The impact of agricultural trade approaches on global economic modeling

Abstract

Researchers explore future economic and climate scenarios using global economic and integrated assessment models to understand long-term interactions between human development and global environmental changes. However, differences in trade modeling approaches are an important source of uncertainty in these types of assessments, particularly for regional projections. In this study, we modified the Global Change Analysis Model (GCAM) to include a novel logit-based Armington trade structure, to examine two approaches to modeling trade: (1) an approach that represents segmented regional markets (SRM), and (2) an approach that represents integrated world markets (IWM). Our results demonstrate that assuming IWM, i.e., homogeneous product modeling and neglecting economic geography, could lead to lower cropland use (i.e., by 115 million hectares globally) and terrestrial carbon fluxes (i.e., by 25%) by the end of the century under the default GCAM scenario, compared with the logit-based Armington SRM structure. The results are highly heterogeneous across regions, with more pronounced regional trade responses driven by global market integration. Our study highlights the critical role that assumptions about future trade paradigms play in global economic and integrated assessment modeling. The results imply that closer harmonization of trade modeling approaches and trade parameter values could increase the convergence of regional results among models in model intercomparison studies.

1. Introduction

Agricultural markets are foundational to the history and future of globalization. Fueled by population and economic growth, reduction of trade costs and barriers, and the evolution of comparative advantage (Anderson, 2010; Costinot et al., 2015), the global trade value of agricultural products reached $1.3 trillion dollars in 2017, about seven times higher (in real terms) than thirty years ago (USDA, 2020). Concerns about global environmental issues are growing in the era of agricultural globalization (Schmitz et al., 2012; Wiedmann and Lenzen, 2018) as international trade plays an ambiguous role in attaining both food and environmental security (Hertel and Baldos, 2016). Although agricultural globalization improves economic efficiency and potentially buffers the impacts of future climate and biophysical shocks (Hasegawa et al., 2018; Liu et al., 2014), agricultural trade may also encourage adverse environmental consequences through indirect effects, e.g., by outsourcing land use and associated emissions from developed countries to developing countries (Meyfroidt et al., 2013; Peters et al., 2011; Weinzettel et al., 2013; Yao et al., 2018). Terrestrial carbon fluxes due to human-induced land use change (LUC) accounted for about 13% of the total net anthropogenic carbon emissions for 2007 – 2016, about 1.4 Gt C per year, as reported by the Intergovernmental Panel on Climate Change (IPCC) (Arneth et al., 2019). LUC emissions vary considerably across regions, mainly because of the high heterogeneity in regional characteristics such as deforestation or afforestation rates, soil carbon density, and socioeconomic and technological drivers (Houghton et al., 2012; IPCC, 2014; Müller and Robertson, 2014; Riahi et al., 2017). As regional agricultural production and land use are indirectly connected through trade, global and regional LUC emissions could be strongly sensitive to the pattern of international agricultural trade and the magnitude of global market integration.

To understand interactions between human development and global environmental change in the long run, socioeconomic and climate scenarios have been developed and evaluated using integrated assessment models (IAMs) (Meinshausen et al., 2011; Popp et al., 2017). The modeling of agricultural trade plays a central role in assessing the impacts of potential future socioeconomic and climate conditions and in estimating the future of global agriculture, land use, and terrestrial carbon emissions. However, differences in trade modeling approaches are an important source of uncertainty in these estimates, as demonstrated by the global agroeconomic model comparisons conducted by the Agricultural Model Intercomparison and Improvement Project (AgMIP) (Nelson et al., 2014; von Lampe et al., 2014).

In the AgMIP exercise, long-term agroeconomic projections were produced by well-established global economic models with harmonized data and assumptions. While global results tended to be generally consistent across the models, regional results varied significantly (Schmitz et al., 2014; von Lampe et al., 2014). This uncertainty in regional economic results further amplifies the uncertainty in assessing regional terrestrial emissions and other biophysical consequences associated with alternative future economic and climate conditions. The disparities in the AgMIP regional results highlighted the key role of agricultural trade assumptions, as the models differed from one another in trade theory, parameter types and values, market structure, and consideration of trade costs and barriers (Ahammad et al., 2015; Robinson et al., 2014).

Trade theories have advanced in the past two decades to feature technology heterogeneity and to consider monopolistic competition when sufficient data are available (Dixon et al., 2016; Eaton and Kortum, 2002; Zhai, 2008). But the core methods for empirical trade modeling have changed little over this period (Bekkers et al., 2020). The Heckscher-Ohlin-Vanek (HOV) and Armington trade specifications remain the workhorses of empirical global agricultural trade modeling for applied partial equilibrium (PE) and general equilibrium (GE) models, respectively. The difference between the two specifications hinges in part on the representation, or the lack thereof, of heterogeneity in consumer preferences (Trefler, 1995). In addition, HOV models generally use a fully integrated world market (IWM) structure, e.g., IMPACT (Robinson et al., 2015) and MAgPIE (Schmitz et al., 2012), while Armington models must use a segmented regional markets (SRM) structure, e.g., AIM (Fujimori et al., 2017), MAGNET (Woltjer et al., 2014), and EPPA (Chen et al., 2015). The IWM structure has several features that are important to this effort: A) markets clear at the world level with a single price, B) consumers treat goods produced in different countries as perfect substitutes, and C) the origin of commodities is not tracked (i.e., only net trade flows are provided), meaning all global production of any given commodity is treated as part a single global supply pool for that commodity, from which every economic region imports for all of their end uses (a phenomenon we refer to hereafter as ignoring “economic geography”, as the concept is often labeled in trade literature) (Hertel and Baldos, 2016; Miljkovic, 1999). In the SRM structure, markets clear at the regional level, and the heterogeneity in regional consumer preferences can be considered. The two market structures are compared visually in Fig. 1 with an example of a global wheat market equilibrium.

Fig. 1. Global wheat market equilibrium in 2010: integrated world markets vs. segmented regional markets.

