will benefit the Nile basin countries by enhancing agricultural production in new land endowments.Such advancements, coupled with trade liberalization, will improve the economic growth and welfare of the Nile basin region in the short term.Nevertheless, climatic effects will worsen long-term water scarcity, and water-saving policies will be of primary importance in alleviating water distress by enhancing irrigation efficiency at both country and basin levels.
Moving to ABMs, they represent a valuable tool in environmental economics, addressing the connections between ecological and economic systems (Costanza 1989).Smajgl et al (2011) emphasizes their significance for studying socio-ecological processes since they enable explicit simulation of the consequences of human decision-making processes.ABMs, aligning with the broad scope of ecological economics, offer a robust mean to represent autonomous and heterogeneous entities, facilitating the analysis of complex systems through the emergence of outcomes at the macro level.Two literature reviews have analyzed the significant role of ABMs in the exploration of socio-ecosystems adapting to climate change (Balbi and Giupponi 2010) and the potential of decision models used in coupled humanenvironment agent-based simulations (An 2012).
In addition to these two reviews, we identified three applications of macroeconomic ABMs focusing on ecosystems.Beckenbach and Briegel (2011) investigate the role of multi-agent systems in examining the relationship between innovations, economic growth, and carbon emissions.The authors conceptualize the economy as a complex adaptive system in which knowledge diffusion, income generation, and environmental externalities are emergent properties.In particular, agents can choose among different actions, selected according to behavioral and aggregate competitive conditions (deriving from the combination of past individual decisions) and generating various levels of carbon emissions.
Building on the framework of Smajgl et al (2011Smajgl et al ( , 2015))models the complexity and cognitive demands associated with Payments for ecosystem services (PES) 11 recently introduced in the context of the current expansion of Chinese rubber monocultures.To assess their effectiveness in the context of biodiversity and land use change, the authors complement an ABM with the empirical results of a participatory research process consisting of a random sample of 1000 households, each with some objective (e.g.location, household size, production, and income) and subjective (e.g.wellbeing, values, intentions) characteristics.Accordingly, agents follow an adaptive process in the model, responding to changes in income level and livelihood following behavioral response functions in the first case and the surveyed intentional data in the second case.Their findings indicate that the current PES scheme will produce perverse incentives if not followed by effective monitoring and enforcement.
Finally, Gonzalez-Redin et al (2018) incorporate an environmental system in a debt-based ABM to explore how debt-driven processes impact the decoupling between economic growth and the availability of natural resources.The agents (households, firms, banks, speculators, and government) interact within three markets and the environment, modeled as a grid of land patches with a given resource stock.Focusing on the environmental aspects of the model, it includes firms exploiting land patches, the related evolution in the stock of natural resources, and the government implementing conservation policies.

WE-water and energy
To study the combined use and management of water and energy resources, it is crucial to account for the multiplicity of feedback and interdependencies that jointly affect their sustainability.From the 'energy for water perspective' , global water sectors constitute between 1.7% and 2.7% of total primary energy consumption (Liu et al 2016).Conversely, in terms of 'water for energy' , 44% of total global water withdrawals are used for energy production (Collins et al 2009).
Most of the literature on the WE nexus in CGE models focuses on the potential future distress in energy production due to water scarcity related to climate change.Indeed, water can enter either as a direct (e.g.hydropower, hydroelectricity, and ocean energy) or indirect (i.e.thermoelectric power) input into energy production.
Considering the direct use of water, the water scarcity topic represents a central research focus within the WE nexus literature (Su et al 2019).By 11 PES are incentives paid to economic agents (e.g.farmers) for managing their resources (e.g.land) while maintaining or providing a certain level of ecological services.
including water as an input factor in all economic sectors (including energy), Teotónio et al (2020) consider a case study on Portugal by projecting its GDP in 2050 under different water availability scenarios as a direct consequence of climate change (i.e. the RCP 4.5 and RCP 8.5 scenarios) 12 .Results for 2050 indicate that when the priority for water consumption is given to other sectors rather than power generation, the economic impacts are stronger when transboundary water competition with Spain is taken into consideration as this intensifies water scarcity in Portugal.
Looking from another perspective, Basheer et al (2021) analyze the economic implications of water supply fluctuations on electricity generation from hydropower dams and water resources availability for industrial and agricultural production.Focusing on a case study of the Nile Basin (i.e.Egypt, Ethiopia, and Sudan), the authors estimate the economic impact induced by the construction of the Grand Ethiopian Renaissance Dam in terms of water availability, hydroelectric generation, and irrigation water capacity when the flow of the river is uncertain.
Similarly, Sun et al (2021) argue that introducing a carbon tax can indirectly change the water footprint by improving energy use.To test this hypothesis, the authors consider the effects of such regulation on the Chinese water footprint and find that it can effectively reduce the projected damages of this externality by 2030.Interestingly, despite the overall improvement in water use, the tax registers opposite impacts in different economic sectors, as primary industries show an increase in water consumption while both secondary and tertiary sectors decrease it.Nevertheless, when considering a different measure of water use, i.e. the virtual water content (VWC) 13 , then all the economic sectors benefit from the carbon tax, significantly impacting secondary industries.
On the side of the indirect use of water, Su et al (2019) address the water scarcity issue by considering the impact of water management improvements on water shocks in China.By upgrading the industrial water recycling technologies and decreasing pipeline leakages by 5%, the analysis shows that such technological upgrade would increase the water use efficiency by 16% (compared to the baseline case with no improvements) and, consequently, reduce water demand for economic activities, also including energy production.Conversely, focusing on the energy sector, Zhou et al (2016) study the effects of different tax rates on fossil fuels to promote improvements in energy production and water use, finding a sharper transition to clean energy at higher tax rates.
IAMs extend CGE models by considering the bidirectional relationship between water supply and energy generation.Bouckaert et al (2011) incorporate a water module into a global energy system model and show that global electricity generation could double by 2050, with an energy mix characterized by consumption of water three times larger than the current levels, reaching a hardly sustainable scenario.Davies et al (2013) analyze the global demand for water in electric power production over this century by incorporating it into a reference scenario.They estimate the water withdrawals and consumption of the electricity sector in different geopolitical regions and study different related uncertainties (including technological change) with projections till the end of this century.Their results underline that the water withdrawal intensity of electric power production can be expected to decrease shortly due to capital stock turnover in the power sector, the ongoing switch from flow cooling systems to evaporative cooling ones, and the deployment of advanced electricity generation technologies.Liu et al (2015) follows a similar approach to study US water withdrawal for electricity generation, which accounts for approximately half of total freshwater use.By modeling water and electricity systems at the state level, they show that even if the scenarios project a significant expansion in electricity generation in the US, as the population grows, the water withdrawals of the US electric sector will decline by 42%-91% by the end of the century, while water consumption will increase by 4.2%-80%.Such variations stem from different factors related to cooling technology mix, population, water-saving technology, fuel portfolio, and electricity trading options.In particular, population change will have a positive relationship with the electric sector water demand variation, while mitigation through renewable energies will reduce water demand.Lastly, climate mitigation strategies focusing on carbon capture and storage (CCS) and nuclear power will have less favorable water consumption effects.
On the other hand, Zhou et al (2018) combine the CGE modeling framework with a global hydrological model to provide consistent WE analyses.The choice of the CGE structure allows them to account for different sectors (energy, waste, health, and agriculture /land use) and regions (in the Asia-Pacific region) to provide environmental policy advice via future scenario simulation.In such a context, the authors project future thermoelectric cooling-water requirements in different regions with no hydrological constraint on water availability.
To improve the representation of economic subsectors and their interactions, as well as to evaluate the synergies or co-benefits emerging from the Resource-Energy-Water nexus, Zhang et al (2019) extends the traditional material flow analysis (MFA), which aims to quantify the flow and stocks of material or substances in a system, to the context of the WE nexus.That allows the inclusion of the materialenergy-water nexus into a CGE modeling framework to study the Chinese steel industry and estimate the effects of improved energy and material efficiency between 2010 and 2050.In particular, they forecast a reduction in GHG emissions and future energy and water consumption but highlight a potential negative spillover due to the resource-energy-environment nexus, which indicates a contemporaneous increase in water withdrawals 14 and PM2.5 emissions.

