## Main

Approximately 11% of the world population in 2017, or 821 million people, suffered from hunger1. Undernourishment has been increasing since 2014 due to conflict, climate variability and extremes, and is most prevalent in sub-Saharan Africa (23.2% of population), the Caribbean (16.5%) and Southern Asia (14.8%)1. Climate change is projected to raise agricultural prices2 and to expose an additional 77 million people to hunger risks by 2050 (ref. 3), thereby jeopardizing the UN Sustainable Development Goal to end global hunger4. Adaptation policies to safeguard food security range from new crop varieties and climate-smart farming to reallocation of agricultural production2,5.

We focused on global hunger projections to 2050 and analysed how climate change and trade interact in their impact on hunger. Our economic (Global Biosphere Management Model (GLOBIOM)) and crop (Environment Policy Integrated Model (EPIC)) modelling approach (see Methods) is well established for investigating agricultural climate change impacts22,23,24,25. We advance on the current literature by analysing 60 integrated scenarios that capture variability in trade barriers and in climate projections originating from general circulation models (GCMs), emissions scenarios (Representative Concentration Pathways (RCPs)) and assumptions about CO2 fertilization. By statistically analysing the scenario sample, we assessed whether, where and how climate change influences the effect of trade on the risk of hunger.

The facilitation and tariff elimination scenarios reduce the global risk of hunger from climate change to a comparable extent, and the facilitation + tariff elimination scenario can even compensate for the impact of all but the most extreme climate change scenario. Trade liberalization and facilitation reduce hunger by enhancing climate-induced trade adjustments—across RCP 8.5 scenarios, total agricultural trade increases by 166% to 262% under the facilitation + tariff elimination scenario—by reducing agricultural prices, and by increasing food availability and crop production efficiency (Supplementary Tables 1 and 2). The hunger effect under extreme climate change (RCP 8.5 without the CO2 effect) is reduced by 31% under the facilitation scenario, 11% under the tariff elimination scenario and 64% under the facilitation + tariff elimination scenario. These effects are consistent with other studies that reported 44% lower hunger effects under market integration13 and 46% lower price effects under trade liberalization10 (Supplementary Fig. 5).

## A larger role for trade under climate change

We ran the regressions presented in Table 1 with regional interaction effects (Supplementary Table 3). In most of the regions, climate-induced decreases in crop yields reduce food availability and increase hunger while reduced trade costs have opposite effects. The food availability impacts of crop-yield changes are largest for SAS, SSA and SEA, whereas the effect of trade costs is largest for regions maintaining net imports under climate change (SSA, MNA and EAS). The corresponding impact on hunger is largest in low-income regions (SSA and SAS), followed by middle-income regions (EAS, MNA, and SEA). The interaction effect, which reveals whether climate change alters the relationship between trade costs and hunger, is most pronounced in SSA, followed by EAS. Figure 3 plots the predicted hunger–yield relationship in EAS and SSA for different levels of trade cost, showing that hunger is less sensitive to climate-induced yield changes under reduced trade costs.

## Inter-regional specialization

Adaptation to climate change occurs through changes in existing and new inter-regional trade flows (Supplementary Tables 811). Across the RCP 8.5 scenarios, the largest export growth originates from major baseline producing regions (corn from USA and LAC, soya from LAC and USA, rice from SAS and SEA, and wheat from EUR and Canada (CAN); Supplementary Fig. 9). The largest new trade flows are new corn exports from USA to EAS, CAN, LAC and SEA, from EUR to MNA and from LAC to EAS; new soya exports from LAC to SAS and from USA to CAN and MNA; and new wheat exports from CSI to EUR, and from MNA to SSA. Climate change does not induce substantial new rice trade flows. There is uncertainty across RCP 8.5 scenarios in bilateral trade patterns, but several exports to hunger-affected regions increase consistently (such as wheat from EUR to SSA, soya from LAC to SAS, or corn from LAC to MNA). However, hunger-affected regions are not only engaging in trade at the importer side, but also increase certain exports (wheat in MNA, corn in SSA, and rice in EAS and SAS; Extended Data Fig. 10).