In fully integrated world markets (a), arrows represent regional production and consumption volume flows and markets clear at the world level. In segmented regional markets (b), arrows in a single region represent domestic wheat supply, arrows between regions and the world represent trade volume flows, and markets clear at the regional level. Regional supplies are distinguished by color. The flows shown are in million tons (Mt). Note that the scales are different in each diagram. Each tick mark represents 16 Mt of wheat in Fig. 1a and 10 Mt in Fig. 1b. See Fig. S1 for the corresponding figure of trade volume flows and Table S1 for region mapping. Data source: GCAM data system

In this paper, we explore the critical role of trade modeling methods and assumptions in estimating the potential future of global agriculture, land use, and terrestrial carbon emissions. We employ a well-established IAM, the Global Change Analysis Model (GCAM) (Calvin et al., 2019). We develop a logit-based Armington approach for agricultural trade modeling and incorporate it into GCAM. This logit-based Armington approach is closely related to the conventional Armington approach but offers a novel view of heterogeneity in consumer preferences in a probabilistic manner.

Following Hertel et al. (2014), we study the impacts of full global crop market integration assumptions by comparing results for an otherwise identical scenario which simulates the future global economy out to 2100, first using SRM Armington-type assumptions about consumer preferences, and then using IWM HOV-type assumptions. In our experimental design, we add each of the sets of assumptions that differentiate the SRM and IWM approaches consecutively, working towards a fully IWM representation that reflects the HOV world view. First, we consider the SRM-type scenario with and without trade costs. IWM approaches typically ignore markup costs of goods shipped internationally as part of their assumption that all production of a commodity is part of a single global pool. These include costs such as the cost of transporting goods internationally and the import duties imposed at country borders. Second, we relax consumer preferences to simulate a world where consumers treat goods produced in different countries as perfect substitutes. Third, we ignore economic geography by simulating the single global pool for each commodity characteristic of the IWM approach, forcing all economic regions to export 100% of their production and then import 100% of their consumption. Furthermore, using an incremental experimental design that introduces these changes in trade modeling assumptions one at a time, we demonstrate how each contributes to differences in our GCAM results and can measure the degree to which these differences are similar across economic regions. In addition to comparing results across trade modeling methods and assumptions, we also test the sensitivity of the reference projections to a plausible set of trade parameter distributions using Monte Carlo simulations.

Our study connects the economic theories of trade modeling to the applied simulation literature of studying the global agroeconomic future. Our results demonstrate notable sensitivity of future projections to trade modeling assumptions. This work enhances our understanding of trade modeling differences in the literature and provides important implications for model intercomparison tasks (Robinson et al., 2014). More broadly, this paper contributes to the literature on the global economic and environmental consequences of socioeconomic, climate, or policy shocks, e.g., those using global economic and integrated assessment modeling frameworks, multiregional input-output (MRIO) analysis, or the telecoupling framework (Cai et al., 2020; Laroche et al., 2020; Schmitz et al., 2014; Yao et al., 2018; Zhao et al., 2019). International trade plays a critical role in each of these areas of research. When using a modeling framework to consider how global human and physical systems may be impacted by changes in future economic or climatic conditions, researchers should consider uncertainty in trade dynamics.

The rest of the paper is structured as follows. In Section 2, we provide the theoretical development of the logit-based Armington approach of trade modeling and introduce the approach into GCAM. In Section 3, we design scenarios to test the sensitivity of future agroeconomic projections to trade modeling specifications for exploring the roles of product differentiation in consumer preferences, economic geography, trade costs, and parameter uncertainty. Section 4 presents the results of these scenarios to demonstrate the impacts of full global market integration for crops on the projection of future agroeconomic and terrestrial emissions. The implications and limitations of the study are discussed in Section 5, and Section 6 concludes the study.

2. Material and methods

In this section, we provide an overview of the GCAM modeling framework and derive the logit-based Armington trade modeling approach. International trade in GCAM was modeled using an HOV approach with the assumption of IWM, and trade costs were not included. We introduce the new trade modeling approach, along with international trade costs, into GCAM for agricultural crop trade modeling and parameterize the model based on trade elasticities reported in the literature.

2.1. GCAM overview

GCAM is a well-established multi-region and multi-sector IAM with a detailed global representation of human and physical systems, including agriculture and land use, water, energy, the economy, and the climate. An earlier version of GCAM was involved in AgMIP and the development of Shared Socioeconomic Pathways (SSP) and Representative Concentration Pathways (RCP) (O’Neill et al., 2014; van Vuuren et al., 2011; von Lampe et al., 2014).

In this study, we use a modified version of GCAM 5.1 (Bond-Lamberty et al., 2019; Calvin et al., 2019). In GCAM 5.1, agricultural production is differentiated across water use (irrigation and rainfed) and management practices (high-yield and low-yield) for 16 crops or crop groups in 384 land use regions, built from the intersection of 232 water basins and 31 geopolitical regions (Calvin et al., 2019). Both the GCAM 5.1 code and the input data processing system are publicly available (Bond-Lamberty et al., 2019; Calvin et al., 2019).

The modified version of the model used in this paper is labeled as GCAM-T-2020-v1.0 (hereafter “GCAM”) in the documentation. A complete description of the GCAM version used in this study can be downloaded from a public repository (Bond-Lamberty et al., 2021). In this version of GCAM, the land protection coefficients have been upgraded, using updated land suitability percentages for each water basin, adapted from Zabel et al. (2014). Another relevant feature developed for this version is the disaggregation of oil crops from the standard GCAM configuration. We have disaggregated this category into soybeans, rapeseed, and other oil crops, which provides additional value for the analysis of regional agricultural markets in the framework of this study. A description of recent GCAM developments is provided in Supplementary information (SI) Section S1.

For this work, we use a GCAM base year of 2010. The model is run to 2100 with external drivers of population and GDP from the SSP2 (O’Neill et al., 2014) and agricultural productivity growth based on the Food and Agriculture Organization (FAO) country- and crop-specific projections (Bruinsma, 2009). For the ease of communication, the results of this study are presented in aggregated crop groups (e.g., coarse grains, wheat, rice, oil crops, and other crops; see mappings in Table S2), and dedicated bioenergy crops and fodder crops (not widely traded) are not included in the main results. Competing uses of land and transitions of production technologies are modeled based on a nested logit land supply framework with a fixed total physical land area in a land use region (Wise et al., 2014; Wise et al., 2015; Zhao et al., 2020a). We run the model in 5-year time steps while also interpolating LUC results linearly to annual results for calculating LUC emission fluxes. The calculation of LUC emissions follows the method in Houghton (1999), including changes in above- and below-ground vegetative carbon stocks and changes in soil carbon stocks (Kyle et al., 2011).