WF-water and food
The interrelation between food production and water resources is a critical issue, especially in the face of a growing population.Since agriculture consumes approximately 70% of all freshwater resources available worldwide (World Bank 2022) economic models exploring the connection between water and food (e.g. by using water as a primary input) are of particular importance, especially for setting priorities among alternative uses and defining proper water management and distribution policies.
According to Dudu et al (2018), the inclusion of water in an economic model is not an easy challenge due to the specific characteristics of this natural resource.In particular, the authors highlight three interrelated elements that need to be considered when modeling water as a direct factor of production in a macroeconomic framework: the (real) volumetric price of water, the income generated by water, and the distribution of this income among different economic agents.However, as stated by Bardazzi and Bosello (2021), water is often a free or, at best, underpriced resource, and defining its actual price is not an easy job.Nonetheless, a criterion used to disentangle the value of water from land takes the price difference between irrigated and non-irrigated crop productions, where the difference represents the contribution of water (Bardazzi and Bosello 2021).Calzadilla et al (2011) and Berrittella et al (2007) provide some examples of water as a direct input factor.While the former introduces water as an explicit production factor of irrigated agriculture, the latter includes water as an endowment of the economy in the form of VWC, namely the quantity of water embodied in each non-food consumer good. 14Water withdrawals indicate the total volume of water recovered (and partly returned) to the environment, while water consumption is the quantity of water used and not returned to the ecosystem.
At the same time, Nechifor and Winning (2017) explore the reverse implications of food production on water resources by considering the impact of different Shared Socioeconomic Pathways (SSPs) 15 on crop production and future water distress.By introducing a global dynamic CGE model with freshwater as an explicit factor of production, their framework distinguishes between irrigated and rainfed crop productions, thus allowing a differentiated specification of yield improvements for the two types of land using fixed productivity parameters.Their results show that the efforts to mitigate global warming will not stop the increasing trend in water withdrawals at the global level by 2050, thus highlighting the need for more efficient water technologies to control crop production and determine a more sustainable use of freshwater resources in the future.
Finally, focusing on CGE models that introduce water as an indirect input in the production system, Dudu et al (2018) highlight the need to link the standard CGE framework to a distinct biophysical model, where water explicitly enters the agricultural sector and affects its total factor productivity.The idea behind this is to leave the calculation of the key parameters related to the water cycle and their impact on the technical conditions of agricultural production (e.g.changes in water availability or changes in crop yields) to the external biophysical model, so that the resulting information on the waterembodied value added of irrigated agriculture can be easily modeled in the CGE framework, without having to deal with the highlighted difficulties in determining water prices and incomes.According to the authors, the same framework could be extended to the WE nexus by incorporating an energy-specific biophysical model into agricultural and hydro-energy production functions, effectively linking all three elements of the WEF nexus.
The modeling of the WF nexus in IAMs focuses on the impact of climate change on crop yields.Nevertheless, the estimation of the effects of water shortages on irrigated crop yields is still a challenge due to the complex nature of the water supply and management system.Blanc et al (2017) integrate a water resources model and a crop yield reduction module into a framework that combines the effects of anthropogenic activities like the evolution of economic, demographic, and technological processes (e.g.GHG emissions, air and water pollutants, and land use/cover 15 The SSPs complement RCPs and describe plausible alternative trends in the evolution of society and natural systems over the 21st century at the global and regional level (O'Neill et al 2014).These trends combine pathways of future radiative forcing and the associated climate changes with alternative pathways of socioeconomic development (i.e. at different population and economic growth rates).changes) with sub-models describing earth systems, thus accounting for physical, dynamical, and chemical processes in the land, freshwater systems, ocean, and atmosphere.Under this framework, the authors assess the effects of climate and socioeconomic changes on water availability for irrigation in the US and the subsequent impacts on crop yields by the middle of the century while accounting for climate change projection uncertainty.
ABMs have predominantly been utilized to assess the link between water and food, primarily focusing on agriculture.Dobbie et al (2018) concentrate on rural Malawi, employing an ABM to investigate community food security and variations among livelihood trajectories.The authors show how to integrate context-specific data within the modeling structure to fit development policies and programs addressing food security in different communities.Subsequently, they develop a model considering the multi-dimensional nature of the problem.Their findings indicate that population growth and increased rainfall variability will lead to a significant reduction in food stability by 2050, with occasional farmers experiencing the most negative effects.
Bazzana et al (2022) study the impact of climatesmart agriculture (CSA) on food security and analyze how social and ecological pressures-such as climate change-affect the adoption of water and soil practices in rural Ethiopia.The authors highlight that ABMs can offer a substantial advantage for future policy analyses by enabling the modeling of individual adaptation paths for each farmer under different scenarios.Overall, they find that CSA adopters exhibit higher food security under climate projections, influenced by the topology of their social network and the integration of the decentralized agricultural markets.However, CSA alone cannot fully compensate for severe climate change, necessitating additional mitigation policies.
Lastly, Schouten et al (2014) employ two complementary methods for performing sensitivity analysis under different scenarios in a spatially explicit rural agent-based simulation.The authors provide a comprehensive guide for studying the impact of agricultural policies on the socioeconomic and ecological aspects of individual farmers and farms in a rural region.Their results show that a mixed approach to sensitivity analysis enhances the understanding of the model's behavior and improves the description of the simulation's response to changes in inputs and parameter settings.That is particularly useful for studying potential policy interventions in the ABM-simulated systems.

