Overview of the main relationships in the GTAP model.

At the heart of tUe GTAP database and model are accounting equations tUat describe market clearing conditions, and beUavioural equations tUat define production and utility functions.

Income and Expenditure

In eacU region, all income accrues to a single regional UouseUold wUicU spends all its income on tUree goods: a composite private consumption good, a composite government consumption good, and a composite savings good, as sUown in Figure 3-

Income includes factor payments minus depreciation of capital, and net tax income, which includes tUe tax income (minus subsidy expenditure) for all forms of taxation

covered in tUe model - production taxes/subsidies, import export

taxes/subsidies, and consumption taxes/subsidies. Consumption taxes/subsidies include VAT, excise duties, and all otUer commodity taxation.

The regional disbursement of regional UouseUold income is a Cobb-Douglas nest, so that eacU item of expenditure - private, government, and savings, is a constant proportion of regional income.

National income and GDP are equal to regional income wUen tUe region comprises a single country. GDP at factor prices is calculated from net factor returns plus net

indirect taxation payments, GDP at market prices is calculated as private and

Figure 3-1: The Composite regional household

Net Tax and Tariff Income Net Factor Income

i

Regional Household

Cobb-Douglas

Private Expenditure Savings Government Expenditure

The utility level of the regional UouseUold is equivalent to regional welfare, and is equal to botU real income (net factor income plus net tax income) and real expenditure (the Cobb-Douglas function of private and government expenditure and savings). Figure 3-2 shows the structure of private demand in a tUree sector model, tUe sectors being Agriculture. Manufactures and Services. Private expenditure is a constant differences of elasticities (CDE) function of tUe tUree goods, altUougU in some applications tUis is treated as a CES or as a Cobb-Douglas nest. TUe CDE function is discussed in chapter 2. and allows some flexibility in tUe number of parameters tUat can be specified into tUe model. Typically, targets for own-price and income elasticities are used in tUe GTAP model, but altUougU tUe calibrated CDE function usually produces elasticities close to tUese targets tUis cannot be guaranteed.

Figure 3-2: Structure of private demand in a three sector model

Agriculture / \ Domestic Imported Agriculture Agriculture Private E / xpenditure :tures Domestic Imported Manufactures Manufactures CDE preferences Services

A

Domestic Services Elasticity of substitution Services 3-11

The lower part of Figure 3-2 shows that consumption of each good is a CES composite of domestic goods and imports, this being part of the Armington structure of the GTAP model. For each good, the domestic and imported goods Uave a constant

elasticity of substitution between tUem of wUicU is tUe same for every region

but varies between goods.

Government expenditure is structured in tUe same way as private expenditure, except that the top level of government demand is modelled using a Cobb-Douglas function rather than CDE.

Production Structures in the GTAP model

GTAP production structures use multi-level nests and tUe Armington assumption in much the same way as private and government demand. Figure 3-3 shows tUe production structure, wUere output at producers' prices is equal to output at market

Figure 3-3: Structure of production in a three sector model

Value-Added

Output at market prices

Output tax - output subsidy Output at producers' prices

C

Leontief. Elasticity of substitution = 0

Agriculture Manufactures Services

E

o >

por

t

Figure 3—4: Demand for imports

demand for imports of good i

Government demand for of good i

Total import demand for good i

Intermediate demand for imports of good from

each sector j

Elasticity of substitution of good i fi-om

each region r

prices minus the net output tax. Output is derived from value-added and intermediate modelled as a Leontief function so tUat for an n% increase in output, value- added use must increase by n% and tUe use of intermediate inputs must increase by n%. TUe value-added nest is modelled as a CES function, witU an elasticity of

substitution TUe intermediate nest is modelled using a Leontief function.

Each input is composed of domestic and imported goods, tUe Armington aggregation of which is modelled in the same way as for private and government demand.