## Discussion

Our study is comprehensive in its scenario design and rigorous in its analysis of the processes driving adaptation through trade. Nevertheless, it is important to emphasize that this study focuses on the global scale in the long term. Trade policies and climate change have important within-country distributional consequences through income and food-access effects33,34,35, which are theoretically ambiguous and which our modelling approach does not consider. Across households with different food access channels, from urban net-consumers to rural subsistence farmers, impacts can differ even in their direction34. Also, current global studies, including ours, focus on crop- and grass-yield impacts, and other direct and indirect climate change effects are not represented to date—for example, heat stress on animals, pest and disease incidence, sea level rise or reduced pollination. Finally, we take a long-term equilibrium perspective ignoring the negative effects of extreme weather events. All of these aspects require substantial new research.

Despite the limitations described above, our study brings novel policy implications. We found that liberalization that has already been achieved under the Doha Round substantially reduces climate-induced hunger impacts. A careful approach to trade integration covering different types of trade barriers can further limit hunger risks. The full removal of agricultural tariffs leads to increases in food availability in SSA, MNA and EAS, but may increase exports and lower regional food availability in SEA and SAS. Further trade facilitation can reduce undernourishment in all hunger-affected regions. However, the effective realization of trade facilitation requires considerable investments in transport infrastructure and technology. Especially in low-income regions, such as SSA, infrastructure is weak36. An estimated US$130–170 billion a year is needed to bridge the infrastructure gap in SSA by 2025 (ref.37). Infrastructure finance averaged US$75 billion in recent years, with the largest contribution from budget-constrained national governments37. Alternative financing through institutional and private investments, called for by the African Development Bank Group and the World Bank Group36,37, could be not only crucial for economic growth, but also for climate change adaptation. In essence, our results demonstrate that trade instruments can mitigate an important part of the adverse hunger effects of long-term climate change. Our results thereby confirm the importance of holistic approaches to international trade negotiations, and could prove also relevant in the face of trade-policy reactions in more acute crisis situations, such as the global COVID-19 pandemic.

## Methods

### Modelling framework

We used the GLOBIOM, a recursive dynamic, spatially explicit, economic partial equilibrium model of the agriculture, forestry and bioenergy sector with bilateral trade flows and costs that can model new trade patterns38. The model computes a market equilibrium in 10-year time steps from 2000 to 2050 by maximizing welfare (the sum of consumer and producer surplus) subject to technological, resource and political constraints. In each time step, market prices adjust endogenously to equalize supply and demand for each product and region. On the demand side, a representative consumer for each of 30 economic regions optimizes consumption and trade in response to product prices and income. Food demand depends endogenously on product prices through an isoelastic demand function and exogenously on GDP and population projections39. We mainly present model results aggregated to 11 regions (Supplementary Table 4): USA, CAN, EUR, OCE, SEA, SAS, SSA, MNA, EAS, CSI and LAC. GLOBIOM is a bottom-up model that builds on a high spatial grid-level resolution on the supply side. Land is disaggregated into simulation units—clusters of 5 arcmin pixels that are created based on altitude, slope and soil class, 30 arcmin pixels, and country boundaries. GLOBIOM’s crop production sector includes 18 major crops (barley, beans, cassava, chickpeas, corn, cotton, groundnut, millet, palm oil, potato, rapeseed, rice, soybean, sorghum, sugarcane, sunflower, sweet potato and wheat) under 4 management systems (irrigated, high input; rainfed, high input; rainfed, low input; and subsistence). The allocation of acreage by the crop and management system is determined by potential yields, production costs and expansion constraints23. Crop production parameters are based on the detailed biophysical crop model EPIC. Additional biophysical models were used to represent the livestock (RUMINANT40) and forestry (G4M41) sectors. Further information on model structure and parameters was described previously42,43.