FE-food and energy
As in the previous analyses, when considering the linkages between food and energy, the approach must be two-fold, namely: from 'energy for food' to 'food for energy' .On the one hand, the food industry consumes almost 30% of global energy every year, mainly from food processing activities and including transport (FAO 2017).On the other hand, food is a fundamental component in the bioenergy industry, whose use is increasing for both electricity generation and heating purposes.
The vision of food as a potential energy source (i.e.bioenergy) plays a predominant role in the CGE literature on FE linkages (Bardazzi and Bosello 2021).The model developed by Birur et al (2008) explicitly accounts for biofuels as a product of the agricultural sector that competes against food in the overall crop production.By extending the work of Burniaux and Truong (2002), the authors define biofuels as an energy input complementary to petroleum, which implies that both sectors participate in energy production.Furthermore, following the work of Lee et al (2005), they integrate the database used to feed the model with an additional dataset on crop production 16 at agro-ecological zone (AEZ) 17 level to account for detailed data on land.According to Birur et al (2008), the extended database completes the biofuel module and gives an accurate estimate of land-use competition between food and biofuel production.
Further extending the model of Birur et al (2008), Taheripour et al (2013a)introduce a distinction between irrigated and rainfed crop activities at the AEZ level by exploiting the biophysical data developed by Portmann et al (2010).Starting from the baseline framework, where each industry produces only one commodity and each commodity derives from only one industry, they move to an extended model with an agricultural multiproduct sector that supplies biofuels with two different industries, one irrigated and one rainfed.
Overall, the consideration of biofuels as an energy source poses a direct follow-up question in terms of environmental impacts, such as the emissions coming from ethanol biofuels, explored in the framework developed by Tyner and Taheripour (2013).Moreover, bioenergy and food can be seen as competitors when considering land over-exploitation.Indeed, the parallel growth in food and bioenergy demand registered during the recent decades has put 16 Including data on covered land by type (e.g.forest, pastureland, and cropland) harvested land, and detailed maps on forestry activity. 17AEZs are defined as homogenous and contiguous areas with similar soil, land, and climate characteristics (FAO 2022).Results are presented in a regular raster format of 5 arcminutes (about 9 × 9 km at the equator) grid cells.Selected maps related to AEZ classification, soil suitability, terrain slopes, and land cover are provided at 30 arcseconds (0.9 × 0.9 km) resolution (FAO-GAEZ Data Portal 2022).
tremendous pressure on land regeneration, which can result in significant land use change, with possible unfavorable impacts on the environment (Birur et al 2008).
The DSGE framework examines the FE link by focusing on the agricultural sector.In this field, Permeh et al (2017) develop a large multi-sector DSGE model for the Iranian economy to study the relationship between oil price and agriculture.The economy encompasses three interconnected sectors: agriculture, non-agriculture, and oil, with two different types of households (urban and rural) consuming agricultural and non-agricultural goods.Lastly, import and export flows enter this analysis with subsidies for imported agricultural goods.In such a framework, the authors focus on the de-agriculturalization phenomena subsequent to an increase in the oil price, the so-called Dutch disease18 .In particular, an exogenous increase in the oil price, by boosting government revenues and central bank foreign reserves, reduces the real exchange rate.As a result, tradeable goods (such as agriculture and industry) suffer from the competition from cheaper foreign products, while non-tradeable goods (such as construction) benefit from it.