2.2. Logit-based Armington trade modeling

The Armington approach assumes products are differentiated by origin, that is, that consumers view goods produced in different countries as imperfect substitutes (Armington, 1969). The conventional Armington approach uses a constant elasticity of substitution (CES) function for aggregating supply from different sources. As an alternative to the CES-based Armington approach, we incorporate the logit framework into the Armington approach to provide a more explicit interpretation of preference heterogeneity with a connection to discrete choice modeling. Note that the SRM structure is required for the Armington approach as markets clear at the regional level, and gross or bilateral trade flows can be provided.

Here, we formally derive a logit-based Armington approach of trade modeling. Consumers in country n shop around the world to buy a continuum of agricultural product j ∈ [0, 1]. The price consumers in country n would pay if buying j from source i is proportional to the unit production cost (c_i) in country i and the international transport margins (m_ni) and tariffs (τ_ni) between countries i and n. As we pursue a probabilistic representation in the discrete choice modeling, we introduce a distribution of preference index z_ni(j) to explain the preference heterogeneity across j, for each source i. Note that the heterogeneity captures differences in variety, quality, and other factors differentiating preference. We define the preference-adjusted price of j as

$$p_{ni}(j)=c_i{m}_{ni}{\tau }_{ni}{z}_{ni}(j)$$ (1)

Note that the preference-adjusted price entails an inverse relationship with the utility of consuming j (Train, 2009; Zhao et al., 2020a). Like z_ni(j), p_ni(j) also follow a distribution defined in the consumption space of j for each source i. That is, the distribution of the preference-adjusted prices is unconditional on j from source i being consumed. Note that p_ni(j) is also negatively related to the productivity of land (g_i) and nonland inputs (l_i) given that $c_i=\frac{r_i}{g_i}+\frac{w_i}{l_i}$ (derived from the zero profit condition), where r_i and w_i are average rental price and nonland input price in country i, respectively. For each (infinitesimal) unit of j, consumers face a discrete choice problem to maximize utility and, thus, buy from a source with the lowest preference-adjusted price, p_n.

$$p_n(j)=\text{min}\left\{p_{ni}(j);i=1,\dots ,N\right\}$$ (2)

where N is the number of sources. As such, the probability that source i provides a unit of j at the lowest preference-adjusted price is also the fraction of j that country n buys from source i, denoted as π_ni.

$${\pi }_{ni}=\text{Pr}\left\{i=\mathit{\text{arg}}{\mathit{\text{min}}}_i\left[p_n(j)\right]\right\}$$ (3)

Following previous applications of the logit framework (Clarke and Edmonds, 1993; Eaton and Kortum, 2002; Sotelo, 2019), we assume z_ni(j) follows a Weibull distribution $\left(\tilde{\gamma }{T}_{ni}^{-1},\theta \right)$, Type III extreme value, with the cumulative distribution function being:

$$F_{ni}(z)=1-e^{-{\left(\tilde{\gamma }{T}_{ni}^{-1}\right)}^{-\theta }{z}^{\theta }}$$ (4)

where $\tilde{\gamma }{T}_{ni}^{-1}$ is the scale parameter and θ is a positive shape parameter. $T_{ni}^{-1}$ is the unconditional mean of the distribution, and $\tilde{\gamma }={\left[\Gamma \left(1+{\theta }^{-1}\right)\right]}^{-1}$ where Γ(·) is the Gamma function. The shape parameter, θ, inversely reflects the variation of the distribution, namely, the heterogeneity in preference across j. Thus, p_ni(j) also follow a Weibull distribution with parameters $\left(c_i{m}_{ni}{\tau }_{ni}\tilde{\gamma }{T}_{ni}^{-1},\theta \right)$. Treating z_ni(j) as independent across sources, the share of consumption in country n across source i, π_ni, can be derived based on the property of extreme value distributions.

$${\pi }_{ni}=\frac{{\left(c_i{m}_{ni}{\tau }_{ni}\right)}^{-\theta }{T}_{ni}^{\theta }}{{\Phi }_n^{\theta }}$$ (5)

where ${\Phi }_n={\left[{\sum }_i{\left(c_i{m}_{ni}{\tau }_{ni}\right)}^{-\theta }{T}_{ni}^{\theta }\right]}^{\frac{1}{\theta }}$ and ${\sum }_i{\pi }_{ni}=1$. As the minimum of Weibull distributions, p_n(j) is also a Weibull with parameters, $\left(\tilde{\gamma }{\Phi }_n^{-1},\theta \right)$. The mean consumer price can be calculated as weighted average price across sources (i.e., ${\sum }_i{\pi }_{ni}{c}_i{m}_{ni}{\tau }_{ni}$). Consumers in country n have a stronger preference for products produced in sources with larger T_ni. A smaller θ implies a more heterogeneous preference or a more pronounced love of variety for consumers (Hummels and Klenow, 2005). Note that a discrete sector index could be added in the derivations for sector-specific trade modeling, and θ could be further differentiated by n. Note that additional details of the logit-based Armington approach and a comparison with other approaches are provided in SI Section S2.1.

We term this approach the “logit-based Armington” approach since it is closely connected to the logit-based discrete choice modeling framework developed originally in McFadden (1973), while also sharing a theoretical foundation with the conventional Armington approach that consumer preferences are differentiated across supply sources. If one were to set the elasticity of substitution (σ) in CES and logit parameter (θ) equal, the two Armington approaches would have identical responses of relative supply to relative prices across sources. Fig. 2 presents an example of the wheat import demand responses calibrated for Western Africa. When the parameters (σ and θ) are both very large (e.g., 30), both CES and logit-based Armington approaches would effectively collapse into the HOV approach, where the relative trade responses are perfectly elastic (i.e., domestic and imported products are homogeneous). However, a logit-based approach does a better job tracing physical trade volume than the CES-based approach. This is because the CES approach preserves monetary value, while the logit approach preserves physical volumes on the margin of the substitution (Zhao et al., 2020b).

Fig. 2. Import demand responses in HOV and Armington.

Curves represent responses of volume share of imported product in the total consumption with respect to the price ratio between imported and domestic products for HOV and Armington with different magnitude of parameters (parameters shown in parentheses). This figure is generated using GCAM data for wheat in Western Africa in 2010. The calibration point shows the initial import consumption share and price ratio. Note that these responses are the same regardless of function form of CES or logit (see SI Section S2.1.3 for details).