As a partial equilibrium model, GLOBIOM focuses only on specific sectors of the economy and does not represent feedbacks on consumer income and GDP from trade and climate change. However, the partial equilibrium model allows for more detail in the represented sectors, and a more accurate assessment of biophysical impacts. This is due to the high spatial and commodity resolution as well as the physical rather than monetary representation of variables compared with the general equilibrium models that explicitly cover income feedbacks. Crop yields adjust endogenously through the management system or location of production, and exogenously according to long-term technological development and climate change impacts23. The output from EPIC was used to compute, for each time step, yield shifters for each climate change scenario and each crop and management system at a disaggregated spatial scale (simulation unit). EPIC simulates scenario-specific yields on the basis of inputs from climate models (daily climatic conditions including solar radiation, minimum and maximum temperature, precipitation, wind speed, relative humidity and CO2 concentration). Climate change impacts on livestock production are modelled through crop and grassland yield impacts on feed availability. EPIC crop and grassland yield impacts, as well as their implementation in GLOBIOM, are further explained in Leclère et al.23 and Baker et al.24.

International trade is represented in GLOBIOM through the Enke–Samuelson–Takayama–Judge spatial equilibrium assuming homogenous goods38,44. Bilateral trade flows between the 30 economic regions were determined by the initial trade pattern, relative production costs of regions and the minimization of trading costs38. The initial trade pattern was informed by the BACI database from CEPII averaging across 1998–2002 (ref. 45). Trade costs are composed of tariffs from the MAcMap-HS6 database46, transport costs47 and a nonlinear trade expansion cost. The MAcMap-HS6 2001 release from CEPII-ITC provides ad valorem and specific tariffs, and shadow tariff rates of tariff rate quotas for the model calibration in the base year 2000 (ref. 48). To incorporate trade liberalization developments under the Doha Round, the tariff data is updated in the 2010 time step with the 2010 release of MAcMap-HS6 (ref. 49; Supplementary Table 6). We used the estimation by Hummels47 to compile input data on bilateral transport costs on the basis of the distance between trade pairs and the weight–value ratio of agricultural products. Transport costs were set to US$30 per ton minimum, on the basis of the fifth percentile of the OECD Maritime Transport Cost database (2003–2007), and were kept constant at base year level over the simulation period as the drivers of transport costs (for example, fuel prices and containerization50) are not represented in the partial equilibrium model. In the scenario simulations, the nonlinear expansion cost raises per-unit trade costs when the traded quantity increases over time to model persistency in trade flows. A constant elasticity function was used for trade flows observed in the base year, and a quadratic function was used for new trade flows. The nonlinear element reflects the cost of trade expansion in terms of infrastructure and capacity constraints in the transport sector and was reset after each 10-year time step. Compared to other global economic models, GLOBIOM’s trade representation is positioned between the rigid Armington approach of general equilibrium models and the flexible world pool market approach of many partial equilibrium models. ### Risk of hunger We measured the population at risk of hunger, or the number of people whose food availability falls below the mean minimum dietary energy requirement, on the basis of previous studies51,52,53. The following four parameters were used: the mean minimum dietary energy requirement, the coefficient of variation of the distribution of food within a country, the mean food availability in the