2.1 Overview

We developed a spatial price equilibrium model that simulates demand, supply, producer and consumer prices, and trade flows across 177 countries. Our model relies on standard datasets of yield, supply, demand and trade, and upon a food production and trade cost dataset constructed in previous research [36–38]. We considered four crops – maize, wheat, rice, soybeans – as they are strongly affected by the different shocks we modeled [34] and because of their importance for global food and feed consumption.

All key model parameters (involving yield, supply, demand, trade) were averaged over the period 2017–2021, our reference period, which we used for our model calibration. This specific time frame was chosen to exclude the effects of the food shocks that emerged from 2022 onward and because the necessary data for several of the cost components used in our model were only fully available for these years. Using a different period would introduce inconsistencies in our calibration procedure. We note that while this period overlaps with the COVID-19 pandemic, the data used for calibration is not greatly impacted by this event, given the averaging across non-COVID-19 years and because the demand and supply of cereals during the COVID-19 were still relatively stable [39]. The five-year averaging period was chosen to smooth year-to-year variations, as is common practice in general equilibrium modelling [40], because it is a good compromise between system representativeness and being able to smooth out interannual yield variability and external shocks. A longer period would have affected the consistency of our calibration, as mentioned above, while a shorter period would have been more susceptible to bias from events such as El Niño or the COVID-19 pandemic.

Our model can be considered a “one-time exogenous shock model” [4]. In other words, it is designed to explore the short-run impacts of a (hypothetical) shock whose impacts occur within a single year in which planting decisions have largely been made, leading to an inelastic supply. In this scenario of inelastic supply, countries can only respond by utilizing grain stocks, withholding exports, adjusting imports from existing suppliers and, at a cost, diversifying their trading partners.

We provide here a brief overview of the methodology in four subsections: (i) the spatial price equilibrium model, (ii) the implementation of the various shocks into the model, (iii) an overview of the factors determining the coping capacity of different countries, and (iv) the impact metrics we employ. Further details are provided in the Supporting Information.

2.2 Global spatial price equilibrium model

Our newly developed spatial price equilibrium model (SPEM) captures producer and consumer prices, supply, demand and trade flows. A SPEM is a multi-region partial equilibrium model that links producers and consumers across geographies [41]. The cost of trade sums all expenses incurred post farm gate including storage, within-country transportation, border and custom compliance, maritime transport, intermodal transfers, port fees, and import tariffs. These trade cost components have been derived separately in our previous work [38] which explored how trade costs contribute to the landed cost of grains, across crops and countries.

The benefits of a SPEM are fourfold. First, it explicitly captures bilateral trade flows, which are absent in most global food systems models. Second, it allows for trade substitution and the establishment of new trading partners. Third, it captures directional trade flows, meaning that countries can both import and export the same product. Fourth, it allows different types of shocks to be modeled, including price shocks, supply shocks, and trade shocks (e.g., tariffs, trade bans). SPEMs are usually constructed to address medium to long term questions such as the response of an economy to changing trade tariffs or demand patterns [40,42]. Here, we have adjusted the standard SPEM formulation to make it suitable for studying more short-term, typically one-off shocks (see Supporting Information). We have also incorporated commodity stock levels in the modelling framework, as these are essential to understand supply shortages in the short-term but are usually omitted in studies with a longer time horizon.

In our model, the decision to supply grain commodities from certain regions is purely based on differentials in the total landed cost of the goods (that is the cost to produce crops and ship them to consumers). However, there are real-world non-cost elements which influence where countries export to, and from where countries source imports. Hence, the model needs to be calibrated using existing trade data to capture these factors and create a representative cost chain for the trade network underpinning our reference period [40,43]. The model was calibrated to reproduce observed trade flows in our reference period (2017–2021) given the previous time period (averaged over 2012–2016) as a starting point (see Validation in S2 Text). This process yielded a calibration constant for each bilateral trade relationship, representing ‘shadow trade costs’ within the current trade network. Given that we imposed shocks to our reference food system, only one calibration constant is required instead of a multi-period calibration procedure. Moreover, only our reference trade system can be realistically calibrated, given that we do not have historical data on agricultural tariffs, production structures and costs, and transport connectivity and related costs.

In our model, countries have interconnected competitive markets between which there are directional trade flows in homogeneous goods. Producers in each country have a fixed amount of the good to supply to the market (either domestic or foreign), which is determined by that year’s harvest and which they sell at the highest possible price. However, countries can utilize their stocks to bridge supply deficits, following their supply curve. Consumers have elastic demand for food commodities which they buy at the lowest possible price (following their demand curve). At equilibrium, we can find the trade flows between countries that determine the producer and consumer prices. For each country, the total production, stocks utilized and imports must match the total consumption and export at equilibrium.

