Trade (21 trade)


This module controls the trade of agricultural products between world regions. It assures that the regional demand is met by domestic production and imports from other world regions. The global trade balance, i.e. the constraint that global production has to exceed global demand, is located in the core. Additionally, the regional production > demand constraint for products that are not traded is located in the core.



Name Description Unit A B C
$vm\_prod\_reg$ regional aggregated production mio. ton DM x x x
$im\_years$ years between previous and current time step years x x
$fm\_DM\_content$ Dry matter content (% fresh matter) - x
$vm\_supply(i,k)$ regional demand for different agricultural products mio. ton DM x x x

The last columns of the table indicate the usage in the different realizations (numbered with capital letters)


Name Description Unit
$vm\_cost\_trade(i)$ transport costs and taxes for the bilateral trade Mio US$
$fm\_trade\_bal\_reduction\_annual(t\_all,k)$ annual trade balance reduction (1). Determines the allocation of trade to different pools -

Interface plot

Figure 0: Information exchange among modules


(A) tb_old (default)

Within this realization, there are two ways a region can fulfill its demand for agricultural products: a self-sufficiency pool based on historical region specific trade patterns, and a comparative advantage pool based on most cost-efficient production (Figure 1).

visualization of the trade implementation for the tb_old moduel
Figure 1: Implementation of trade in the tb_old module [Stevanovic et al1 (2014)]

In the self-sufficiency pool, regional self-sufficiency ratios ($f21\_self\_suff\_seedred\_1995(i,k)$) define, how much of the demand of each region (i) for each product (k) has to be met by domestic production. Self sufficiency ratios smaller than one indicate that the region imports from the world market while self-sufficiencies greater than one indicate that the region produces for export.
The global excess demand ($v21\_excess\_dem(k\_trade)$) for all tradeable goods, i.e. the sum of the regional imports for each crop, is calculated as follows:

v21\_excess\_dem(k\_{trade})=\sum_i\Big\{vm\_supply(i,k\_trade)\times\Big[1 - min \big(1,f21\_self\_suff\_seedred\_1995(i,k\_trade)\big)\Big]\Big\}
,where the index $i$ stands for the regions, $vm\_supply$ is the demand and $f21\_self\_suff\_seedred\_1995$ is the seed-share corrected self sufficiency ratio.

Regional self sufficiency ratios are derived from FAO data (see Schmitz et al2 2012 for details).
The allocation of the excess demand to exporting regions is based on regional export shares ($f21\_exp\_shr\_1995(i,k\_trade)$)

v21\_excess\_prod(i,k\_trade) = v21\_excess\_dem(k\_trade) \times f21\_exp\_shr\_1995(i,k\_trade)
,where $v21\_excess\_prod$ is the regional contribution to the excess production.
Export shares are derived from FAO data (see Schmitz et al2 2012 for details). They are 0 for importing regions.

In the comparative advantage pool, no regional constraints on production exist. The only active constraint is that the global production is larger or equal to demand constraint. This means that production can be freely allocated globally based on comparative advantages.

The share of regional demand that has to be fulfilled through the self-sufficiency pool is determined by a trade balance reduction factor for each commodity ($ic21\_trade\_bal\_reduction(k\_trade)$) according to the following equation. If the trade balance reduction equals 1, all demand enters the self-sufficiency pool. If it equals 0, all demand enters the comparative advantage pool. The regional trade constraint for the self-sufficiency pool thus is:

vm\_prod\_reg(i,k\_trade)\geq \left\{ \begin{array}{l l}
\big( vm\_supply(i,k\_trade) + v21\_excess\_prod(i,k\_trade)\big) \times ic21\_trade\_bal\_reduction(k\_trade), \quad if \quad f21\_self\_suff\_seedred\_1995(i,k\_trade) \geq 1\\
vm\_supply(i,k\_trade)\times f21\_self\_suff\_seedred\_1995(i,k\_trade) \times ic21\_trade\_bal\_reduction(k\_trade), \quad if \quad f21\_self\_suff\_seedred\_1995(i,k\_trade) < 1
\end{array} \right.