country (kcal per capita per day) and total population. Minimum dietary energy requirements are exogenously calculated on the basis of demographic composition (age, sex) of future population projections. Future changes in the inequality of food distribution within a country are exogenous and follow projected national income growth. This is based on an estimated relationship between income and the coefficient of variation of food distribution with observed historical national-level data. Poor infrastructure, remoteness and a high prevalence of subsistence farming limit local markets in distributing food equally across households7. Income is lowest in SAS and SSA, regions in which the share of land under subsistence farming is the largest (27% in SAS and 43% in SSA)54. Food availability in kcal per capita per day is endogenously determined by GLOBIOM at the regional level. One limitation of the approach is that it does not include within-country distributional consequences of trade integration and/or climate change through income effects. Trade policies and climate change alter food prices, which affects individual incomes, purchasing power and food access depending on households being net consumers or net producers of food33. At the aggregate regional level, the bias from not considering these distributional effects may be upward or downward, depending on the share of net-consuming versus net-producing households; degree of subsistence farming versus agricultural wage work; and share of rural versus urban population in each country. ### Climate change adaptation Climate change adaptation is defined by the IPCC as “the process of adjustment to actual or expected climate and its effects”26. Adaptation of the agricultural sector to climate-induced changes in crop yields may include adjustments in consumption, production and international trade2. Demand-side adaptation is captured in GLOBIOM by changes in regional consumption levels in response to market prices. Supply-side adaptation includes the reallocation of land for each crop by a grid-cell and management system, and the expansion of cropland to other land covers23. Whereas Leclère et al.23 assess supply-side adaptation, here we focused on international market responses, in which our analysis approach is inspired by the ‘adaptation illusion hypothesis’ postulated by Lobell15 and confirmed by Moore et al.55. They argue that farm-level practices identified as adaptation measures by many crop modelling studies cannot be referred to as climate adaptation as they have the same yield impact in current climate as under climate change. In a similar manner, we intended to investigate whether, where and, if so, why trade integration has a larger positive impact on the risk of hunger under climate change. We defined the adaptation effect of trade as the sum of the effect of reducing trade costs on hunger under current climate (direct trade effect), and any additional positive or negative impact of trade integration under climate change (climate-induced trade effect). The adaptation effect of trade can be understood through Ricardo’s theory of comparative advantage (Supplementary Text)11,12. Reducing trade costs promotes trade according to comparative advantage56 and facilitates the role of trade as a transmission belt in linking food-deficit and food-surplus regions57. Climate change impacts differ across crops and regions8. Depending on the spatial distribution of these impacts, the current pattern of comparative advantage may be intensified, maintained or substantially altered. This may lead to increased food deficits in certain regions. Trade is argued to have a larger role under climate change as it facilitates adjustment to changes in comparative advantage11,12 and enables food surplus to be linked with food deficit regions6,7,57. ### Scenario design Our choice of climate change scenarios was determined by the ISI-MIP Fast Track Protocol used by crop modellers to calculate crop and grass yield impacts8,58. We used