The WEF nexus
In light of the several synergies and trade-offs between the sometimes competing uses of water, energy, and food resources, the WEF nexus approach aims to draw attention to the interrelated nature of such systems.That is especially important considering the increasing demand for water, energy, and food resources driven by the growing population, industrialization, and urbanization (Lalawmpuii and Rai 2023).Such human activities, in turn, can degrade and pollute water resources while consuming increasing amounts of fossil fuels, with detrimental effects in terms of GHG emissions.
Following the work of Berrittella et al (2007), Taheripour et al (2013b) provide an interesting (and the only) application covering the entire WEF concept by introducing water among primary production factors in a CGE framework.Specifically, they consider water as an explicit input into irrigated crop production while defining distinct production functions for irrigated and rainfed crops, biofuels, and petroleum energy sectors.
In the context of the WEF nexus, one of the first analytical tools in the IAM field developed to analyze the interlinkages and interconnections between all three resources has been the CLEW (Climate, Land, Energy, and Water) modeling framework, developed by the International Atomic Energy Agency (IAEA).This integrated assessment tool allows for addressing food, energy, and water security issues while taking into account the indirect impact of those resources on the climate and how climate change may affect the future exploitation of these resources.Among its various applications, Hermann et al (2012) show that a coordinated approach to increase water, energy, and food security is essential.Their case study of Burkina Faso demonstrates that energy policies are strongly interrelated with water constraints, while agricultural-related policies have substantial implications for energy use.
Another relevant case study is the one presented in Yang et al (2016a), investigating the WEF nexus in the Indus River of Pakistan by extending a hydroagro-economic model with an agricultural energy use module.Their outcomes show that the negative impacts of climate change on energy use and agricultural water can be mitigated through more flexible surface water allocation policies, which allow for larger crop and hydropower production and a reduction in energy use.Bonsch et al (2016) instead provide an analysis of the role of bioenergy in the future energy mix.Such a prospect is significant in the field of the WEF nexus since large-scale bioenergy cultivations affect land exploitation and water consumption.The complexity of such a relation refers primarily to productivity since irrigated bioenergy production provides higher yields and can reduce the pressure on land but may increase the degradation effects of freshwater ecosystems.
Walsh et al (2016) examine the trade-offs associated with fuel and food production and find that it is possible to realize significant emissions savings and avoid land-use change by shifting a portion of global food production to a high-yield crop such as algae.However, that would be insufficient to offset the potential growth in emissions due to the expected increase in meat and dairy production.Therefore, the co-rendering of a fuel product is necessary to generate ongoing emissions savings.
Miralles-Wilhelm and Muñoz-Castillo ( 2018) study the near and medium-term implications of the Paris Agreement on the WEF nexus in Latin America and the Caribbean.Under an emissions mitigation scenario-explicitly modeled to represent the Paris Agreement framework-they find that the potential conflicts regarding the use of nexus resources may exacerbate because of the induced changes in the energy and food sectors that would impact water availability and use.Kim et al (2016) use the same modeling structure to study the scarcity of fresh water while accounting for the interactions between population, economic growth, land, energy, and water resources.In their framework, water becomes a binding factor in agriculture, energy, and land use decisions in a global IAM, with profound implications on the optimal international responses to water scarcity, particularly in the local land use and agricultural commodities trade.Similarly, de Vos et al (2021) focus on quantifying the competing water demands between food production, freshwater ecosystems, and utilities (energy, industries, and households) under different SSP scenarios.They estimate that an additional 1.7 billion people could potentially face severe water shortages for electricity, industries, and household consumption if priority is given to food production and environmental flows.
Moving to the country level, Schlör et al (2018) use an IAM to study the heterogeneity of the WEF nexus in Germany and its management through social learning and decision-making processes.
Lastly, van Vuuren et al (2015) study the relationship between technology and SDGs to analyze how different combinations of technological measures could contribute to their achievement.By designing different pathways to reach SDGs objectives simultaneously, the authors find that all of them require substantial transformations in the energy and food systems while changing the approach to progress and policies' design.Smajgl et al (2016) provide one of the first theoretical examples of ABMs studying the WEF nexus by synthesizing the results of a Mekong Region Simulation model (Smajgl and Ward 2013).Their model explores the heterogeneous responses of simulated households to environmental changes, revealing critical insights around potential interventions in both individual and cross-sectoral WEF sectors.In particular, they propose a dynamic and balanced WEF nexus framework, challenging the prevailing water-centric perspectives.
Li et al (2017) present and simulate an ABM for analyzing the WEF nexus in Chinese urban development.Conceptualizing the urban space as a complex environmental system with various WEF production and consumption activities influenced by and influencing different agents, the authors examine how social interactions impact the distribution of urban WEF consumption.The model includes three types of agents: households, which can only consume WEF, firms, which demand and supply WEF, and a government, which can control the demand for WEF.This approach enables the simulation of WEF consumption distribution in a city as well as the interaction of various agents over time.
Building upon the same notion, according to which WEF systems influence economic outputs and human activities impact the WEF nexus, Molajou et al (2021) explores the nexus with a focus on agriculture.The authors introduce a socio-hydrological ABM to investigate the impact of agricultural activities on the anthropogenic drought of Lake Urmia in Iran.By incorporating the results of interviews and previous analyses, they model farmers' choices regarding crop type selection, energy demand, and water exploitation, considering the effects of financial constraints on these decisions.Their findings indicate that unfavorable economic conditions increase water-intensive crops because of their higher profits, thus reducing surface water and boosting energy consumption to exploit groundwater sources.
Lastly, Gebreyes et al (2020) and Bazzana et al (2021) develop two ABMs to investigate the effects of land competition on WEF availability.Focusing on the case of eucalyptus plantation in Ethiopia, Bazzana et al (2021) explore the complex nonlinear decision of land-use allocation between cash (i.e. the eucalyptus plantation) and food crops.Indeed, while eucalyptus plantations have a higher monetary value, they generate a negative externality in the surrounding fields by reducing their fertility.Accordingly, the authors investigate the highly nonlinear gametheoretical problem through an ABM and assess the fundamental role played by the government in coordinating agents' actions and maximizing the overall welfare.At the same time, Gebreyes et al (2020) study the WEF nexus via analysis of the competition between water and energy infrastructures (specifically, water canals and electric grid development).Considering environmental heterogeneity, the authors show how hydropower infrastructure construction can create land competition between rural communities and the energy sector.