Our logit-based Armington approach also has a unique connection to the Ricardian trade model developed by Eaton and Kortum (2002). Instead of explicitly specifying heterogeneity in technology from the supply as did in Eaton and Kortum (2002), our approach emphasizes the implicit heterogeneity in consumer preferences. Our approach can be reconciled to the Ricardian approach by linking the heterogeneity index distributions to the total factor productivity (TFP) in the cost of production (c_i). However, compared with Eaton and Kortum (2002), our approach has an important empirical advantage of permitting different prices (conditional mean of the distributions) across sources.

Similar to other traditional approaches (e.g., CES-based Armington and Ricardian), the logit-based Armington approach developed in our study can be formulated using gravity equations, which describe the relationships between bilateral trade flows and trade costs with the consideration of factors representing economic geography, e.g., distance and culture (Anderson, 1979; Eaton and Kortum, 2002). However, an essential concern with these approaches arises on the extensive margin of trade that trade partnerships will be locked at the initial state. E.g., if a country is not currently buying a product from a source, it will never do so in future projections (i.e., T_ni = 0 in calibration). That is, the Armington approach cannot endogenously generate new trade partnerships or significantly reverse historical trading partnerships. In addition, bilateral trade Armington models may also be subject to the missing globalization issue (i.e., high rigidity in bilateral trade patterns) (Yilmazkuday, 2017), mainly because of fixed bilateral preference parameters over time. Both missing potential changes in future trade flows and rigid trade patterns could be critical issues, particularly for long-term modeling with highly disaggregated regions and sectors and significant future changes in socioeconomic and environmental drivers. In our study, to mitigate the extensive margin and the missing globalization issues, we model gross trade flows globally as opposed to bilaterally, as discussed in detail in Section 2.3. Modeling gross trade also alleviates computational burdens and data quality concerns. Note that the prospects for future work of incorporating bilateral trade responses is discussed in Section 5.3.

2.3. GCAM trade representation

We incorporate the logit-based Armington approach with SRM into GCAM to illustrate the impacts of modeling agricultural crop trade. Similar to previous studies using the Armington approach (Hertel et al., 2007), we pursue a two-level nesting structure to allow more flexible governance of trade responses, and the trade modeling is implemented by sectors (i.e., differentiating θ across GCAM crop sectors). However, an international market is introduced in the second level where supplies from all regions are aggregated with the logit sharing function (i.e., equation 5), and, as a result, bilateral trade flows are aggregated to gross trade flows in the modeling. For each agricultural commodity in GCAM, the composite of products supplied from all other regions competes with the domestically produced product in each region- or country-level market (see Fig. 1b for an illustration of the structure). Regional markets are segmented so that regional prices can be differentiated between domestic and imported goods, and gross export and import flows can be provided. We also incorporate trade costs implied in the GTAP Database Version 9 (Aguiar et al., 2016) in an aggregated way at the border of each importing region. The logit parameters are calibrated to Armington elasticities reported in the literature (Hertel et al., 2007). Since logit and CES functions imply a similar import demand elasticity when using the same value of the parameter, we simply set the logit parameter equal to the equivalent elasticity of substitution in the calibration. The international (foreign – foreign) logit of crop sectors in GCAM is mapped to the international elasticity of substitution of crop and processed crops used in the GTAP Database documented in Hertel et al. (2007). The regional (domestic – foreign) logit is tied to the international logit based on the “rule of two” (Liu et al., 2004), where the regional logit is half of the international logit. A more detailed description of the structure and logit-based Armington parameters used in our version of GCAM is provided in SI Section S2.2.

3. Experimental design

We begin with a scenario that uses the logit-based Armington trade modeling approach representing SRM with trade costs incorporated, referred to hereafter as the reference scenario (E0) (see Table 1). Note that the same GCAM baseline was used for all experiments. This GCAM baseline projects future agricultural production and consumption, land use, and associated emissions to 2100 under an SSP2 backdrop of an approximately 30 percent increase in world population (peaks in the 2070s at about 9.5 billion) and a five-fold increase in world GDP, compared with 2010 (Fig. S2). Agricultural productivity is also expected to grow globally, with narrowing gaps among regions.

Table 1. Experimental design.

Descriptions of the reference (E0), alternative scenarios including trade modeling approach scenarios (E1 – E3) and a scenario testing trade parameter uncertainty (E4).

Scenario	Experiment	Description
Reference	E0: Armington with margins and tariffs	The logit based Armington trade modeling approach with calibrated parameters and international transport cost margins and tariffs are introduced into data and model. This experiment provides the updated reference projections to 2100 (5-year step).
	E1: Armington with no margins and tariffs	From the reference scenario (E0), margins and tariffs are removed in data and model.
Alternative scenarios: Different trade modeling approach	E2: HOV segmented markets	From E1, large logit parameters (30) are used in Armington to effectively simulate the HOV approach with segmented agricultural markets.
	E3: HOV integrated markets	From E2, regional agricultural productions are pushed to the international market in data and model to effectively simulate the HOV approach with fully integrated global agricultural markets.
Parameter uncertainty	E4: E0 with random draws on trade parameter	From the reference scenario (E0), trade parameters are defined as distributions and Monte Carlo simulations are conducted with 1000 random draws from regionally independent parameter distributions.

In the alternative scenarios, we investigate how gradually shifting model assumptions until they represent a full global market integration for crops affects our simulation of the global agroeconomic future and the related terrestrial emissions, relative to our logit-based Armington approach in the reference scenario. We design a set of experiments to show the incremental impact of relaxing the regional trade preferences step by step (i.e., E1 to E3 in Table 1), with E3 essentially mimicking an IWM HOV approach. First, we remove trade costs in scenario E1. Second, we collapse preferences for domestic and international goods in scenario E2 using very large logit parameter values (i.e., 30 as discussed in Section 2) to effectively model goods produced in different countries as perfect substitutes, per the HOV approach. Third, we simulate HOV with IWM in scenario E3, by removing regional markets in the model to force regions to export all production to the international market, which is also the only source of consumption, such that there is only one global market for each commodity and only net trade flows can be provided.

By comparing across scenarios E0 – E3, we can isolate and quantify (1) impacts from the inclusion or exclusion of trade costs (E1 vs. E0), (2) impacts from product differentiation in consumer preferences based on origin (HOV in E2 vs. Armington in E1), and (3) impacts from the global trade market structure or economic geography (i.e., net trade from an IWM in E3 vs. gross trade from an SRM in E2) on the projected global agriculture and land use future.