all four RCPs that reflect increasing levels of radiative forcing by 2100 (the 2.6 W m−2, 4.5 W m−2, 6 W m−2 and 8.5 W m−2 scenarios)59 as projected by the HadGEM2–ES GCM60,61. RCP 8.5 was implemented with four additional GCMs to reflect uncertainty in climate models: GFDL–ESM2M62, IPSL–CM5A–LR63, MIROC–ESM–CHEM64 and NorESM1–M65. RCP 2.6 represents climate stabilization at 2 °C and RCP 8.5 a temperature range of 2.6–4.8 °C (ref. 26). Yield impacts are based on simulations from the crop model EPIC23,24. Each RCP × GCM combination was modelled including CO2 fertilization effects. RCP 8.5 × HadGEM2–ES was additionally simulated without the CO2 effect, which reflects the most severe climate change scenario. These scenarios represent the tier 1 set of ISI-MIP scenarios and climate change impacts are simulated individually for all 18 GLOBIOM crops, except for oil palm, and for grasslands. Scenarios without CO2 fertilization for RCPs other than RCP 8.5 were considered to be of secondary importance in the ISI-MIP Fast Track—and in the latest simulation protocol for ISI-MIP 3b—and were therefore available only for the four main crops (corn, rice, soya and wheat). We carry out a comprehensive sensitivity analysis with respect to the CO2 fertilization effect for all RCPs, however, as this requires extrapolating climate change impacts from the four crops to the other crops, and thus would introduce inconsistency with the Tier 1 scenarios, the analysis is presented separately in Supplementary Text. In the no climate change scenario, exogenous yield change originates only from long-term technological development assumptions. We implemented six trade scenarios to analyse the role of trade in climate change adaptation. The first scenario—fixed imports—limits imports to the level observed in the no climate change scenario or less. This represents restricting trade flow adjustments in response to climate change, or limiting trade as an adaptation mechanism. The second scenario, pre-Doha tariffs, excludes the tariff update in 2010, representing the trade environment before global trade liberalization launched by the Doha Round (a comparison of average tariff rates is provided in Supplementary Table 6). We also implemented three trade integration scenarios to assess promotion of the trade adaptation mechanism. In the first scenario, the facilitation scenario, the nonlinear part of trade costs is set close to zero from 2020 onwards on the basis of Baker et al.24. This reflects the impact of reducing transaction costs, infrastructure costs and other institutional barriers limiting the expansion of trade. Trade facilitation is defined by the WTO as the “simplification of trade procedures”66. In economic literature it refers to the reduction in trade transaction costs that are determined by the efficiency of customs procedures, infrastructure services and domestic regulations 18,66. Other trade costs that are relevant in agricultural trade, which were not included in this study, are non-tariff measures (NTMs). UNCTAD defines NTMs as “all policy-related trade costs incurred from production to final consumer, with the exclusion of tariffs”67. Typical examples of NTMs are technical measures, such as sanitary and phytosanitary measures (SPS), and price and quantity control measures, such as quotas and subsidies. Some studies include also the above-mentioned transaction costs in the category of NTMs68,69, whereas others make the explicit distinction18,70. The per-unit transport costs were kept constant at the base year level. In the second scenario, tariff elimination, all agricultural tariffs were progressively phased out between 2020 and 2050, that is −25% in 2020, −50% in 2030, −75% in 2040 and −100% in 2050. This scenario leads to a 70% growth in total agricultural trade (Supplementary Table 1), comparable in magnitude to the agricultural import (+36%) and export (+60%) growth under tariff liberalization reported by Anderson and Martin71. The final scenario, facilitation + tariff