ANNEX 2 - WORLD FOOD MODEL SPECIFICATIONS

The following notations are the most common ones used in the model equations. In order to avoid repetition, they are not indicated in the subsequent presentation.

Data

Calendar year data are used throughout. Cereal data are taken from the cereal country balance sheets (CCBS) maintained by the Commodities and Trade Division of FAO; livestock and dairy data come respectively from the Commodity Balance (CB), and Supply Utilization Account (SUA/FAOSTAT); and oilseed, oil and oilmeal data are taken from the OCBS/ESC and CO3/FAOSTAT (the latter of which calculates oil and oilmeal equivalent of oilseeds). Population data and growth assumptions for each country are taken from the demographic projections prepared by the Population Division of the United Nation’s Secretariat and correspond to the "medium variant". Historical GDP and its growth assumptions are mainly based on the long-term economic forecasts prepared by the International Economics Department of the World Bank, supplemented where such forecasts are not available, by estimates derived from other sources.

Model parameters

The basic model parameters (price and income elasticities) included in the model are inherited from previous versions of the FAO’s World Food Model. They are mainly estimates produced by FAO, supplemented by the elasticity database of the SWOPSIM model of the United States Department of Agriculture and the MTM model of OECD.

World market equilibrium

The model determines for each simulation year and for each commodity gross exports and imports for each country/group. A world market equilibrium price index is then obtained from the following equilibrium condition through the use of the Gauss-Seidel algorithm:

where

i = all commodities
r = all countries/country groups
t = all the time (year)

Henceforth, the subscript "r", indicating a country or a country group, is suppressed for simplicity of the presentation.

Gross trade equations

Gross export and import equations depend upon the country’s net trade position. Gross imports for a net importing country and gross exports for a net exporting country are determined on the basis of commodity balances, while alternative specifications are used to compute the "minor" flows - gross imports for a net exporting country and gross exports for a net importing country.

Gross imports

For a net importing country, imports are what is needed to balance the domestic market:

For a net exporting country, imports are the larger of a specified minimum access (MQ) or an amount related to total use (CC):

where ^a = elasticity of import demand with respect to total consumption

Gross exports

For a net exporting country, exports are the exportable surplus remaining after domestic uses have been satisfied:

For a net importing country, exports are linked to the change in world price relative to domestic price:

where:

OH = production
MQ = specified minimum access level under the Uruguay Round
e = price elasticity of export demand

Price linkage equations

Two types of price linkage equations are used in the model. For countries that did not undertake to liberalize their trade, domestic producer and consumer prices are linked to the world market price through constant price transmission elasticities. For the liberalizing countries, changes in bound rates of tariffs and the price effects due to changes in export subsidies determine domestic prices.

For non-liberalizing countries, the domestic price index is:

where a (is a price transmission elasticity.

For liberalizing countries, the domestic price index is:

where:

TC = specific tax;

TL = ad valorem tariff rate;

a = direct and indirect support not directly related to movements in world market prices (i.e. structural protection);

d = price wedge accounting for the difference between border prices and world reference prices due to differences in quality standards, insurance, transportation and marketing costs;

DEE = price effects of export subsidies.

1. Cereal Markets

Production

Crop production is the product of estimated harvested area, yield and a crop condition index (XY_i,t):

Area harvested is a function of lagged area, lagged producer price and a trend growth factor:

for i,j = all the cereals included in the model.

Crop yield is determined on the basis of lagged yield and a trend factor:

.

Total use

Total use is the sum of food, feed and other uses:

Food use

for i,j = all the cereals included in the model.

Feed use

For crops other than milled rice:

for i, j = all the cereals, except milled rice.

G.AC = basic feed requirement of cereals (see definition under Aggegated Variables, below);

For milled rice:

for j = all the cereals included in the model.
Here, R.OH = rice production

Other use

for i = all the cereals included in the model.
where AH = harvested area

Closing stock

For a net importing country:

.

For a net exporting country:

where:
YH = yield;
a's = own and cross price elasticities of supply
b's = income elasticity of demand

2. Meat markets

The notations used for this sub-section are:

For all meats, production is:

Cattle numbers

Bovine meat market:

Beef cow number (X.AL):

for j = beef and milk prices.

Milk market - milking cow number:

for j = milk and butter prices.

Pig, ovine meat markets:

for i = pig and ovine meats.

Poultry meat markets:

.

Number of livestock slaughtered

Bovine meat market:

with 1< a<0 for selected countries; else a=0.

Pig, ovine meats:

.

Poultry meat:

.

The carcass weight of the slaughtered livestock is:

for i = all the meats included in the model.

Total use

for j = all types of meat included in the model.

Trade adjustments for China and EU-15

For the bovine meat market, a maximum level of imports is imposed for China (Mainland) and EU-15, and a maximum level of exports is imposed for China (Mainland:)

where a is an exogenously specified trade volume.

Stocks

A stocks equation is defined only for the bovine meat of EU-15. It is formulated to allow closing meat stocks to increase by a maximum of 200,000 tonnes per year (notations defined in 1.1 above).

3. Milk markets

The notifications used in this sub-section are:

Milk production

Total production:

.

Production from milk cows:

Yield:

.

Other milk production:

Total use

.

Food use

for j = milk and butter.

Feed use

.

Other use

4. Oilseed, oils and oilmeals markets

The notations used in this sub-section are:

Oilseed production

Production (major oilseeds):

for i = groundnuts, soybeans, sunflowerseed, rapeseed and linseed.

Harvested area:

for j = oil and oilmeal

Yield:

for j = oil and oilmeal.

Cottonseed production:

.

Oil and oilmeals markets

Production:

where i = oil and oilmeal and j = all types of oil or oilmeals.

For oils from groundnuts, soybeans, rapeseed, sunflowerseed, linseed and cottonseed, the levels of production are obtained by applying with the country-specific composite rate of crush and extraction rates to the levels of oilseed production.

For oil from oilseeds production is given by:

where i = groundnuts, soybeans, sunflowerseed, rapeseed and linseed

D is a dummy for location of producing country (1 for the northern hemisphere, 0 for the southern hemisphere).

For oilmeal from oilseeds production is given by:

where i = groundnuts, soybeans, sunflowerseed, rapeseed and linseed

D is a dummy for location of producing country (1 for the Northern hemisphere, 0 for the Southern hemisphere).

Production of olive oil:

Production of coconut oil, palm and palm kernel oils, other vegetable oils and marine oil:

.

Production of copra protein, palm and palm kernel meals, other vegetable meal, and fish meal:

.

Production of lard and tallow (the fat content of each type of meat is considered to be the same):

for k = bovine, ovine and pigmeat.

Production of butter in oil equivalent:

.

Oil and oilmeal use

Oil, total use:

.

Food use of oil:

for j = oil and butter.

Other use of oil:

.

Oilmeal, total use:

.

Oilmeal, feed use:

.

Oilmeal, other use:

.

Closing stocks

Oils

Net importing country:

.

Net exporting country:

.

Oilmeals

Net importing country:

.

Net exporting country:

Aggregated variables

Average feed price

for i = all cereals in the model, and oilmeal
w's = aggregation weights

Average price of meat

for i = all meats in the model

Feed requirement of cereals

for i = all meats in the model, and milk
G.AC = feed requirement of cereals
w's = use of feed cereal per unit of meat produced

Feed requirement of oilmeals

for i = all meats in the model, and milk
G.AP = feed requirement of oilmeals;
OH = production of meat and milk;
w's = use of feed oilmeal per unit of meat produced.