Lastly, we conduct two complementary sets of model parameter sensitivity analyses. The first is a set of Monte Carlo simulations to test the sensitivity of key trade parameters (E4 in Table 1). Note that parameter sensitivity is only tested using the reference scenario (E0) since there are no trade parameters in the HOV approach. Previous tests of trade parameter sensitivity in the literature have assumed perfectly correlated parameter distributions across all regions. In our study, as an exploratory sensitivity test, we allow different regional trade parameters by using independent regional trade parameter distributions in the Monte Carlo simulations. Input trade parameter distributions are constructed based on information and formulae from previous studies (see details in SI section S2.3). But, crucially, each region is given its own parameter distribution in our analysis, which differs from previous work and allows us to consider the relative importance of trade parameters in specific regions of the world.

In addition to Monte Carlo simulations from random trials, we also add two additional extreme parameter scenarios using identical trade parameters across regions of the mean ± 2 times the standard deviation. These are included to quantify the bounds of the range of potential outcomes, articulating what is possible in the model if it is “pushed” strongly in one direction or the other. This is not an insight that can be gained from Monte Carlo simulation since, in a given Monte Carlo simulation, it is unlikely that all regions will draw extreme parameters from the same end of their distributions all at once, particularly when independent distributions are used. It is therefore unlikely that the Monte Carlo simulation will articulate the full range of possible model outcomes. By examining sensitivity through both the lenses of Monte Carlo simulation and extreme parameter scenarios, we offer both a set of bounds and a probabilistic distribution of more and less likely modeling outcomes. Both are informative for future modeling of trade and together provide a more holistic understanding of model sensitivity with respect to trade parameters.

4. Results

In this section, we describe the results of our experiments. We first provide a brief overview of the results from the reference scenario (E0), which uses our novel logit-based Armington approach. We then demonstrate how this projection is altered by the introduction of the various components of full global crop market integration in scenarios E1, E2, and E3. Following this comparison, we examine the sensitivity of these projections to the values of our logit-based Armington trade parameters. One would expect alteration of agricultural trade assumptions to primarily impact agricultural market projections, and so we review these impacts first. However, international trade of crops can also be viewed as virtually trading the land used in crop production (Würtenberger et al., 2006). Thus, changes in future crop trade patterns driven by changes in trade modeling assumptions will have a direct impact on the estimates of regional land use and related emissions. Therefore, we review these impacts as well.

4.1. Overview of the logit-based Armington agroeconomic projections in E0

In order to establish a reference point for the results reviewed in Section 4.2, we first consider the scenario E0 projections in isolation. In this scenario, world aggregated crop demand is estimated to increase by 45% by the end of the century relative to 2010. This is largely driven by growth in population, income, and agricultural productivity; these trends are described in Fig 3. Total world agricultural supply is projected to grow to meet this increase in demand through a 10% expansion in global harvested area and a 31% increase in global average crop yields. Over the same period, the total volume of crop trade between GCAM regions increases by 70%. The global value of agricultural crop trade increases by 41%, as shown in Fig. 4. Notably though, Fig. 4 also demonstrates that the general pattern in gross trade value does not change dramatically between 2010 and 2100.

Fig. 3. Projections of agroeconomics to 2100 relative to 2010 for the aggregated world in the reference scenario (E0).

Results are presented as percent change relative to 2010 for variables including agricultural crop harvested area (a), price (b), producer production (c), consumption (d), export (e), import (f), and yield (g) by crops (distinguished by color). Shadows denote full ranges of results across crops (i.e., coarse grains, wheat, rice, oil crops, and other crops) in a region. The boxplots present the mean values (points), the median values (lines), the first and third quartiles (boxes), and the full ranges (whiskers) across crops in a region in 2100. Note that export (e) and import (f) are identical besides the axis scales since world export equals world import in volume. The full distribution of the results across GCAM crop-region and the summary statistics of the world level results are presented in Fig. S6 and Table S6, respectively. Data source: GCAM simulation results

Fig. 4. Projections of gross agricultural crop trade value flows in the reference scenario (E0).

Crop trade value flows measured in producer prices in 2010 billion dollars are provided for 2010 (a) and 2100 (b). Note that the scales are different in each diagram. Each tick mark represents 6 billion dollars in Fig. 4a and 8 billion dollars in Fig. 4b. The international transportation costs and tariffs are not included to maintain value balance in the results presentation.

The global results in scenario E0 mask considerable variation across crops and regions. For example, In Fig. 5 China and Western Africa demonstrate two extremes in the global distribution of results. The disparity in projections between these two regions is mainly driven by differences in the socioeconomic trends throughout the 21^st century projected by SSP2. Projected rapid growth in population and income in Western Africa leads to a considerable increase in the production, harvested area, and net import of crops by 2100. In contrast, even with growing income and crop yields, decreasing population after the 2030s drives decreases in Chinese crop production and harvested area by 2100. China is also projected to become a net exporter of rice, wheat, and other crops in the second half of the century. As a result of these divergent trends in trade position, we will show in Section 4.2 that altering our assumptions about trade creates very different effects in Western Africa than it does in China.

Fig. 5. Projections of regional agricultural economics to 2100 relative to 2010 for China and Western Africa in the reference scenario (E0).

Results are presented as percent change relative to 2010 for variables including agricultural crop harvested area (a), producer price (b), production (c), consumption (d), export (e), import (f), net trade (g), and yield (h) for China (dotted curves) and Western Africa (Solid curves) by crops (distinguished by color). Shadows denote full ranges of results across crops (i.e., coarse grains, wheat, rice, oil crops, and other crops) in a region. The boxplots to the right of each plot present the mean values (points), the median values (lines), the first and third quartiles (boxes), and the full ranges (whiskers) across crops in a region in 2100.

Cropland expands over the 21^st century to provide greater volumes of food, feed, fiber, and energy to a larger and wealthier global population (Fig. 6). This expansion peaks in the 2070s and decreases thereafter as crop yields continue to improve while the pace of population and income growth simultaneously weaken. Cropland and land use for bioenergy crops expand at the expense of forest, pasture, grassland, and other natural lands, which consequently causes emissions from carbon stored in soil and natural vegetation. LUC emissions continue to rise along with cropland use through the 2070s, with cumulative emissions between 2010 and 2070 of 17 Gt C. As cropland declines thereafter and carbon begins to re-sequester in forests, grasslands, etc., cumulative emissions between 2010 and 2100 are somewhat less, about 14 Gt C. LUC impacts are spatially heterogeneous in our results, owing to regional differences in cropland and biomass expansion, sources of the land being converted, and emission intensities of the land sources. These details and other additional results from scenario E0 projections are discussed in SI Section S3.1.