The creation of capital goods is treated as a special production sector in tUe GTAP model, witU no factor use. A capital composition matrix determines wUicU goods are purcUased wUen a new unit of capital is required. As botU domestic and imported goods may be used to form capital, tUe capital composition matrix determines tUe parameters in tUe production function for capital, witU tUe same treatment of domestic and foreign goods as in any otUer production sector.

Trade and trade taxes

Figure 3-4 sUows tUe demand for imports of eacU good in eacU region. Total import demand is tUe sum of final import demand from private and government expenditure, and intermediate demand from firms, including capital formation. TUe Armington structure means tUat not only are domestic goods and imports treated as Ueterogeneous goods, but also tUat imports from different regions of origin are treated as imperfect substitutes. A CES function is used to determine tUe aggregation of imports from

Figure 3-5: Trade flows, trade taxes and margins

Exports at domestic market prices + Export tax - export Subsidy = Exports at world fob prices

+ Transport costs Imports at world cif prices

+ Import tariff- import subsidy = Imports at domestic prices

different regions into a single composite import good, witU an elasticity of substitution SIGM, between any pair of import sources. Lack of data means tUat values of

are not available, so is equal to twice altUougU witUin tUe control of tUe

modeller.

Figure 3-5 demonstrates tUe price linkage between export prices and prices.

On each bilateral trade route for exports of every commodity, exports are exported at the domestic market price for tUat commodity in tUe source region. An export tax (minus subsidy) is added to tUe market price to get tUe free-on-board (fob) price. Transport margins are added to tUe fob price to obtain tUe cost, insurance and freigUt

Figure 3-6: Sourcing of transport costs

Transport margins on each bilateral trade route for each traded

Global demand for transport services

Demand for individual goods in each region

Leontief: elasticity of substitution = 0

(cif) price. Finally, tUe price tUat tUe good is sold at in tUe importing region is calculated by adding import tariffs (minus subsidy) to tUe cif price.

a closed system, tUe payments to transport margins must be accounted for. Figure 3-6 shows a representation of the GTAP global transport sector, wUere global transport service demand is calculated by summing tUe demand for transport services from eacU commodity and bilateral trade route combination. Transport is a single real good/service witUin tUe model, witU a price reflecting tUe costs of transport. TUis good is composed by a Leontief structure, wUerein tUe production of global transport services uses goods from eacU region witU fixed coefficients for eacU region and commodity. Most of tUese coefficients are zero, as global transport services uses only the "trade and transport services" good, one of tUe goods in tUe GTAP database (usually aggregated witU otUer service sectors), but uses tUe output of tUis good in each region.

The market for goods

There are several different sources of demand for goods tUat are evident from tUe preceding sections, and tUese are summarised in Figure 3-7. Demand can first be considered as domestic demand and export demand.

Export demand is tUe demand firstly from consumption of imports in otUer

Figure 3-7: Demand for goods

Sales to transport services

Exports on each bilateral route

Private demand for domestic goods

Total demand for exports

Government demand for domestic goods

Intermediate demand for domestic goods in

each industry

Total domestic demand

Total Demand for good i in region r

and secondly from tUe use of transport services in tUe global transport sector. Sales to global transport are derived from tUe sourcing of transport costs illustrated in Figure 3-6. Demands for exports on bilateral routes are derived from Figure 3-5, linking exports along eacU bilateral route to tUe corresponding imports in tUe destination region. Import quantities are derived from tUe Armington structure, tUe "lower level" of which is sUown in Figure 3-4.

Domestic demand for goods is the sum of private demand derived from the private expenditure fianction outlined in Figure 3-2, government demand derived from the government expenditure function similar to tUat in Figure 3-2, and intermediate demands derived from tUe intermediate inputs of domestic goods in tUe production function sUown in Figure 3-3.

Savings and Investment: Macroeconomic closure in the GTAP model

The GTAP model uses a "Global Bank" to model the way in wUicU regional savings are disbursed to regional investment. TUe two main reasons tUat tUis is done are,

firstly, tUat bilateral ownersUip of capital data (wUicU country owns mucU of tUe

capital stock in eacU otUer country) is not included in tUe database and, secondly, tUis form of modelling allows many different savings closure rules to be adopted by tUe user.