The WEFE nexus
Amidst climate change and population growth concerns, the WEFE nexus aims at enriching the WEF nexus with the ecosystems' component, focusing on the impacts of external stressors, such as population, and drivers, namely climate change (Godfray et al 2010).
Focusing on the entire WEFE nexus, Veerkamp et al (2020) stress its importance for the future of biodiversity and ecosystem services to inform decision-makers about possible options for their conservation in the EU.To do so, they use two IAMs under four socio-environmental scenarios: the first to quantify the global human impacts on biodiversity and ecosystems, and the second to explore the complex multi-sectoral issues surrounding impacts, vulnerability, and adaptation to climate and socioeconomic change across the EU within the fields of agriculture, forestry, biodiversity, water, coastal and urban ones.
Similarly, Kebede et al (2021) investigate the trade-offs and synergies across food, water, land, and ecosystems in the EU.Their results indicate that food production will be the principal driver of a future change in EU landscape.While sustaining the current level of food production at the European level could be achievable under most climate and socio-economic scenarios, there are significant regional differences.Among the European countries, Spain, Portugal, Southern Italy, Romania, Bulgaria, and Poland are water-stress hotspot areas due to climate change.For some scenarios, the same occurs on the side of biodiversity vulnerability for alpine areas in continental Europe, Denmark, southern Italy, and France due to the decline in arable habitats and climate suitability for some species.At the same time, countries such as Romania, Ireland, southern Finland, and alpine areas in Scandinavia can experience significant improvements.Concerning the coastal and fluvial floods, the hotspot areas are mainly concentrated in the western EU because of a projected increase in precipitations.Land use diversity shows a major decline in the Mediterranean, specifically in south-east France and north-west Italy, driven by changes in agricultural land use.Food production is declining in parts of southern and northern Europe, while the expansion of intensive agriculture in some areas leads to an increase in production in northern and western ones, making these regions key agricultural lands for maintaining EU-wide baseline level production under various climate scenarios.

Strengths and weaknesses
This section discusses the main strengths and weaknesses of the different modeling approaches, covering both environmental/resources and macroeconomic dimensions.In particular, we consider the models' suitability for designing and evaluating policies and their ability to analyze the interlinkages between different WEFE elements.Moreover, we assess the stringency and consistency of the underlying theoretical assumptions, data dependency, complexity, and development time.

Interlinkage analysis
CGE models provide a reliable tool for analyzing the interlinkages among the elements of the WEFE nexus, thanks to their reliance on input-output matrices, which provide a comprehensive overview of intersectoral and international relationships in the markets for factors and intermediate inputs, final output, demand, and government transfers.Although at a lower level of detail, IAMs demonstrate a high potential for WEFE nexus modeling, integrating land dynamics, management, and various environmental issues.That explains their vast diffusion together with CGE models in analyzing WEFE single components and combinations.Conversely, DSGE models are still at an early stage in the comprehensive assessment of the interlinkages between the different nexus components.Due to their analytical complexity, most research is limited to a maximum of two elements in a single setup, with the energy sector being predominant.Lastly, ABMs offer a flexible and realistic characterization of socioeconomic systems, capturing the role of complexity and nonlinearities in the WEFE components and their nexus and allowing a characterization of their linkages at the micro level.

Policy design and evaluation
CGE models are excellent instruments for policy evaluation since they allow scenario comparisons through separate simulations.After computing the general equilibrium state of the economy in the calibration year (i.e. the baseline scenario), policy analysis can be carried out by simply perturbing one or more exogenous parameters of the model to calculate the counterfactual scenario.To infer the impact of the shock is sufficient to compare the initial and counterfactual equilibrium vectors of prices, output, and utility.However, the reliability of the results largely depends on the accuracy of the calibration, which decreases the further one moves from the baseline year/scenario (Wing 2011).
At the same time, by integrating economic and environmental processes in an intertemporal setting, IAMs further extend the analysis of WEFE components and their nexus, with the capability to provide insights around specific trade-offs and optimal policies.While relying on neoclassical assumptions as CGE models, they overcome some of their limitations by offering a dynamic perspective of human and natural phenomena at the cost of a lower resolution.However, IAMs (as CGE models) cannot represent some relevant features of the WEFE nexus, such as complex behavior, nonlinearities, tipping points, and uncertainties.Moreover, the lack of a representation of the financial sector is one of the main limitations of CGE models and IAMs, a weakness that has been overcome in the DSGE framework.
DSGE models work similarly to CGE models but can study the impact of stochastic shocks in a simulated economy.The possibility of explicitly incorporating uncertainty about the future by introducing perturbations to output, consumption, availability of a natural resource, or weather shocks represents a powerful tool for policy simulations and analysis.While this is their main peculiarity, it also limits them in the spatial dimension of their modeling framework.Furthermore, their advanced level of technicality, both at the theoretical and computational level, makes difficult the design and assessment of complex policies.Nevertheless, DSGE forecasts are comparable in terms of accuracy to existing macroeconometric models for a small number of variables (Arora 2013).

Theoretical assumptions
While the neoclassical assumptions of CGE models allow computing the optimal allocation of input and the analytical solution of the general economic equilibrium in the presence of multiple sectors and industries, they often do not account for agent heterogeneity, technological barriers, and behavioral limits.That also applies to IAMs, which solve the lack of intertemporal optimization in CGE models but face challenges in assigning proper discount rates for climate change impacts and underestimating intergenerational environmental issues.
Along this line, DSGE models are well known for their robust theoretical background, such as strong microeconomics foundations and consistency in terms of real-world business cycle dynamics.However, those strengths also pose significant obstacles to their application within more intricate structures, particularly when integrating interconnected components while accommodating related uncertainties.This challenge is further compounded when addressing interdependent levels within the model.
Lastly, ABMs represent real-world systems as the complex interactions of individuals behaving under the assumption of bounded rationality.On the one hand, that allows modeling agents' heterogeneity, nonlinear dynamics, complex feedback, as well as behavioral and technological barriers.On the other hand, the absence of a common framework, together with the lack of economic micro-foundations and farsighted behavior by agents, limit their application in the WEFE field.