Fig. 6. Projections of land use change and emissions to 2100 relative to 2010 in the reference scenario (E0).

Results are presented for land use change decomposed by land type (a), harvested area change decomposed by crop (b), cumulative land use change emissions decomposed by land type (c), and by region (d). Note that biomass (dedicated bioenergy crop) is separated from cropland in the presentation of the results.

4.2. Impacts from market integration assumptions

In this section, we compare results from scenario E0, which uses the logit-based Armington trade theory and an SRM market structure with trade costs, to results from scenarios that gradually relax these regional trade assumptions towards an integrated world market structure that reflects an IWM HOV approach.

Fig. 7 presents a step-by-step comparison of projected 2100 net agricultural crop trade value flows for each GCAM region as we progress through the procedure of shifting from regional segmented market assumptions to global market integration assumptions. Net trade flows (i.e., total net export equals total net import) are used for consistent comparison since the scenario with IWM can only generate net trade flows. The results indicate that, with a full global market integration assumption (Fig. 7d), the projected global total net traded crop value in 2100 would increase by 254% from $140 to $495 billion (in 2010$) relative to scenario E0 (Fig. 7a). Decomposing this effect into its constituent parts, removing trade costs in scenario E1 increases trade value by a modest 2% or $3 billion, relative to E0. Removing product differentiation in scenario E2 (Fig 7b) leads to an additional 39% increase ($56 billion). Easing economic geography by assuming an IWM in scenario E3 (Fig 7c) leads to another 148% increase ($296 billion). If we decompose these changes using a log linearization method to isolate the contributions to the change in world trade value, the share of the impacts from the various sources of market integration would be 2% from E1, 26% from E2, and 72% from E3. In general, we find that including both economic geography and product differentiation in the model contributes to a significantly smaller global volume of trade in scenario E0 relative to E3, because regions are less accessible to international markets.

Fig. 7. Step-by-step decompostition of the full global market integration impact on net agricultural crop trade value flows projections in 2100.

Net crop trade value flows measured in producer prices in 2010 billion dollars are shown for 2100 for the reference projection (a), impacts from homogeneous product modeling in HOV (b), impacts from neglecting economic geography in IWM (c), and impacts from assuming full global market integration. Positive bars represent net exporting and negative bars represent net importing. Note that regional impacts from removing margins and tariffs (E1 – E0) were negligible and are not presented. See Table S7 for detailed regional and world level data and SI Section S3.2 for additional discussions.

The impacts of product differentiation and easing economic geography on trade patterns are also significant and are heterogeneous across regions. In most regions, we observe a substantial expansion of trade when markets become more integrated. For example, in 2100, the net crop trade (export) value for China increases from $18 billion in E0 to $239 billion in E3. In Western Africa, in 2100, net crop trade (import) value increases from $2 billion to $133 billion (Fig. 7 & Table S7). Conversely, we observe reduced trade flows from several other regions (e.g., Brazil, Canada, and Southeast Asia). These reductions in trade flow in some regions appear to be driven, at least to some extent, by shuffling exports from one region to another. For example, relative to E0, scenario E3 projects reductions in the export of rapeseed from Canada and rice from Southeast Asia by the end of the century, mainly driven by increased exports of these commodities from China. We can surmise, therefore, that greater global market integration may not necessarily lead to an increased volume of trade for all regions.

In response to impacts on regional trade patterns, agricultural market equilibria in each region adjust accordingly. For example, in scenarios E2 and E3, China sees an increase in demand for agricultural commodity exports, which encourages an expansion of Chinese crop production and harvested area, while also moderately reducing domestic consumption toward the end of the century due to higher domestic prices (Fig. S19). Conversely, as Western Africa sources more products from the international markets under the homogeneous preferences and integrated market assumptions of scenarios E2 and E3, respectively, the impacts on agricultural markets in Western Africa (Fig. S20) are mostly in the opposite directions to China.

The full global market integration assumption impacts the global average projection of future agricultural markets less than most regional projections on a percentage basis (Figs. S18-S24). This is mainly because the strong but heterogeneous impacts on regional results offset each other in the global results. Fig. 8 shows the wide range of agricultural market impacts across all region-crop pairs (i.e., USA-Corn, Brazil-Soybeans, etc.) for scenarios E1, E2, and E3 relative to E0. The wide range of outcomes for specific crop-region pairs contrasts with the relatively much smaller global average (Fig. 8) or aggregate (Fig. S18) impact. This figure mirrors a result from the AgMIP model intercomparison (von Lampe et al., 2014), where models showed closer agreement on world aggregated trade results than they did for regional results.

Fig. 8. Comparison of global agricultural economic projections across alternative scenarios relative to the reference scenario (E0).

Solid curves, dotted curves, and shadows denote mean, median, and 10 – 90 percentile ranges of results across all crop-region combinations (i.e., Wheat-India, Rice-Brazil, etc.) for scenarios E1, E2, and E3 relative to E0. The boxplots present the mean values (points), the median values (lines), the first and third quartiles (boxes), and the 10 – 90 percentile ranges (whiskers) of values in 2100.

In addition, the reallocation of global crop production, driven by more pronounced trade responses under global market integration assumptions, leads to higher world average crop productivity (+10% in E3 relative to E0). Under the E3 assumptions, crop production becomes more concentrated in the regions with the highest yields for those crops. As a result, scenario E3 requires less harvested area than E0 (−10% in 2100), and crop producer prices decline as well (−1% in 2100). Global cropland is lower in E3 as a result (115 Mha lower in 2100), and global cumulative land use change emissions are about 25% or 3.4 Gt C lower by the end of the century (Figs. 9 and 10). Decomposing cumulative LUC emissions across scenarios, we find a reduction of 0.2 Gt C from excluding trade costs in E1 vs. E0, a reduction of 1.2 Gt C from neglecting product differentiation in E2 vs. E1, and a reduction of 2.4 Gt C from ignoring economic geography in E3 vs. E2. This shift in global carbon emissions broadly corresponds in magnitude to the net impact of these methodology changes on the magnitude of global trade value flows. As with trade responses, the global market integration assumption also has mixed impacts on regional LUC emissions. The net global results in E3 relative to E0 are mainly driven by a small subset of regions with large changes in cropland, e.g., Western Africa (−4.6 Gt C), China (+2.4 Gt C), and India (−1.0 Gt C) and a subset of regions with high LUC emission intensity, e.g., Southeast Asia (−0.7 Gt C) and Brazil (+0.5 Gt C) (see Table S8 for detailed regional results). Additional discussions are provided in SI Section S3.2.

