Structure of GTAP
∗
∗∗
∗
by Thomas W. Hertel and Marinos E. Tsigas
∗
This is a draft of Chapter 2: "Structure of GTAP," published in T.W. Hertel (ed.), Global Trade Analysis:
Modeling and Applications, Cambridge University Press, 1997.
I. INTRODUCTION AND OVERVIEW
The purpose of this chapter is to develop the basic notation, equations, and intuition behind
the GTAP model of global trade. The computer program documenting the basic model,
GTAP94.TAB, is available in electronic form via the Internet (see Chapter 6). It provides complete
documentation of the theory behind the model, and when converted to executable files using the
GEMPACK software suite (Harrison and Pearson, 1994), it forms the basis for implementing the
applications outlined in Part III of this book.
The organization of this chapter is as follows. We begin with an overview of the Global
Trade Analysis Project (GTAP) model. Next, we develop the basic accounting relationships
underpinning the data base and model. This involves tracking value flows through the global data
base, from production and sales to intermediate and final demands. Careful attention is paid to the
prices at which each of these flows is evaluated, and the presence of distortions (in the form of
taxes and subsidies). The relationship between these accounting relationships and equilibrium
conditions in the model is then developed. This leads naturally into a discussion of the implications
of alternative "partial equilibrium" closures whereby these equations are selectively omitted and the
associated complementary variables are fixed. The chapter then turns to the linearized
representation of these accounting relations. This is the form in which they are implemented in
GEMPACK, which solves the nonlinear equilibrium problem via successive updates and
relinearizations.
Section VI of this documentation turns its attention to the equations underpinning economic
behavior in the model. We deal in turn with production, consumption, global savings, and
investment. There is also a special discussion of macroeconomic closure in the GTAP model. This
material is reinforced in the closing section of the chapter by means of a numerical example using a
three-region, three-commodity aggregation, in which there is a shock to a single bilateral protection
rate.
II. OVERVIEW OF THE MODEL
1
Closed Economy Without Taxes
Figure 2.1 offers an overview of economic activity in a simplified version of the GTAP
model [see Brockmeier (1996) for a more comprehensive, graphical overview]. In this first figure,
there is only one region, so there is no trade. There is also no depreciation, and no taxes or subsidies
are present. At the top of this figure is the regional household. Expenditures by this household are
10
governed by an aggregate utility function that allocates expenditure across three broad categories:
private, government, and savings expenditures.
2
The model user has some discretion over the
allocation of expenditures across these types of final demand. In the standard closure, the regional
household's Cobb
category. However, real government purchases and savings can also be dictated exogenously (i.e.,
fixed or shocked), in which case private household expenditure will adjust to satisfy the regional
household's budget constraint.
This formulation for regional expenditure has some distinct advantages, as well as some
disadvantages. Perhaps the most significant drawback is the failure to link government expenditures
to tax revenues. Cutting taxes by no means implies a reduction in government expenditures in the
GTAP model. Indeed, to the extent that these tax cuts lead to a reduction in excess burden, regional
real income will increase and real government expenditure will likely also rise. This lack of fiscal
integrity is dictated by the fact that the GTAP data have incomplete coverage of regional tax
instruments. Therefore the model cannot accurately predict what will happen to total tax revenue,
and the user who is interested in focusing on government expenditure effects would be required to
make some exogenous assumptions in any case.
The greatest advantage of the formulation of regional expenditure displayed in Figure 2.1 is
the unambiguous indicator of welfare offered by the regional utility function. A particular
simulation might lead to lower relative prices for savings and the composite of government
purchases, and higher prices for the private household's commodity bundle. If real private purchases
fall, while savings and government consumption rise, is the regional household better off? Without
a regional utility function we cannot answer this question.
An alternative approach to this problem of welfare measurement involves fixing the level
of real savings and government purchases, and focusing solely on private household consumption as
an indicator of welfare. However, private consumption is only slightly more than 50% of final
demand in some regions. Forcing all the adjustment in the regional economy's final demand into
private consumption seems rather extreme. We believe that the assumption of fixed expenditure
shares dictated by the Cobb
That is, a rise in income implies an increase in savings and government expenditures, as well as
private consumption.
Since Figure 2.1 assumes the absence of taxes, the only source of income for regional
households is from the "sale" of endowment commodities to firms. This income flow is represented
by
VOA
(
endw
) which denotes
Value of Output at Agents' prices
of endowment commodities. (A
complete glossary of GTAP notation is provided at the end of this book.) Firms combine these
endowment commodities with intermediate goods (
VDFA = Value of Domestic purchases by Firms
at Agents' prices
) in order to produce goods for final demand. This involves sales to private
households (
VDPA = Value of Domestic purchases by Private households at Agents' prices
),
government households (
VDGA = Value of Domestic purchases by Government household at
Agents, prices
), and the sale of investment goods to satisfy the regional household's demand for
savings (
REGINV
). This completes the circular flow of income, expenditure, and production in a
closed economy without taxes.