The SPEM model thus required data on trade, transport and trade costs, stocks, prices, supply and demand, and information on the shape of the demand and supply curves (the demand and supply elasticities). We included 177 countries for which we could collect all the data required and provide an overview of the data sources in S1 Table. In the S1 Text, we describe the trade cost formulation used, the model set-up and the calibration process. A separate SPEM was constructed for each of the four crops, without considering any cross-grain substitution effects.

2.3 Shock implementation

Four shock scenarios were superimposed on a “weather-only” baseline scenario. It is important to clarify that our study used shocks that are motivated by the events of 2022–2023, rather than attempting to precisely reproduce the effects of these specific events. Instead, the main goal of this study is to explore the resilience of the food system to plausible and representative shocks against a wide range of simulated weather outcomes. Reproducing historical events would require more granular inputs than adopted in this paper. Below, we describe the different scenarios, with further details provided in the S1 Text.

Baseline “weather-only” scenario: Food production is influenced by year-to-year weather variations. Therefore, the impact of any additional shock depends upon the coincident weather in the year in which it occurs. To comprehensively analyze weather-related variability in food production, a baseline was adopted that incorporates weather variations from 54 years of observed global meteorological data, which was fed in a calibrated crop model [44]. For each grid cell, this resulted in a probabilistic yield realization based on past observed weather conditions. It should be emphasized that the resulting yield distribution should be interpreted as plausible variations in production based on historical weather, and not a historical reconstruction reflecting changes in productivity, harvest area and other factors [44]. Modeled grid-level crop yields were aggregated to country level to derive 54 samples of national crop yield (and hence production). Linear regression was used to filter out trends in the data and derive annual production deviations from the mean. These deviations were then added to the calibrated supply as input to the trade model (see S1 Text), after which the model equilibrium was re-evaluated.

Ukraine war scenario: For this scenario, three adjustments to the baseline model were added. First, the food supply from Ukraine was lowered to 60% of its baseline, in line with observed reductions in 2022/2023 [45]. Second, the trade costs of all food trade to and from Russia was increased by 50% to represent a surge in insurance costs for trade with Russia and rerouting costs given disruptions in Black Sea trade. Third, the effects of the blockage of Black Sea ports were modeled by doubling [46] the costs of trade from Ukraine to any non-European country. This captured the difficulty of sourcing Ukraine exports via sea and the additional costs to reroute goods via rail to alternative European ports.

Price shock scenario: In this scenario, a price shock was introduced to capture the increase in fertilizer, pesticide and diesel costs that occurred due to the energy crisis after Russia’s invasion of Ukraine as well other supply issues over the last few years. We follow a similar methodology to that in our previous work [38] and estimated for every country the share of fertilizer, pesticide and diesel costs to total production costs. An input price shock was imposed in the model, increasing fertilizer costs by 200% and diesel costs and pesticide costs by 100% (see S2 Table). This input price shock was assumed to be passed on to consumers via an equivalent increase in producer prices (see S1 Text).

Trade bans scenario. In the trade ban scenario, the impacts of trade restrictions were evaluated in a similar way to those implemented by countries between 2022 and 2023. To do so, the Global Trade Alert (GTA) database (https://www.globaltradealert.org/) was utilized, which is considered the most comprehensive database on Non-Tariff Measures (NTM) available. The GTA database is constructed using an automated data collection system described in Evenett et al. [47,48]. The GTA database covers which countries imposed trade restrictions, which countries were affected by them, and for which commodities these restrictions were applied. Information on all implemented import and export trade bans (hereafter trade bans) was extracted for the four crops considered, and subsequently encoded in the model by preventing trade between the countries affected.

All “compound” shock scenario. In the compound shock scenario (“All”), all three shocks were implemented simultaneously on top of our “weather only” baseline.

2.4 Coping capacity indicators

There is a long-standing debate about the factors that determine a country’s food system resilience, i.e., the factors that shape a country’s capacity to cope and respond to shocks [17], including the role of trade [9,20]. A variety of indicators have been proposed to measure the coping capacity of countries. Here we considered five of these:

• Import dependency (ID) measures the percentage of consumption (production + imports – exports) derived from imports [17,27]. Higher ID makes countries vulnerable to shocks elsewhere, but reduces the impacts of domestic yield fluctuations (S1 Fig).
• Supply diversification, measured by the Herfindahl-Hirschman Index (HHI) which is an estimate of the degree to which supply is concentrated in a restricted number of countries (including from domestic production) [17,49]. Countries with larger supply diversification, so a lower HHI, can more easily substitute supply but are also more exposed to a greater number of shocks (42).
• The stocks-to-use ratio (S-t-U) measures the availability of stocks that can be used to meet shortfalls in supply and address domestic demand [18,29,50] (S3 Fig).
• The export-to-production ratio (E-t-P) is a proxy for a country’s ability to withhold exports to meet shortfalls in domestic supply or withhold exports to lower domestic prices [17] (S4 Fig).
• The demand elasticity (DE) of countries determines its willingness to forego consumption if prices increase, and vice versa [18,51]. This is determined by a country’s dietary preferences and GDP, among other factors (S5 Fig).