Fig. 9. Comparison of land use change across alternative scenarios relative to the reference scenario (E0).

Results shown are the land use difference between alternative scenarios and the reference scenario (Armington with margins and tariffs). Global results projected to 2100 by land type (colored bars) are presented for alternative scenarios, including Armington without margins and tariffs (a), HOV with segmented global markets structure (b), and HOV with integrated global market structure (c). The cropland use change results for cropland by 2100 are also presented at GCAM regional level for the two HOV scenarios (d – e). See Fig. S25 for results of harvested area changes and Fig. S26 for water basin level results of Fig. 9 d – e.

Fig. 10. Comparison of land use change emissions across alternative scenarios relative to the reference scenario (E0).

See scenario descreptions in Fig. 9 caption. Points represent the net total of land use change emissions from all lands (a - c). The total land use change emissions by 2100 are presented at GCAM regional level for the two HOV scenarios (d – e). See Fig. S27 for water basin level results of Fig. 10 d – e and Table S8 for regional summary statistics.

4.3. Trade parameter sensitivity

The results from the scenario E0 trade parameter sensitivity tests for regional cropland expansion and LUC emissions are presented in Fig. 11. The mean values of the output distributions from the Monte Carlo simulations are very close to deterministic result values from scenario E0. In general, regions that were more sensitive to assumptions about economic geography and product differentiation were also more sensitive to changes in the value of trade parameters, which reflect regional elasticity of price transmission between regional and international markets. The regional distributions of LUC emissions mostly mirror the regional distributions of cropland expansion, though there are some differences due to differing carbon intensity of lands across regions. For example, the Middle East and Pakistan regions show larger magnitudes of cropland sensitivity than the Indonesia and SE Asia regions. But the latter show larger magnitudes of carbon emissions sensitivity because they have much more carbon-dense land; each hectare of land converted to or from cropland in Indonesia or SE Asia has greater emissions implications than a hectare converted in the Middle East or Pakistan.

Fig. 11. Sensitivity of regional cropland change and LUC emissions by 2100 to trade parameters.

Cropland change (a) and LUC emissions (b) results are presented as the deviation relative to the deterministic reference results (E0). Regions are ranked by the sensitivity range of the LUC emissions. Dashes represent the distribution of results from one thousand sets of trade parameters randomly drawn from independent regional distributions. The red square and black triangle represent results from extreme scenarios of using uniform regional trade parameters of mean plus and minus two times of the standard deviation. See summary statistics in Table S9.

The sensitivity results indicate an uncertainty range of [−4.8, +4.8] Mha for cropland expansion and [−95, +69] Mt C for LUC emissions at the world level in 2100 due to trade parameter uncertainty. These ranges are small compared to the differences in cropland expansion and LUC emissions seen from assuming full market integration, described in Section 4.2 (cropland expansion uncertainty is [−4 %, 4%] of the E3-E0 change in cropland expansion, and LUC emissions are [−3%, 2%] of the E3-E0 change in LUC emissions). As with many of the other results presented in this work, since regional results have responses of different signs and offset each other globally to some extent, world total sensitivity results mask relatively higher regional sensitivity, particularly in percentage terms.

For most regions, modeled cropland expansion or LUC emissions results from extreme parameter value scenarios are also extremes in the output distributions, but there are exceptions (as among them, the SE Asia and USA regions) (Fig. 11). We conducted regression analysis using the cropland expansion results from the Monte Carlo simulation to explore the interdependencies in the regional trade responses (see SI Section S3.3). The results of this analysis demonstrate that the sensitivity of cropland expansion to the region- and crop-specific trade parameters may vary significantly by region. We find that results for the volume of export flows and cropland expansion in major crop exporting regions, such as SE Asia and the USA, are more sensitive to the trade parameter values of their importing partners. By contrast, the responses of trade flows and cropland expansion for Western Africa, China, and other regions that are not major crop exporters, are more sensitive to their own regional trade parameters.

5. Discussion and implications

5.1. Global market integration

Global agricultural markets are likely more integrated today than at any point in history, and the volume of agricultural trade continues to increase with integration (Costinot and Donaldson, 2016). Nevertheless, global agricultural markets remain far from fully integrated. The historical validation experiments conducted in Hertel and Baldos (2016) for the period from 1961 to 2006 using an SRM Armington trade specification reproduced historical regional agricultural production with greater accuracy compared to the same model using IWM assumptions. While future trade patterns may look quite different from even recent history, this work suggests that assuming an IWM modeling structure is likely to project larger and more volatile volumes of trade than assuming an SRM modeling structure. Empirical studies have demonstrated that both consumer preference and economic geography play critical roles in explaining persistent historical trade patterns (Hillberry et al., 2005; Villoria and Hertel, 2011). Thus, incorporating SRM with heterogeneous preferences into GCAM implements a method that may reproduce historical observations better than the assumption of HOV with IWM, while also retaining the capability to alter these market integration or segmentation assumptions to consider possible alternative futures.

Studying alternative scenarios of full global agricultural market integration, while notably different from today’s trade reality, can be valuable. Such scenarios provide important counterpoints to the segmented agricultural markets implied by history. They also depict what agricultural markets might look like if subjected to the kind of integration which has been observed in some other, more highly-globalized markets like crude oil and electronics (Hertel and Baldos, 2016; Hertel et al., 2014). More importantly, such experiments cast light on the sensitivity of global and regional environmental modeling results (e.g., for land use change and associated emissions) to assumptions about agricultural trade, which offers important implications for researchers and model intercomparison in particular.

5.2. Implications for model intercomparison

As noted earlier, long-term agroeconomic projections produced under AgMIP have shown considerable variability in regional results across models. Results from our study cannot be directly compared with AgMIP results due to the inconsistencies in base year, spatial resolution, and detailed trade modeling specifications (e.g., bilateral vs. gross and CES vs. logit). However, our study implies that regional agroeconomic projections are highly sensitive to trade modeling assumptions. Therefore, echoing Ahammad et al. (2015) and Schmitz et al. (2014), differences in the trade modeling approaches across AgMIP models could play a key role in explaining the variation in regional results across models. For example, Schmitz et al. (2014) demonstrated that models with stronger assumptions of global market integration (e.g., HOV or IWM) generally showed lower projections of cropland expansion in Africa and the Middle East (AME) in the AgMIP reference scenario (SSP2). Similarly, our study quantitively demonstrates that, from the same scenario, global market integration assumptions can result in lower cropland expansion projections in the AME regions. Additional model intercomparison implications are discussed in SI Section S3.4.