If region $i$ is an importer of product $k$, regional production has to equal at least the self-sufficiency share of domestic demand, reduced by the amount of demand entering the comparative advantage pool. If region $i$ is an exporter of product $k$, regional production has to meet regional demand plus the regions share in the excess production, both reduced by the fraction entering the comparative advantage pool. The trade balance reduction for each time step is calculated by:

i21\_trade\_bal\_reduction(t,k\_trade) = i21\_trade\_bal\_reduction(t-1,k\_trade)*(1-fm\_trade\_bal\_reduction\_annual(t,k\_trade))^{im\_years(t)}

,where $t$ denotes the timestep, $fm\_trade\_bal\_reduction\_annual$ is the annual reduction of the trade balance and $im\_years$ is the length of the timestep. Initial values for the trade balance reduction in 1995 are 1, i.e. all trade in 1995 happens through the self-sufficiency pool. For later time steps, three scenarios of trade liberalization (i.e. of allocation to the comparative advantage pool) are implemented based on Schmitz et al. 20122: A "regionalized" one with slow trade liberalization, a "globalized" one with faster trade liberalization and a "fragmented" one with almost no trade liberalization(Figure 2).

trade libralization
Figure 2: Trade liberalization scenarios

The default choice of the trade liberalization is connected to the setting for the socio-economic scenario:

Scenario Trade liberalization
B1 globalized
B2 regionalized
A1 globalized
A2 regionalized
SSP1 globalized
SSP2 regionalized
SSP3 fragmented
SSP4 globalized
SSP5 globalized
b2_ethics regionalized

There are no costs associated with trade between world regions and the variable $vm\_cost\_trade$ is fixed to 0.

It is not possible to determine bilateral trade flows between two specific world regions.
No costs are associated with inter-regional trade

(B) tb_new

The tb_new module works very similar to the tb_old module. There is one difference: In the tb_old module, regional self-sufficiency ratios ($f21\_self\_suff\_seedred\_1995(i,k)$) and export shares ($f21\_exp\_shr\_1995(i,k)$) are constant over time. In the tb_new module, regional self-sufficiency ratios ($p21\_self\_suff(t,i,k)$) and export shares ($p21\_exp\_shr(t, i, k)$) are time dependent. In 1995, the values correspond to the values from the tb_old module. For later time periods, the values are updated ased on regional production and demand in the previous timestep:
p21\_self\_suff(t+1,i,k) = vm\_prod\_reg(i,k)/vm\_supply(i,k) \\
p21\_exp\_shr(t+1,i,k) = \frac{vm\_prod\_reg(i,k) - vm\_supply(i,k)}{\sum \limits_i \big(vm\_prod\_reg(i,k) - vm\_supply(i,k)\big)}\\

This means that the new self sufficiency is based on the current production to demand ratio and the new export share is defined as the current regional excess production over current global excess production. Thus, production shifts due to trade in the comparative advantage pool influence the trade patterns in the self-sufficiency pool.
The equations are slightly modified due to the different names for the self-sufficiency parameters:

v21\_excess\_dem(k)=\sum \limits_i \Big \{vm\_supply(i,k) \times \Big[1 - min \big(1,pc21\_self\_suff(i,k) \big) \Big] \Big \} \\
v21\_excess\_prod(i,k) = v21\_excess\_dem(k) \times pc21\_exp\_shr(i,k)

vm\_prod\_reg(i,k)\geq \left\{ \begin{array}{l l}
\big(vm\_supply(i,k) + v21\_excess\_prod(i,k) \big) \times ic21\_trade\_bal\_reduction(k), \quad if \quad pc21\_self\_suff(i,k) \geq 1\\
vm\_supply(i,k)\times pc21\_self\_suff(i,k) \times ic21\_trade\_bal\_reduction(k), \quad if \quad pc21\_self\_suff(i,k) < 1
\end{array} \right.