We tested the relationship between these coping capacity indicators and the impacts as a result of the shocks modeled (see Section 2.5).

2.5 Impact metrics

Food system resilience in this study is measured in terms of fluctuations in consumer surplus. The consumer surplus is a measure of welfare that captures the difference between consumers’ willingness to pay for a given quantity of food and the price they actually have to pay. It has been used as an impact metric in a number of other studies of exogenous food system shocks [52–54]. Changes in consumer surplus track welfare impacts of price changes impacting both expenditure and consumption. A country’s food system resilience can thus be defined as the ability to buffer impacts to its consumer surplus given the shocks imposed nationally and internationally.

Apart from country-level impacts, we also evaluated the globally systemic impacts of specific shock scenarios. We measured the globally systemic impacts as the simultaneous negative consumer surplus experienced across countries for a given shock scenario. A negative consumer surplus measures the deviation in consumer surplus for a certain weather realization compared to the mean consumer surplus experienced across the 54 weather years in the Baseline scenario. The global systemic impact is thus defined as the total number of countries experiencing a negative consumer surplus and the total cumulative negative consumer surplus across countries.

To explore how coping capacity, as measured by the different indicators (Section 2.4), influences a country’s food system resilience, the relationship between the cross-country differences in the coping capacity indices and the modeled deviations in consumer surplus was evaluated. To do so, the severity of consumer surplus impacts per country were ranked across the stochastic shock scenarios (from 1 to 54). Then, the Spearman rank correlations between the modeled impacts and the five coping capacity indicators were evaluated. A non-parametric statistic was more appropriate than a standard Pearson correlation as the data was ordinal and to capture the potential non-linear relationship.

3.1 The influence of weather on yields and hence consumer prices

We investigated the effects of typical patterns of weather fluctuations on domestic and foreign prices using 54 instances of annual weather data (Baseline scenario). In Fig 1 we show price volatility and average consumer prices for this scenario, for all four crops combined (Fig 1A) and for each crop separately (Fig 1B-1E). In S6-S7 Figs, we provide further information on fluctuations in supply and the degree to which domestic price fluctuations are influenced by global price fluctuations.

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Fig 1. Risk profile of consumer prices related to climate-driven yield variations (A) Bivariate plot of the mean consumer price averaged across the 54 yield years, and the coefficient of variation (COV) of consumer prices over the same period across all four crops (weighted average), all under the baseline scenario. (B-E) Show the same as (A) but for Maize (B), Wheat (C), Rice (D) and Soybean (E) specifically. Darker red colors indicate that the price variability is high, but consumer prices low. Darker gold colors indicate that price variability is low, but prices are high. Black colors indicate that both are high. The basemap is from Global Administrative Areas project (gadm.org).

https://doi.org/10.1371/journal.pclm.0000825.g001

Despite weather-related variations in crop yield, most of Europe and North Africa exhibit low prices and low volatility, due to the deep and diverse grain markets operating in these regions. Regions with high production serving predominantly domestic markets (Central Asia, Eastern Europe, Australia, South Africa) have low prices but relatively high volatility, as domestic food prices are very sensitive to weather-related variation in domestic production (see S6 Fig). In contrast, some large importers (China, Bolivia, the Middle East and Sub-Saharan countries) have higher average prices because they are subject to large transport costs, but lower volatility because they can diversify across several food-producing trade partners. Countries in Sub-Saharan Africa face both high consumer prices and high volatility. This is caused by high transport costs [38], a dependence on suppliers whose production is highly variable (S6 Fig), and an isolation from global markets that prevents countries from buffering yield shocks (S7 Fig).

