THE GTAPinGAMS CORE STATIC MODEL

The GTAPinGAMS model is a static, multi-regional model of the global economy that determines the production and allocation of goods. Sectors are perfectly competitive and outputs are produced by linear homogenous production functions. Factors of production are perfectly mobile between sectors in each region but are immobile internationally. There is a representative consumer in each region who maximises utility over private consumption subject to fixed levels of public expenditure and investment demand. Interactions between regions are captured by a full set of bilateral trade flows. Transport costs, export taxes and support and protection data, expressed in the form of ad valorem equivalent, tariff and nontariff barriers are also included.

Figure 5.1

Production in the GTAPinGAMS model Output

σ = 0

Intermediate Inputs (σ = 0 over j)

σ = CES Value Added

σ = CD

. . .

Domestic Imported Factor f Factor k

5.3.1 Production

Production technology is characterised by a multilevel nest of intermediate inputs and primary factors, as depicted in Figure 5.1. A Leontief nest of primary factors and intermediate inputs composites produces output. Intermediate inputs by product type are combined using a further Leontief nest and the value-added composite is derived from a Cobb-Douglas aggregation of primary factors.

Following Armington (1969), intermediate inputs are defined by a constant elasticity of substitution (CES) aggregation of the domestic variety and a composite of imported varieties. A further Armington aggregation, of imports from different regions, is employed to generate the import composite (see sub-section 5.3.3).

The value-added nest in the GAMS model differs from that in the GEMPACK model. Specifically, the value-added nest in the GEMPACK model utilises a CES and not a Cobb-Douglas aggregator.

Figure 5. 2

Consumption in the GTAPinGAMS model Consumption Output

Government (σ = CD over i)

σ = CES Investment Private (σ = CD over i) σ = CES

Domestic Imported Domestic Imported

5.3.2 Consumption

Consumption is each region is determined by a representative agent, who allocates expenditure across public demand,³ investment demand and private demand in order to maximise utility. Expenditure is equal to the aggregate of factor income, tax revenue and an exogenous net transfer from other regions. The structure of consumption demand is illustrated in Figure 5.2. Private and public demand are determined by utility-maximising behaviour, subject to the constraint that public expenditure is fixed in absolute value. Private demand is nested in several levels. At the top level, preferences are defined by a Cobb-Douglas aggregation of composite commodities, these being derived from Armington aggregations of domestic and imported varieties (see sub-section 5.3.3). Public sector preferences are modelled in an identical fashion to private tastes. This allows the composition of public expenditure to respond to changes in relative prices, even though the level of public expenditure is exogenous. Investment

3 Public demand refers to demand by the public sector. There are no publicly produced goods in model.

demand is exogenous. New capital is produced in the same way as tradable commodities, except that primary factor services are not required.⁴

Consumption in the GAMS model differs from that in the GEMPACK version in two ways. First, the top level of the consumption nest in the GEMAPCK model is Cobb-Douglas. The aggregate value of government purchases and investment expenditure in the GEMPACK model, therefore, can change so long as they remain a constant share of total expenditure, unlike in the GAMS model where both government and investment expenditure are fixed in absolute value. Second, there is a difference in the functional form of the private consumption nest in the two models. Instead of using a Cobb-Douglas aggregator, composite consumption goods (of domestic and imported varieties) are aggregated using a constant difference in elasticities (CDE) function in the GEMPACK model.

Accordingly, preferences over private demand are homothetic in the GAMS model but non-homothetic in the GEMPACK version.

5.3.3 Imports

There are three sources of demand for intermediate inputs: (a) by producers as intermediate inputs, (b) by the public sector, and (c) by the private sector. It is assumed that import shares have the same regional composition in the three sources but the aggregate share of imports may differ across sources.

4 Primary factor services are embodied in the intermediate inputs assembled by the investment sector.

Figure 5.3

Imports in the GTAPinGAMS model

Government Imports Intermediate Imports Private Imports

Imports σ = CES

. . .

From Regions r (gross of transport costs)

σ = 0 From Region s (gross of transport costs)

σ = 0

Transport Services

σ = 1 From Region r (net of transport costs) Transport Services

σ = 1 From Region s (net of transport costs)

From Region r From Region s From Region r From Region s

Imports are differentiated by region of origin using an Armington aggregation and incur transport costs. Transport costs are proportional to trade values and therefore enter in a Leontief nest. Transport services are produced by a Cobb-Douglas aggregation of international transport inputs from different countries.⁵ The aggregation of imports and transport costs is illustrated in Figure 5.3. The domestic price of imports arriving at regions r from region s is equal to the summation of the fob export price in region s, per-unit export tax revenue accruing to region s, transport costs, and the import tariff levied by region r.

5.3.4 Closures

External and government closure in the two models are similar. Both models are global so one regions imports are sourced from other regions production, which negates the need to explicitly specify an external closure rule. Although government expenditure is variable in the GEMPACK model but fixed in the GAMS model, both treat the private and public sector as a single consumer.

Although both models are static, and hence investment does not increase the production capacity of sectors in future periods, a significant difference between the GAMS and GEMPACK models concerns macroeconomic closure. The GAMS model uses what Dewatripont and Michel (1987) classify as a non-neoclassical closure while macroeconomic closure in the GEMAPCK model is neoclassical. The two different macroeconomic closures can best be illustrated by

5 International transport services are exclusively provided by the trade and transport (t_t) sector.

equating national expenditure from the sources and uses sides. This implies that savings (S) minus investment (I) is equal to exports (X) minus imports (M)⁶

M X I

S− = − (5.1)

In the GTAPinGAMS model, the current account balance is exogenous, which, with rigid investment, fixes regional savings. Since both investment and savings in each region are exogenous, the imposition of equilibrium between global savings and global investment in the benchmark equilibrium ensures that such an equilibrium is present in post-simulation equilibria.

Macroeconomic closure in the GEMAPCK model is more sophisticated. The left-hand side of equation (5.1) is permitted to adjust in such a model, which necessitates an instrument to ensure that the demand for global investment equals the demand for global savings. This is achieved through a “global bank” whose purpose is to assemble savings and disburse investment. The global bank gains revenue from the sale of a homogenous savings commodity to regional households, which is used to purchase shares in a portfolio of regional investment goods. In such a setting, equilibrium between global savings and investment is achieved by the size of the portfolio adjusting to accommodate any changes in global savings. The global bank allocates investment across regions according to one of two possible decision rules. The first equalises regional rates of return to capital across regions and the second assumes that regional and global investment move together so that the regional composition of the capital stock is unaltered.

6 Strictly speaking, the right-hand side of equation (5.1) should include international transfer receipts. In the GTAP database, due to data constraints, however, international transfer receipts are set equal to zero and savings are derived residually.