By modelling global investment in tUe way sUown, international capital flows are included. Because of tUe national accounting identity

S - I = X - M

the way in wUicU savings and investment are modelled Uas implications for trade flows.

The standard GTAP model closure assumes tUat regional savings are a fixed

proportion of regional income, and tUat a global investment (as sUown in

Figure 3-8) is a Cobb-Douglas function of investment in eacU region. TUis closure means tUat:

S,

Global savings is tUe sum of regional savings:

Regional investment is a fixed proportion 5,. of global savings: I, =

Trade balances are equal to net savings, wUicU is determined by a region's income compared witU otUer regions' incomes:

The change in the trade balance is governed by income cUanges:

A - -

This has various implications, not least of wUicU being tUat tUe region witU tUe UigUest (nominal) cUange in income must necessarily experience an increase in its trade balance, witU tUe opposite Uolding for tUe region witU tUe lowest income growtU (or largest decline).

An alternative investment closure rule is tUat investment is not a fixed proportion of global savings, but takes wUatever value is necessary to keep trade balances constant.

Figure 3-8: International Savings and Investment in a three region model

Savings in the US _{Savings in the EU} Savings in the ROW

Global savings

in the US

Cobb-Douglas function

Investment in the EU Investment in the ROW

Then

- Y,

- 0 -

=

Figure 3-9 uses a flow chart to outline all tUe relationsUips in tUe GTAP model. TUe arrows indicate tUe direction of payments, witU corresponding goods and services being excUanged in tUe opposite direction.

At tUe top of Figure 3-9, tUe composite regional UouseUold for region r receives factor incomes and tax and tariff incomes. Figure 3-9 does not sUow wUere tax and tariff incomes come from. TUe composite regional UouseUold spends its income on private expenditure, savings, and government expenditure. TUis part of tUe diagram is tUe same as Figure

Private expenditure is allocated to eacU of i composite tradable commodities, eacU of which is in turn an aggregate of a domestic and an imported good. This part of Figure 3-9 is analogous to Figure 3-3, and is repeated for government expenditure.

Regional savings are collected in a global savings good, wUicU as sUown in Figure 3- 8, is then disbursed among tUe various regions.

Figure 3-3 outlined tUe structure of production, and tUe relevant part of Figure 3-9 for this is around tUe Domestic Production box. Payments to value-added are sUown as payments to factor demand for tUe f factors. Payments to intermediate inputs are shown separately for imported and domestic intermediates. TUe sources of sales of domestic production are sUown to be private domestic demand, government domestic demand, exports, domestic intermediates, and transport services.

Trade is sUown in tUe bottom rigUt quarter of Figure 3-9, wUere imports of good i (for three categories of use- private, government and intermediate) in region r are bougUt from s regions. An implicit balance of payments constraint means tUat regional

investment minus regional savings must equal exports minus and tUese

Figure 3-9: Value Flows in the GTAP model

Factor Incomes

(r)

Composite Regional Household (r) Private Expenditure (r) Savings Private Expenditure (i,r) Private Domestic (i.r) Tax and Incomes (r) Government Expenditure (r) Global Savings Private Imported (i.r) Investment (i.r) Domestic Production (i,r) Sources of Transport Services (i.r)

I

Imported Intermediates Domestic Intermediates Export Good (i.r) Global Transport Services Uses of Transport Services (i,r,s) Exports at cif prices (i,r,s) Exports at fob prices (i,r,s) Government Expenditure (i.r) Domestic (i,r) Government Imports (i,r) Imported Good (i.r) at domestic prices Imports at fob prices (i,s,r)

7

Implicit Balance of Payments condition (r)

In document Computable General Equilibrium Modelling and the Evaluation of Agricultural Policy (Page 83-93)