There are interesting differences between the four crops (Fig 1B-1E). For maize, low consumer prices and price fluctuations are predicted in Northern Africa (because of large and quite stable domestic supply) and in Eastern and Central Europe due to their proximity to major maize suppliers in Europe. In contrast, high transportation costs and reliance on variable production (AS6) leads to high prices and high price variability in most Sub-Saharan African countries and landlocked South America. For wheat, high import-dependency leads to high consumer prices in most of Africa, yet results in relatively stable supplies and prices due to imports from a diversity of countries (Eastern Europe, North America, Latin America and Western Europe). On the other hand, large wheat producers in South America, Eastern Europe and Central Asia are among the lowest cost producers, yet are subject to price fluctuations induced by production variability (see S6 Fig) For rice, lower consumer prices are experienced in parts of Latin America, Central Asia, and South Asia and South-East Asia, due to relatively low-cost production for domestic markets. Low price variability is found in Western Europe and North America because of stable imports from rice producing countries (S6 Fig). Soybean patterns are dominated by high prices and high price variability in most of Africa, East and South-East Asia, due to their reliance on soybean imports from Latin America where production volumes are quite sensitive to the weather (more so in Argentina than Brazil).

3.2 The impacts of compound shocks

The shocks to the global grain supply that we modeled affect consumer prices, leading to a loss in consumer surplus (see S8 Fig). When the compound shock (All scenario) is superimposed on weather-related production variability, it causes a median (taken across years with different weather) increase in global consumer price (weighted by demand) of 22.6% for soybean, 40.1% for maize, 47.8% for rice, and 51.5% for wheat. This results in a reduction of median global consumption of 4.4% for soybean, 4.1% for maize, 4.5% for rice, and 8.9% for wheat. Taken together, the compound shock reduces median global consumer surplus by 8.2% for soybean, 7.3% for maize, 7.9% for rice and 16.5% for wheat (S8 Fig). These reductions reflect the impact of food prices on domestic budgets and the food consumption of these crops that would be foregone because food is less affordable.

The drivers of consumer surplus losses differ across regions (Fig 2, equivalent plots for consumer prices and consumption are given in S9-S12 Fig and S13-S16 Fig, respectively). For maize, the energy price shock has the greatest effect in most regions, and is particularly severe for Central Asia, Oceania, and Sub-Saharan Africa where consumer prices rise by 50–100% (S9 Fig). For wheat, the energy price shock is also dominant, except in Eastern Europe (mainly Ukraine and Russia) where the supply shock associated with the Ukraine war is more important. The widespread effects of energy price shocks reflect the ubiquitous dependence of agriculture on fuel. Trade bans are predicted to have a large impact on wheat prices in Central Asia (due to export bans imposed by Russia, Kyrgyzstan, and India) and Oceania (largely due to an Indian trade ban). The latter has a knock-on effect on increased demand for wheat from Australia, which raises consumer prices locally, a dynamic that was also observed in 2022 [55].

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Fig 2. Regional impact of shocks to consumer surplus.

(A) Median deviation (across the 54 events) of the normalized total consumer surplus (CS) under the various shock scenarios compared to the average regional consumer surplus for the baseline scenario (across the 54 events). (B-E) Show the same results but for the crop-specific CS. See S3 Table for a classification of the regions. A low fraction indicates a more severe impact on consumer surplus.

https://doi.org/10.1371/journal.pclm.0000825.g002

For rice, the consumer surplus in Sub-Saharan Africa, East Asia, Central Asia, Western Asia, and Eastern Europe was found to be severely impacted by trade restrictions, particularly a rice export ban imposed by India. The same ban results in a reduction in domestic prices and so positively impacts domestic Indian consumer surplus, a response observed after India restricted rice exports in 2023 [56]. Consumer surpluses for rice in Central Asia are extremely sensitive to the different shocks. This can be explained by a combination of high weather-related production volatility in the region, combined with dependencies on trade from South Asia (affected by trade restrictions) and Eastern Europe (affected by the Ukraine war). Soybean consumer surpluses are most influenced by the energy price shock which is felt relatively uniformly across all regions.

Our country-level analysis (S17 Fig) further shows that, especially for wheat and rice, countries within the same region can be affected in quite different ways by the shocks, something that could not be studied using a more aggregated (regional) model.

3.3 Global systemic impact

Local or regional production shocks can give rise to systemic impacts that are felt everywhere because of the interconnected global food supply network. This may happen when shocks occur simultaneously (e.g., multiple breadbasket failures) or when a local shock is of such magnitude that it has global ramifications. To illustrate the potential worst case scenarios, we rank years from worst to best in terms of the cumulative negative consumer surplus (a log scale is used to highlight the effects of poor weather years) (Fig 3).

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Fig 3. Global systemic impacts of shocks.