Data dependence
CGE models heavily depend on calibration data, which reduces the predictive power the more one moves away from the starting point of the simulation.Similarly, IAMs in which external evidence is used for the determination of the system parameters and overtime dynamics.
Conversely, the DSGE literature has made considerable progress in their estimation in recent years (Fernández-Villaverde and Guerrón-Quintana 2021).However, modeling and simulating DSGE frameworks can also be technically demanding, but their empirical outcomes are grounded on a robust theoretical background.
ABMs can integrate data from multiple sources, both qualitative and quantitative, which is particularly useful within data-scarce contexts (Janssen andOstrom 2006, Robinson et al 2007).As Dobbie et al (2018) highlight the scarcity of data in some regions can be overcome using qualitative approaches.However, most of the time, collected and available empirical data have a coarse resolution, which complicates the validation of the model through lengthy codes and complicated feedback.Accordingly, several papers present models that have not been rigorously tested on empirical data in the general ABM literature.
Overall, the reviewed literature highlights a widespread lack of data, recommending the creation of innovative protocols for data collection, storage, and inference (McCarl et al 2017b).

Complexity and development time
The main challenge for researchers is the design of models that are theoretically rigorous but can also reproduce and forecast real-world phenomena.When natural resources are considered in economic frameworks, the degree of complexity rises, and advanced techniques must be used.
In the case of CGE models, incorporating the WEF nexus in this field requires a reasonable effort, as they inherently consider sectoral interdependencies within their baseline economic versions, further supported by the extensive literature on their development and resolution.Generally, IAMs use simplified numerical approaches to represent complex physical systems.Consequently, they rely on strong economic assumptions regarding their input to account for crucial aspects of the model.Furthermore, this kind of simplification allows combining different modules to explore their interactions while running in a reasonable amount of time.
DSGE models are well known for their rigor in terms of microeconomics foundations and ability to assess structured frameworks on the side of financial shocks, as well as monetary and fiscal policies.However, these strengths potentially result in heightened modeling complexity, and, as a consequence, this approach only focuses on single components in the WEFE field.Advancing to a higher level entails substantial modeling exertion, which may lead to insoluble mathematical frameworks.
ABMs, while being recognized as powerful tools for studying complexity, are also time-consuming in their development due to modeling dynamics at the agent level.
Overall, it is also worth acknowledging that challenges related to complexity and computational issues could be significantly overcome in the future thanks to the introduction of artificial intelligence.

Conclusion
Understanding the WEFE nexus paradigm necessitates the development of studies that can analyze its diverse physical layers, economic dimensions, and spatial scopes.The effective integration of various macroeconomic modeling structures plays a central role in shaping policy interventions capable of addressing the intricate interdependencies within the nexus and its associated criticalities.This work compiles a selection of the most relevant scientific publications within macroeconomic models for the WEFE nexus and its components, thus providing a comprehensive overview of the field's state of the art in the past two decades.
Based on a review conducted by searching specific target words around the WEFE nexus and its components in prominent online research repositories, we identified 77 papers published between 2002 and 2021.Our focus is directed toward four distinct categories of macroeconomic models: CGE models, IAMs, DSGE models, and ABMs.To maintain a specific focus and incorporate precise modeling details, we limit the search to a twenty-year time frame and the four main macroeconomic models.That inevitably leaves out some significant contributions to the literature.
During the referenced time frame, CGE models emerge as the most prevalent, with 27 publications.At the same time, IAMs address the majority of the WEF and WEFE nexuses in their integrity.In contrast, DSGE models primarily concentrate on the energy side despite its significant correlation with climate change, GHG emissions, mitigation and adaptation policies, and temperature variability.Lastly, while they do not exhibit a clear pattern, ABMs perform well at the WEF level, with a specific emphasis on ecosystem as individual component.In this sense, our findings indicate that the development of DSGE models and ABMs is still in its early stages.DSGE models potentially allow the analysis of uncertainty and risk in this field, while ABMs might offer new insights into the complex interactions between natural and human systems but still lacking a common framework.
Specifically, IAMs exhibit a structure best suited to portray the complexities of the nexus, while DSGE models majorly focus on single components.Nevertheless, DSGE models demonstrate efficacy in accounting for the randomization of exogenous shocks.Nonetheless, researchers interested in employing DSGE for modeling the WEFE nexus must invest more effort, as references to the complete WEFE nexus are only found for two components concurrently, specifically water and energy, whereas most DSGE models center on a single WEFE component.
From a policy perspective, CGE models and ABMs appear to be the most suitable options.The notable advantage of CGE models lies in their capacity to account for interlinkages across sectors and countries.On the other hand, the versatility in modeling various agents' behavior provided by ABMs enables scholars to define theoretical frameworks that better approximate real-world scenarios.Conversely, the integrated approach characteristic of IAMs aligns more effectively to understand the WEFE nexus as a cohesive entity, thanks to a well-defined combination of physical and economic structures.
The literature review delves into the applications of four distinct macroeconomic models for analyzing the WEFE nexus and its components.However, by confining the exploration of WEFE to (i) an economic lens and (ii) exclusively macroeconomic models, certain limitations naturally arise.
The initial emphasis on economic models excludes other valuable perspectives and disciplines, such as ecology and sociology, which offer unique insights into the WEFE nexus.It is essential to recognize that the economic approach is just one of many, and, with its focus on quantifiable factors and market mechanisms, it may oversimplify the intricate web of relationships and dependencies within the WEFE nexus.The economic lens might struggle to comprehensively capture qualitative aspects, non-market values, and the complex social and ecological dynamics integral to sustainable resource management.
Furthermore, the exclusive focus on macroeconomic models introduces potential limitations by narrowing the scope of the analysis.While macroeconomic models are adept at systemic assessments and examining interconnected relationships like the WEFE nexus, their exclusive consideration may neglect the nuanced dynamics present at finer scales, such as sector-specific or localized interactions within the nexus.
To conclude, it is imperative to acknowledge the requirement for further research efforts in macroeconomic modeling within the field of the WEFE nexus.The models considered in this review can be a relevant tool for policy purposes in this field.Strengths and weaknesses arise at different levels of the analysis, underscoring the need for careful and contextspecific utilization of each model.Ultimately, integrating diverse perspectives is pivotal in shaping a comprehensive collection of research outcomes, enhancing the ability to confront future theoretical and empirical challenges in the WEFE context.