It has to be noted that all equations are defined over all products k. Thus, this interferes with the production larger or equal to demand constraint for non-tradeable goods. In addition, the global production > demand constraint from the core is duplicated in this module realization:

\sum\limits_i vm\_prod\_reg(i,k)\geq \sum\limits_i vm\_supply(i,k)

The module realization can lead to strong path dependencies of trade patterns which can give strange results when comparing different scenarios.
The trade constraints in the module realization interfere with the constraints for non traded goods in the core.
It is not possible to determine bilateral trade flows between two specific world regions.
No costs are associated with inter-regional trade

(C) bilateral

Within this realization agricultural goods can be traded between regions by adding trade costs to the goal function. The specific transport costs, taxes and subsidies for each good and trade flow determine the costs. The costs for bilateral transport for each commodity are derived by calculating the difference between bilateral export values at FOB prices (Free On Board) and bilateral import values at CIF prices (Cost Insurance and Freight) and dividing it by the traded quantity. Since the data are based on the GTAP database (Narayanan and Walmsley, 2008)[3] and GTAP reports all quantities in US$ values, the trade volume is divided by FAO prices (FAO, 2010)[4] to receive the traded quantity in tDM. In a similar manner, the trade barriers are calculated. Import duties are derived as the difference between bilateral import values at market prices and at world prices, whereas export duties are derived as the difference between bilateral export values at world prices and at market prices. As with transport costs, we divide the results by the traded quantities to obtain trade margins per metric ton.

vm\_cost\_trade(i) = \sum\limits_{i2,k} \Big[v21\_trade(i2,i,k) \times \big(ic21\_transp\_costs(i2,i,k) + ic21\_taxes(i2,i,k) + ic21\_subsidies(i2,i,k)\big) \Big]

Imports to a region (including the import to the own region) must satisfy the regional demand

\sum\limits_{i2} v21\_trade(i2,i,k) > vm\_supply(i,k)

Exports from a region have to be equal to the production in this region
\sum\limits_i v21\_trade(i2,i,k) < vm\_prod\_reg(i2,k)

This module is fully functional, but trade flows are still not comparable to data, since the calibration of the module is still work in progress.


Name Description Units A B C
$v21\_excess\_dem(k)$ global excess demand $10^6$ton DM x x
$v21\_excess\_prod(i,k)$ regional excess production $10^6$ton DM x x
$f21\_self\_suff\_seedred\_1995(i,k)$ Self Sufficiency rate (reduced by seed use) (1) [FAO - FBS] - x x
$f21\_exp\_shr\_1995(i,k)$ regional and crop-specific export share (1) - x x
$ic21\_trade\_bal\_reduction(k\_trade)$ current trade balance reduction (1) - x x
$i21\_trade\_bal\_reduction(k\_trade)$ trade balance reduction in each time step (1) - x x
$p21\_self\_suff(t,i, k)$ self sufficiency ratio (1) - x x
$pc21\_self\_suff(i, k)$ current self sufficiency ratio (1) - x x
$p21\_exp\_shr(t,i,k)$ each region's share in total exports(1) - x x
$pc21\_exp\_shr(i,k)$ each region's current share in total exports(1) - x x
$pc21\_exports(k)$ current total exports $10^6$ tON DM x x
$v21\_trade(i2,i,k)$ amount of traded goods for every good and route $10^6$ ton DM x
$ic21\_transp\_costs(i2,i,k)$ transport costs US$ per ton x
$ic21\_taxes(i2,i,k)$ taxes US$ per ton x
$ic21\_subsidies(i2,i,k)$ subsidies US$ per ton x

The last columns of the table indicate the usage in the different realizations (numbered with capital letters)


Anne Biewald, Xiaoxi Wang, Christoph Schmitz, Markus Bonsch

See Also



1 [Stevanovic et al. (2014)] Climate Change Impacts on Agricultural Welfare; under review for PNAS

2 [Schmitz et al. (2012)] Trading more food: Implications for land use, greenhouse gas emissions, and the food system; Global Environmental Change

3 [Narayanan, B., Walmsley, T., 2008] Global Trade, Assistance, and Production: The GTAP 7
Data Base. Center for Global Trade Analysis, Purdue University ed.

4 [FAO, 2010] Faostat — food and agriculture organization of the United Nations Statistics
Division. Last Access: 11/07/2010