Total amount of a negative consumer surplus (CS) during a single event (sum of all negative CS across countries). The quantiles indicates the rank of the weather year compared to the total number of weather years in our sample (N = 54), ordered by severity (rank 1 is worst case). A lower quantile indicates a higher severity event in terms of total negative consumer surplus.

https://doi.org/10.1371/journal.pclm.0000825.g003

Under the Baseline scenario (Fig 3, grey curve), the worst annual consumer surplus loss is USD90.8 billion for maize, USD31.2 billion for wheat, USD64.4 billion for rice, and USD72.3 billion for soybean. This is equivalent to a 5% reduction in consumer surplus for maize, wheat and rice, and 10–15% for soybeans (S18 Fig). When this is compounded with the All shock scenario, the episodic loss can rise to up to USD246.4 billion, USD145.6 billion, USD135.6 billion, and USD78.6 billion for maize, wheat, rice, and soybean, respectively. In relative terms, this refers to a 10–15% reduction in consumer surplus during the worst years for maize and rice, and 15 – 20% for wheat and soybeans (S18 Fig). Comparing All with the other three shock scenarios, we find that the energy price shock can explain most of the response for maize while for the other crops the different shocks all contribute to the drop in global consumer surplus. Trade restrictions for wheat and rice also cause widespread negative consumer surplus across countries. These shocks together can cause almost all countries to simultaneously experience a negative consumer surplus (S19 Fig).

What is also apparent from the results is the importance of weather-related variability as a driver of systemic risk. If the worst year represented in our weather data is compared with the median year (the 0.5 quantile), the difference in consumer surplus is in many cases larger than the additional effect of the shock scenarios. In other words, the impact of a very good harvest or breadbasket failure can be as great or greater than the additional effects of non-climatic shocks, emphasizing the importance of looking at them together.

We further test whether certain country groups are more prone to these systemic shocks than others. Small Island Developing States (SIDS), which are often import-dependent, are considered to be more vulnerable to shocks originating abroad. Our results (S20 Fig) shows that the systemic shock they face in terms of consumer surplus reduction is almost twice as high for maize and rice, but negligible for wheat and soybean. We perform the same test by grouping countries in terms of their income classification (Low and Lower Middle Income; Upper Middle Income; High Income), see S21 Fig. Here, again, crop-specific differences dominate. Upper Middle Income countries show lower impacts for wheat and rice, while Low and Lower Middle Income countries show higher systemic shock impacts for maize and soybean, but not for wheat and rice. In other words, crop-specific differences dominate specific characteristics of specific country groups, at least in our modelling framework.

3.4 Country food system resilience

A country’s food system resilience is shaped by different country characteristics that influence its coping capacity (see S1-S5 Figs for the country characteristics). Here, we test to what extent the coping indicators help explain the between-country variations in consumer surplus impacts under the Baseline scenario (S22 Fig) and All scenario (Fig 4). In particular, the HHI and ID indices measure the ability of countries to shift trade patterns, which were explicitly considered in our modelling framework as shown and discussed in S3 Text.

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Fig 4. Country coping capacity to compound shock.

(A) The Spearman rank correlation coefficient between country consumer surplus impacts and the different coping capacity indicators. (B-D) Show the same Figs but for Wheat (B), Rice (C) and Soybean (D). The quantiles indicate the rank of the shock year compared to the total number of years in our sample (N = 54), ordered by severity (event 1/54 is the worst case). ID = import dependency, HHI = the Herfindahl-Hirschman Index (HHI), S-t-U = stocks-to-use ratio, DE = demand elasticity and E-t-P = export to production ratio. All results are for the compound (All) shock scenario. A higher positive or negative coefficient indicates a stronger relationship between the coping capacity indicator and the across-country consumer surplus impacts.

https://doi.org/10.1371/journal.pclm.0000825.g004

For maize, the impacts on consumer surplus increase for countries with a higher demand elasticity, a low diversity of suppliers, and low import dependency. These countries (such as Uganda, Afghanistan and Côte d’Ivoire) have a limited ability to replace domestic supplies with imports from different sources. For wheat, a combination of having high demand elasticity, high supply concentration and low stocks-to-use ratios was found to reduce food system resilience, while the effect of import dependency is less important. This explains the large impacts of the compound shock on countries such as Zambia, Madagascar and Mongolia. For rice, supply concentration is the leading factor driving between-country variation in consumer surplus, harming the ability of countries (such as Rwanda and Burundi) with a low diversity of suppliers to cope with systemic shocks. For soybean, countries with high self-sufficiency (through low export ratios, low import dependency, and high primarily domestic concentration) and high demand elasticities are most affected (for example Brazil, Serbia and Zambia). These results underline that a combination of factors together influence the food system resilience of a country to compounding global shocks.