elimination, is a combination of the previous two scenarios and presents the most extensive open trade scenario. In the baseline trade scenario, trade barriers are kept constant at 2010 levels, but trade patterns vary endogenously across the different climate impact scenarios. Supplementary Table 7 provides a comparison of average trade costs across the different scenarios. Socioeconomic developments were modelled according to the SSP2, which reflects a middle-of-the-road scenario in which the population reaches 9.2 billion by 2050 and income grows according to historical trends in each region27. The technological development assumed by SSP2 leads to an increase in global average crop yields of 66% between 2000 and 2050 (Supplementary Table 12). The SSP scenarios are widely discussed and are often used as a basis for harmonizing key macroeconomic assumptions for integrated assessment modelling of different climate futures72. SSP2 projects a decrease in the global population at risk of hunger from 867 million in 2000 to 122 million by 2050. This because of an increase in food consumption—global food availability increases from 2,700 to 3,007 kcal per capita per day—and an improved food distribution within regions, which are both related to the assumed income growth under SSP2 (ref. 53). Income projections lead to changes in food preferences. Under SSP2, the share of livestock products in diets increases globally from 16% in 2000 to 17.3% in 2050, with the largest increases in Asian regions73. Such changes affect the baseline trade pattern—for example, increased production and consumption of livestock products in SAS, EAS and SEA imply an increase in imports of feed crops such as corn and soya by 2050. ### Hunger statistical analysis We analysed the results of the scenario runs using a regional-level linear regression model to infer the underlying relationship between trade costs, crop-yield changes and hunger as predicted by GLOBIOM. The following models were estimated using OLS (Table 1): $$\begin{array}{l}{\mathrm{Population}}\,{\mathrm{at}}\,{\mathrm{risk}}\,{\mathrm{of}}\,{\mathrm{hunger}}_{itr} = \\ \beta _1^{\left( 1 \right)}{\mathrm{Crop}}\,{\mathrm{yield}}_{ir} + \beta _2^{\left( 1 \right)}{\mathrm{Trade}}\,{\mathrm{costs}}_{itr}\\ + \beta _3^{\left( 1 \right)}{\mathrm{Crop}}\,{\mathrm{yield}}_{ir} \times {\mathrm{Trade}}\,{\mathrm{costs}}_{itr} + \mathop {\sum }\limits_i \beta _{4i}^{\left( 1 \right)}{\mathrm{Region}}_i + \varepsilon _{itr}^{\left( 1 \right)}\end{array}$$ $$\begin{array}{l}{\mathrm{Food}}\,{\mathrm{availability}}_{itr} = \\ \beta _1^{\left( 2 \right)}{\mathrm{Crop}}\,{\mathrm{yield}}_{ir} + \beta _2^{\left( 2 \right)}{\mathrm{Trade}}\,{\mathrm{costs}}_{itr}\\ + \beta _3^{\left( 2 \right)}{\mathrm{Crop}}\,{\mathrm{yield}}_{ir} \times {\mathrm{Trade}}\,{\mathrm{costs}}_{itr} + \mathop {\sum }\limits_i \beta _{4i}^{\left( 2 \right)}{\mathrm{Region}}_i + \varepsilon _{itr}^{\left( 2 \right)}\end{array}$$ We estimated the models also with regional interaction terms (Fig. 3, Supplementary Table 3): $$\begin{array}{l}{\mathrm{Population}}\,{\mathrm{at}}\,{\mathrm{risk}}\,{\mathrm{of}}\,{\mathrm{hunger}}_{itr}= \\ \mathop {\sum }\limits_i \left( {\beta _{1i}^{\left( 3 \right)}{\mathrm{Crop}}\,{\mathrm{yield}}_{ir} \times {\mathrm{Region}}_i + \beta _{2i}^{\left( 3 \right)}{\mathrm{Trade}}\,{\mathrm{costs}}_{itr} \times {\mathrm{Region}}_i}\right.\\ \ +\left. {\beta _{3i}^{\left( 3 \right)}{\mathrm{Crop}}\,{\mathrm{yield}}_{ir} \times {\mathrm{Trade}}\,{\mathrm{costs}}_{itr} \times {\mathrm{Region}}_i + \beta _{4i}^{\left( 3 \right)}{\mathrm{Region}}_i} \right) + \varepsilon _{itr}^{\left( 3 \right)}\end{array}$$ $$\begin{array}{l}{\mathrm{Food}}\,{\mathrm{availability}}_{itr} = \\ \mathop {\sum }\limits_i \left( {\beta _{1i}^{\left( 4 \right)}{\mathrm{Crop}}\,{\mathrm{yield}}_{ir} \times {\mathrm{Region}}_i + \beta _{2i}^{\left( 4 \right)}{\mathrm{Trade}}\,{\mathrm{costs}}_{itr} \times {\mathrm{Region}}_i}\right. \\ \ \left.