5.3. Limitations and future studies

In our study, we develop a logit-based Armington trade modeling framework in a way that could support bilateral trade modeling. However, we have aggregated bilateral trade flows to a global market in this work mainly due to concerns of the extensive margin and the missing globalization issues. Had we modeled trade bilaterally in this work, our GCAM scenarios would have been unable to consider changes in trade partnerships, and bilateral trade response with fixed preference parameters would have been structurally rigid. For long-term modeling, it is critical to maintaining flexibility in trading relationships in scenario analysis. Nevertheless, an important limitation is that, without bilateral trade flows, gross trade modeling cannot evaluate trade policies that are bilaterally specified, e.g., an EU palm oil ban from regions with high deforestation risks. Future work should extend the logit-based Armington framework to model trade bilaterally, with carefully designed future trade scenarios, e.g., market integration scenarios of preference bias erosion (Liu et al., 2004) by shocking bilateral preference parameters (i.e., T_ni in Equation 5). In the context of long run models like GCAM, the ability to consider trading relationships outside of the historical sample remains a significant unanswered question. Future work should also consider how this may be overcome within an Armington trade framework.

In our results, assuming integrated world markets, particularly in the form of homogeneous consumer preferences and easing economic geography, leads to larger variations in regional terrestrial carbon emissions but lower global total terrestrial carbon emissions relative to assuming segmented regional markets. However, the results we have presented are best understood within the specific context of the SSP2 socioeconomic assumptions made in our scenarios. It is possible that alternative assumptions about future underlying socioeconomic conditions (e.g., by assuming a different SSP) may lead to different results. Future work could examine this possibility. Future investigations are also needed to dynamically study the economic and environmental consequences of potential future shocks that promote broader global market and economic integration, such as weakening product heterogeneity by sources, global technology dispersions, further removal of trade barriers, and increasing trade partnerships (Costinot and Donaldson, 2016; Donaldson, 2015).

Our results imply that harmonization in trade modeling approaches and parameters would likely increase the convergence of regional results among models in model intercomparison studies. However, there are also many other drivers of the differences in regional results across models, such as data, model structure, and the magnitude of supply and demand response (Robinson et al., 2014; Schmitz et al., 2014; von Lampe et al., 2014). Further study is needed to quantify the impacts of modeling differences on future agroeconomics projection.

Our results also indicate that assumptions about the state and magnitude of market integration (e.g., product differentiation and economic geography) matter in future regional agroeconomics projections. The resolution of regional economic modeling also matters as intraregional trade responses are muted when regions and sectors are highly aggregated (Donaldson, 2015). These aspects of regional economic and trade modeling require further exploration. Models with a subnational resolution, such as GCAM-USA or GCAM-China (Yu et al., 2014; Zhou et al., 2014), may be useful in such work. In addition to growth in existing trade flows, trade partnerships will change, and intraregional trade may expand as a result of future global market integration or agricultural adaptation (Costinot et al., 2016). All of these remain areas of potential future work.

The Monte Carlo simulations conducted for trade parameters demonstrate the need for caution when studying the sensitivity of an aggregated result to regional trade parameters, particularly when regional responses are heterogeneous and nonlinear. Our study focused on a reference agroeconomic projection with shocks (socioeconomic or technological) in all regions. Model results could be more sensitive to trade parameters when studying alternative scenarios focusing on regional shocks (e.g., regional agricultural policies) (Plevin et al., 2015). However, we had limited data from which to differentiate distributions of trade parameters across regions. Future studies are needed to improve the estimates of regional trade elasticities (Olekseyuk and Schürenberg-Frosch, 2016), to consider alternative estimates based on physical trade quantity data (Ferguson and Smith, 2021), and also to test sensitivity for a broader range of factors and parameters. For example, regional terrestrial carbon emissions could also be sensitive to several other assumptions or parameters, such as land supply elasticity, yield intensification responses, and emission factors (Plevin et al., 2015; Taheripour et al., 2017).

6. Conclusion

In this paper, we have developed a trade modeling framework using a logit-based Armington trade modeling approach with segmented regional markets (SRM) and introduced it into GCAM. The framework is able to consider product differentiation by origin (through heterogeneity in consumer preference), economic geography, and trade costs, and allows GCAM to model regional trade responses in a more flexible manner. We studied the sensitivity of GCAM projections of future agroeconomic outcomes, land use, and terrestrial carbon emissions to assumptions about the state and magnitude of global market integration. Our results demonstrate that the assumption of full global market integration may lead to significant differences in model results for cropland use (-115 million hectares) and terrestrial carbon fluxes (-25%) by the end of the century, compared to assuming segmented regional markets. These results were highly heterogeneous across regions; regions with more pronounced net export responses generally had more pronounced changes in cropland expansion and LUC emissions as well.

The contributions of this paper are threefold. First, the logit-based Armington trade modeling framework developed in this paper offers a probabilistic view of heterogeneity in consumer preference. Second, it demonstrates notable sensitivity of future agroeconomic outcomes and terrestrial carbon emissions projections to trade modeling assumptions around product differentiation, economic geography, and parameter use. Third, the results from the paper enhance our understanding of trade modeling differences in the literature and provide important implications for model intercomparison tasks. Our results imply that closer harmonization of trade modeling approaches and trade parameter values would likely increase regional convergence in model intercomparison tasks. In addition, we highlighted future research needs for improving the modeling of the extensive trade margins and estimating parameters for regional trade responses.

Highlights.

• We develop a logit-based Armington trade modeling method and apply it to GCAM.

• We study the impacts of global market integration assumptions on future projections.

• Agroeconomics projections are sensitive to trade modeling methods and parameters.

• China and Africa are the most sensitive regions to global market integration.

• Ignoring product differentiation and economic geography affects LUC estimations.

Data and code statement

Data used in this paper were from GCAM data system or simulation results. Both the core GCAM model and data system are publicly available (github.com/jgcri/gcam-core). A repository of the version of the model (GCAM-T-2020-v1.0), main results, and the R code for generating main figures are available https://zenodo.org/record/5673427#.YwyfVxzMLws.