11
Open Economy Without Taxes
Figure 2.2 [also taken from Brockmeier (1996)] introduces international trade by adding
another region,
Rest of the World
(ROW), at the bottom of the figure. This region is identical in
structure to the domestic economy, but details are suppressed in Figure 2.2. It is the source of
imports into the regional economy, as well as the destination for exports (
VXMD = Value of
eXports at Market prices by Destination
). It is important to note that imports are traced to specific
agents in the domestic economy, resulting in distinct import payments to ROW from private
households (
VIPA
), government households (
VIGA
), and firms (
VIFA
). This innovation departs
from most models of global trade, and was adopted from the SALTER model (Jomini et al. 1991). It
is especially important for the analysis of trade policy in regions where import intensities for the
same commodity vary widely across uses.
In moving from a closed to an open economy, we also require the introduction of two
global sectors, one of which is displayed in Figure 2.2. The
global bank
, shown in the center of this
figure, intermediates between global savings and regional investment. As will be discussed in more
detail below, it assembles a portfolio of regional investment goods, and sells shares in this portfolio
to regional households in order to satisfy their demand for savings.
The second global sector (not shown in Figure 2.2) accounts for international trade and
transport activity. It assembles regional exports of trade, transport, and insurance services and
produces a composite good used to move merchandise trade among regions. The value of these
services precisely exhausts the differences between global
fob
exports, and global imports,
evaluated on a
cif
basis.
III. ACCOUNTING RELATIONSHIPS IN THE "LEVELS"
Distribution of Sales to Regional Markets
The basic accounting relationships in the data base/model are best understood in the
context of a flow chart. For example, Table 2.1 portrays the sources of sectoral receipts in the
global data base. (In the data and the model all sectors produce a single output. Thus there is a one-
to-one relationship between producing sectors and commodities.) At the top of the figure,
VOA
(
i,r
)
refers to the
Value of Output at Agents' Prices.
(The general explanation for this choice of notation
is as follows: value/type of transaction/type of price. See the appendix to this chapter for an
exhaustive listing of variables used in the model and their description.)
VOA
(
i,r
) represents the
payments received by the firms in industry
i
of region
r
. As we will see, these payments must be
precisely exhausted on costs, under the zero pure profits assumption. The terms
PS
(
i,r
) and
QO
(
i,r
)
to the right of
VOA
represent the price and quantity indices that make up
VOA
. They will be
discussed in more detail below.
If one adds back the producer tax (or deducts the subsidy) denoted by
PTAX
(
i,r
), then we
arrive at the
Value of Output at Market prices
,
VOM
(
i,r
). This may be seen to be the sum of the
Value of Domestic sales at Market prices, VDM
(
i,r
) and the exports to all destinations, denoted as
Value of eXports of i from r evaluated at domestic Market prices (in r), and Destined for s,
VXMD
(
i,r,s
). In addition, we must take account of possible sales to the international transport
sector, denoted
VST
(
i,r
). These sales are designed to cover the international transport margins. They
12
are evaluated at market prices and face no further (border) taxes. Similarly, since domestic sales do
not cross a border, they do not face such taxes either.
In order to convert exports to
fob
values, it is necessary to add the export tax, denoted
XTAX
(
i,r,s
). Note that these taxes are written in a form that is destination
destination/source-specific trade policy measures at the level of
disaggregated
regions and
commodities (this varies by type of policy intervention), once the data base has been aggregated
over either commodities or regions, bilateral rates of taxation will vary due to compositional
differences. Therefore, it is important to maintain this bilateral detail in the modeling framework.
Once the export taxes are added in, we obtain the
Value of eXports at World prices by Destination,
VXWD
(
i,r,s
). The difference between this and the
cif
-based
Value of Imports at World prices by
Source,
VIWS
(
i,r,s
), is the international transportation margin:
VTWR
(
i,r,s
) refers to the
Value of
Transportation at World prices by Route
for commodity
i
, shipped from
r
to
s
.
At this point we have taken commodity
i
from its sector of origin in region
r
to its export
destination in region
s
. In order to evaluate these sales at internal domestic prices in
s
, it is
necessary to add import taxes,
MTAX
(
i,r,s
) to get
VIMS
(
i,r,s
), the
Value of Imports at Market prices
by Source
. These imports from alternative sources may then be combined into a single composite,
VIM
(
i,s
), the
Value of Imports of i into s at Market prices
. Just as sales in the rth market had to be
distributed across various destinations, so composite imports of
i
into
s
must be distributed across
sectors and households in the sth market. Possible uses of imports include:
VIPM
(
i,s
)
Value
of Imports by Private households, evaluated at Market prices: VIGM
(
i,s
)
Value of Imports by
the Government, evaluated at Market prices
; and
VIFM
(
i,j,s
)
Value of Imports by Firms in
industry j,
at Market price
. In a similar fashion, domestic sales, denoted
VDM
(
i,r
), must be
distributed across private household, government, and firms' uses, as shown at the bottom of Table
2.1.