{ + \beta _{3i}^{\left( 4 \right)}{\mathrm{Crop}}\,{\mathrm{yield}}_{ir} \times {\mathrm{Trade}}\,{\mathrm{costs}}_{itr} \times {\mathrm{Region}}_i + \beta _{4i}^{\left( 4 \right)}{\mathrm{Region}}_i} \right) + \varepsilon _{itr}^{\left( 4 \right)}\end{array}$$ where Population at risk of hungeritr gives the number of people at risk of hunger (million) and Food availabilityitr gives the food availability (kcal per capita per day) in 2050 in each region i, trade scenario t and climate change scenario r. Crop yieldir gives the change in average crop yield (kcal ha−1) compared with the average crop yield in the no climate change scenario in 2050. Trade costitr gives the log-transformed weighted average trade costs (US$ per 106 kcal) on all trade flows in 2050. To obtain a measure that reflects the implication of trade scenarios on overall trading costs, we calculated the trade-weighted average of trade costs over all agricultural imports, exports and intraregional trade flows for each region i, trade scenario t and climate change scenario r: $${\mathrm{Average}}\,{\mathrm{trade}}\,{\mathrm{cost}}_{itr} = \mathop {\sum}\nolimits_k {\frac{{x_{iktr}}}{{{\mathrm{Total}}{_{x{_{itr}}}}}}} \times {\mathrm{Trade}}\,{\mathrm{cost}}_{iktr}$$ where xiktr are the trade flows of crop k in, out and within region i in each scenario (t,r) and $${\mathrm{Total}}{_{x{_{itr}}}}$$ is the sum of all trade flows in, out and within region i in each scenario (t,r). The variables Crop yieldir and Trade costitr are centred (demeaned) to solve structural multicollinearity. For the regional fixed effects (Regioni) dummy variables were used.
$$\beta _{ki}^{\left( m \right)}$$ are the slope coefficients to be estimated for variable k in regression model m (with k = 1, …, 4 and m = 1, …, 4). $$\varepsilon _{itr}^{\left( m \right)}$$ is an independently and identically normally distributed error term with zero mean and $$\sigma _{\left( m \right)}^2$$ variance. Standard errors were estimated robust to heteroscedasticity using the HC3 method as recommended by Long and Ervin74. HC3 is a refined version of White’s method for estimating heteroskedastic s.e. (HC0). Long and Ervin74 demonstrated using Monte Carlo simulations that the HC3 method outperforms HC0 for small sample sizes (n < 250). The calculation of s.e. of the regional interaction effects was performed using the delta method. The F statistic of overall significance rejects the null hypothesis at the 1% significance level for all of the models. The sample was composed of GLOBIOM regional output under five different trade scenarios (baseline, pre-Doha tariffs, facilitation, tariff elimination and facilitation + tariff elimination) and ten climate change scenarios in 2050. The sample size was 550 for models with regional fixed effects (11 regions × 5 trade × 10 climate change scenarios) and 450 for models with regional interaction terms (9 regions (EUR and CAN excluded) × 5 trade × 10 climate change scenarios). Summary statistics of all of the variables are shown in Supplementary Table 5.
$$\begin{array}{ll}{\mathrm{Share}}\,{\mathrm{of}}\,{\mathrm{world}}\,{\mathrm{production}}_{itr}= &\mathop {\sum }\limits_i \beta _{1i}^{\left( 5 \right)}{\mathrm{Trade}}\,{\mathrm{costs}}_{itr} \times {\mathrm{Region}}_i\\&\quad \quad + \beta _{2i}^{\left( 5 \right)}{\mathrm{Region}}_i + \varepsilon _{itr}^{\left( 5 \right)}\\{\mathrm{Share}}\,{\mathrm{of}}\,{\mathrm{regional}}\,{\mathrm{crop}}\,{\mathrm{production}}_{itr}= &\mathop {\sum }\limits_i \beta _{1i}^{\left( 6 \right)}{\mathrm{Trade}}\,{\mathrm{costs}}_{itr} \times {\mathrm{Region}}_i\\&\quad \quad + \beta _{2i}^{\left( 6 \right)}{\mathrm{Region}}_i + \varepsilon _{itr}^{\left( 6 \right)}\\{\mathrm{Share}}\,{\mathrm{of}}\,{\mathrm{production}}\,{\mathrm{exported}}_{itr} = &\mathop {\sum }\limits_i \beta _{1i}^{\left( 7 \right)}{\mathrm{Trade}}\,{\mathrm{costs}}_{itr} \times {\mathrm{Region}}_i\\&\quad \quad + \beta _{2i}^{\left( 7 \right)}{\mathrm{Region}}_i + \varepsilon _{itr}^{\left( 7 \right)}\end{array}$$