Appendix B. General background of macroeconomic models
This section provides some general background about the four modeling approaches studied in the review.

B.1. CGE models
CGE models combine economic theory with realworld data to study the impact of structural changes (e.g.factors endowment, shifts in sectoral employment, changes in productivity patterns) and exogenous shocks (e.g.financial crises, climate-related disasters) on economic systems, and test alternative policies to mitigate them.These models represent the functioning of a real economy through a set of structural equations, which describe the optimal behavior of the economic agents and, as a result, the endogenous dynamics of the system.In a typical CGE framework, government, private households, and businesses from various sectors interact in competitive markets to maximize welfare, expected utility, or profits.Accordingly, they can easily account for consumer choices, firm behaviors, related interdependences, and feedback effects in a closed economy.Moreover, they can also include a foreign sector, which opens the domestic economy to trade input factors, goods, and services with the rest of the world.The computation of an equilibrium satisfies the Walrasian general equilibrium rule, which implies that supply and demand are perfectly balanced in all the interconnected markets of the economy (i.e. the market clearance condition).
At the same time, CGE models incorporate realworld economic data through a calibration process.The values of the structural parameters, which remain unchanged over time, are set to reproduce the regularities observed in real economies (e.g. the share of production inputs in each sector) or by using previous empirical studies as a reference point.As a result, they allow quantifying production possibilities, welfare, different aspects of the trade, and consumption of the simulated economy (Arora 2013).

B.2. IAMs
IAMs analyze the effect of human activity on natural earth systems by introducing climate change, energy, and land use in standard economic models (Yang et al 2016b).Their core study is the intertemporal relationship between GHG emissions and the impact of climate change on socio-economic systems, aiming to provide relevant insights into the economic policies needed to mitigate or adapt to global warming (Cretì and Fontini 2019).In particular, they juxtapose a standard intertemporal economic framework to a climate/environmental box that internalizes the externality produced by human activities (e.g.GHG emissions).
Given their interdisciplinary nature, IAMs rely on several assumptions covering the economic environment, long-term growth, population dynamics, technological change, land use management, fossil fuel emissions, and atmosphere and ocean concentration dynamics.In this way, scenarios prescribing targeted GHG stabilization levels in the long term can be implemented to evaluate the social cost of possible mitigation interventions 19 .Accordingly, their output strictly relies on the underlying assumptions, the historical data used for the initial calibration, and the design of the different scenarios (Yang et al 2016a).
In this approach, the major distinction is between three main groups:policy-optimization models, policyevaluation models and policy guidance models 20 .The first type includes a strictly formal, unidimensional assessment of 'better' and 'worse' outcomes and uses this to select the 'optimal' policy from several 'whatif ' exercises.Conversely, the policy-evaluation models (simulation models) study the consequences of a set of specific policies in a 'what-if ' exercise.Lastly, policy guidance models focus on identifying those policies that satisfy specific constraints subjectively defined.Over the years, different political and scientific institutions, from the EU to the IPCC, have based the design or assessment of medium and longterm policy plans on such models.
Even though these models are widely used because of their holistic perspective and ability to provide relevant climate-economic policy insights, they suffer some limitations.Among others, Ackerman et al (2009) highlight that the discount rates used for assessing long-term climate damages are too high, favoring short-term decisions and underestimating the relevance of inter-generational environmental issues.Gambhir et al (2019) review the criticisms surrounding the use of IAMs for policyrelevant recommendations on long-term mitigation pathways, focusing on the lack of transparency in the key underlying assumptions of the models, such as energy resource costs, constraints on technology take-up, and demand responses to carbon pricing.

B.3. Dynamic stochastic general equilibrium (DSGE) models
DSGE models are macroeconomic modeling tools grounded on solid microeconomics foundations and consistency in terms of real-world business cycle dynamics 21 .Such a mix allows economists to operate with empirical models characterized by a robust theoretical background, which makes them suitable for policy design purposes.As in IAMs, DSGE models assume that the economic agents (e.g.households and firms) make decisions by solving an infinitely forward-looking inter-temporal optimization problem given a set of assumptions regarding their preferences, technology, information, fiscal and monetary policy regimes (Fernández-Villaverde et al 2016).Prices assure market clearance in all sectors and reflect the maximization process of agents' objective functions.Lastly, aggregate fluctuations depend on exogenous technological progress and unexpected changes in public policies.
In contrast to CGE and IAMs frameworks, DSGE models can incorporate uncertainty by adding a dynamic and stochastic component.Such a feature is crucial for the dynamical properties of the model, whatever the time horizon since agents must internalize the effects of unexpected random shocks in their decisional process (Tonini et al 2013).These stochastic processes are not limited to technological progress or government decisions (which has been the main focus of researchers at the beginning) but also extend to the structural parameters of the model, thus allowing the analysis of the dynamic consequences of any permanent or temporary perturbation of their value.However, productivity shocks are the fundamental driving forces of uncertainty in the conventional DSGE framework (Korinek 2018).
While their mathematical rigor is one of the positive features of these models, it exposes them to criticism (Christiano et al 2018).Indeed, as for other economic models, some inconsistencies and ad hoc assumptions have been at the center of the academic debate.On this side, Korinek (2018) provides a critical evaluation of their benefits and costs by grouping them into conceptual methodological restrictions and quantitative ambitions.In the former case, the author focuses on the peculiarities of such models, namely dynamic characteristics, stochasticity, and general equilibrium properties, while the latter refers to the models' aim to describe the macroeconomy in an engineering-like fashion.