Sources of Household Purchases
Having distributed sales across various markets and taken full account of intervening taxes
and transport margins, we are now in a position to consider household and firms' purchases within
each of these individual markets. Table 2.2 outlines the distribution of household purchases of
tradeable commodities. The top half of this figure pertains to private household purchases, denoted
VPA
(
i,s
), to represent the
Value of Private household purchases at Agents' prices.
This represents
the sum of expenditures on domestically produced goods,
VDPA
(
i,s
), and composite imports,
evaluated at agents' prices,
VIPA
(
i,s
). Once private household commodity taxes,
IPTAX
(
i,s
), are
deducted, this brings us to the
Value of Imports by the Private household at Market prices,
VIPM
(
i,s
), which is the point where we left Table 2.1. Similarly, deducting domestic commodity
taxes,
DPTAX
(
i,s
), from
VDPA
(
i,s
) yields
VDPM
(
i,s
), the
Value of Domestic purchases by the
Private household, at Market prices.
Thus we have completed the link between industry sales at
agents' prices (top of Table 2.1) and private household purchases at agents' prices (top of Table 2.2).
The bottom half of Table 2.2 is completely analogous, only
P
is replaced by
G
in order to represent
purchases by the government household.
13
Sources of Firms' Purchases and Household Factor Income
Next, turn to firms' purchases of intermediate and primary factors of production. The top of
Table 2.3 tackles the intermediate inputs, starting with the
Value of Firms' purchases of i, by sector
j, in region s at Agents' prices, VFA
(
i,j,s
). This may be broken into the domestic and imported
components,
VDFA
(
i,j,s
) and
VIFA
(
i,j,s
). Deducting intermediate input taxes,
DFTAX
(i,j,s) and
IFTAX
(
i,j,s
), reduces these values to market prices,
VDFM
(
i,j,s
) and
VIFM
(
i,j,s
), which are the
same as the values reported at the bottom of Table 2.1.
Firms also purchase services of nontradeable commodities, which in this model are termed
endowment commodities
. (In the current data base, these include: agricultural land, labor, and
capital.) The next part of Table 2.3 traces the value flows from the firms employing these factors of
production, back to the households supplying them. Note that by deducting taxes on endowment
i
used in industry
j
,
ETAX
(
i,j,s
), we can move from the
Value of Firms' purchases at Agents' prices,
VFA
(
i,j,s
), to the
Value of Firms' purchases at Market prices, VFM
(
i,j,s
). The final section of Table
2.3 makes the link between firms' receipts [i.e.,
VOA
(
j,s
)], as developed in Table 2.1, and firms'
expenditures [i.e.,
VFA
(
i,j,s
)], as shown in Table 2.3. Zero pure economic profits means that
revenues must be exhausted on expenditures, once accounting for all tradeable (i.e., intermediate)
inputs and endowment (i.e., primary) factors of production.
Table 2.4 details the sources of household factor income. Here, it is necessary to
distinguish between endowment commodities that are perfectly mobile, and therefore earn the same
market return (
ENDWM_COMM
), and those that are sluggish to adjust and that therefore sustain
differential returns in equilibrium (
ENDWS_COMM
). In the former case, we may simply sum over
all usage of the factor
supply of primary factor
i
in region
s
,
HTAX(i,s)
, in order to obtain the
Value of this endowment's
"Output" at Agents' prices
(
VOA
). The latter is the amount actually received by the private
household supplying the factor in question.
In the case of the sluggish endowment commodities (e.g., land), shocks to the model will
introduce differential price changes across sectors. This is reflected in the presence of an industry
index (
j
), in the price component of
VFM
(
i,j,s
). These differential prices are then combined into a
composite return to the sluggish endowment, at market prices, via a unit revenue function. The
resulting
Value of endowment Output at Market prices, VOM
(
i,s
), is then handled in the same way
as for mobile commodities, deducting household income taxes to arrive at the
VOA
(
i,s
).
Disposition and Sources of Regional Income
When taxes are present, the computation of disposable income for the regional household
in Figures 2.1 and 2.2 becomes much more complex. At the top of Table 2.5, we have the condition
that expenditures on private, government, and savings commodities must precisely exhaust regional
income. This is followed by the expression that decomposes income by source. We begin by adding
up endowment income (recall Figures 2.1 and 2.2). Note that all such income earned within a region
accrues to households in that same region. From this, we must deduct depreciation expenses
required to maintain the integrity of the initial capital stock,
VDEP
(
r
), thereupon adding net tax
receipts and rents associated with any quantitative restrictions.
Rather than keeping track of individual tax/subsidy flows in the model, the approach taken
here is to compare the value of a given transaction, evaluated at agents', market, or world prices. If