B.4. ABMs
ABMs depart from the representative agent assumption and focus on the complex nature of real phenomena.The simulated system is populated by a multitude of heterogeneous agents interacting autonomously among them following adaptive behaviors (e.g.rule of thumb or learning procedures).Macro results are then obtained by aggregating individual micro transactions in decentralized local markets and then used in scenario analysis to study the endogenous response of the system to exogenous shocks (Tesfatsion 2003).
Following Dawid and Gatti (2018), we can define ABMs as 'an encompassing modeling approach building on the interaction of (heterogeneous) agents whose expectation formation and decision-making processes are based on empirical and psychological insights' .At the same time, Dosi and Roventini (2019) state that when the economy is conceived as a complex evolving system, that is, an ecology populated by heterogeneous agents (such as firms, workers, banks) with continuously changing interactions, it is easy to see why 'the more is different' .Indeed, the assumption of a micro representative agent is not sufficient to describe real-world aggregate dynamics because agents' complex interactions create, at the macro level, new phenomena as well as hierarchies.That generates a lack of isomorphism between the micro and the macro levels and explains why ABMs are a valuable instrument to model complex economies from the bottom-up while simultaneously maintaining robust empirically-based micro-foundations.Bazghandi (2012) summarizes the main advantages of ABMs.Firstly, they can capture emergent phenomena resulting from the interaction of individual actors.Secondly, they provide a natural description of a system composed of 'behavioral' entities.Lastly, they are cost and time-saving, and flexible as well.On this side, Hammond (2015) stresses that ABMs' flexibility can help researchers in addressing the following challenges: heterogeneity, spatial structure, individual interaction, and adaptation.
As in many other modeling techniques, the accuracy and completeness of the inputs of ABMs influence the nature of the output.Grüne-Yanoff (2009) points out that such models tend to be good instruments for theorizing, providing potential functional explanations, but not for inferring causal explanations about the real world.Nevertheless, Leombruni and Richiardi (2005) address those critiques and provide solid reasons for rejecting the perceived lack of mathematical rigor and the difficulty of estimating ABMs.Another issue with ABMs is that they model, by definition, the dynamics of a system at the level of its agents and not at the aggregate one.Accordingly, it is straightforward to say that simulating the interactions and behavior of multiple agents in a large system can be extremely time-consuming.Finally, Windrum et al (2007) state that, while the neoclassical synthesis has consistently developed a core set of theoretical models and applied these to a range of research areas, the ABM community has produced a wide range of alternative models over the years.Furthermore, they are difficult to compare since they differ in terms of both the theory and the phenomena they investigate.

Figure 2 .
Figure 2. Number of reviewed papers by WEFE component, combinations, and model type.

Table 1 .
Keywords and related combinations.

Table A . 1 .
Summary of reviewed scientific papers.

Table A
Note: summary of the scientific papers reviewed, organized for macroeconomic model type and classified for each WEFE nexus component: water (W), energy (E), food (F), and ecosystems (EC).Figure A.1.Number of reviewed papers by model type and WEFE component and combinations.
Camilla Gusperti  https://orcid.org/0009-0004-1283-9863Ilenia Gaia Romani  https://orcid.org/0000-0002-9885-0542Emanuele Ciola  https://orcid.org/0000-0001-8404-290XSergio Vergalli  https://orcid.org/0000-0003-2279-5011Vatankhah T, Moosavi S N and Tabatabaei S M 2020 The economic impacts of climate change on agriculture in Iran: a CGE model analysis Energy Sources A 42 1935-49 Veerkamp C J, Dunford R W, Harrison P A, Mandryk M, Priess J A, Schipper A M, Stehfest E and Alkemade R 2020 Future projections of biodiversity and ecosystem services in Europe with two integrated assessment models Reg.Environ.Change 20 1-14 Voisin N, Liu L, Hejazi M, Tesfa T, Li H, Huang M, Liu Y and Leung L R 2013 One-way coupling of an integrated assessment model and a water resources model: evaluation and implications of future changes over the US Midwest Hydrol.Earth Syst.Sci. 17 4555-75 Walsh M J, Van Doren L G, Sills D L, Archibald I, Beal C M, Lei X G, Huntley M E, Johnson Z and Greene C H 2016 Algal food and fuel coproduction can mitigate greenhouse gas emissions while improving land and water-use efficiency Environ.Res.Lett.11 114006 Windrum P, Fagiolo G and Moneta A 2007 Empirical validation of agent-based models: Alternatives and prospects J. Artif.Soc.Soc.Simul. 10 8 (available at: www.jasss.org/10/2/8.html)Wing I S 2011 Computable general equilibrium models for the analysis of economy-environment interactions Research Tools in Natural Resource and Environmental Economics (World Scientific) pp 255-305 Yang Y C E, Ringler C, Brown C and Mondal M A H 2016a Modeling the agricultural Water-Energy-Food Nexus in the Indus River basin, Pakistan J. Water Resour.Plan.Manage.142 04016062 Yang Z, Wei Y-M and Mi Z 2016b Integrated assessment models (IAMs) for climate change Oxf.Bibliogr.(https://doi.org/10.1093/obo/9780199363445-0043) Zhang S, Yi B-W, Worrell E, Wagner F, Crijns-Graus W, Purohit P, Wada Y and Varis O 2019 Integrated assessment of resource-energy-environment nexus in China's iron and steel industry J. Clean.Prod.232 235-49 Zhou Q, Hanasaki N, Fujimori S, Yoshikawa S, Kanae S and Okadera T 2018 Cooling water sufficiency in a warming world: projection using an integrated assessment model and a global hydrological model Water 10 872 Zhou Y, Li H, Wang K and Bi J 2016 China's energy-water nexus: Spillover effects of energy and water policy Glob.Environ.Change 40 92-100