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- Development of these tools has been supported by the Electric
Power Research Institute and the United States Department of Energy
in joint work with David Montgomery, Paul Bernstein and Thomas
Hertel. I have had excellent research assistance from Mustafa
Babiker and Miles Light. Robert McDougall, Gerard Malcolm, and Ken
Pearson were helpful answering my questions about the GTAP database,
and Alex Meeraus has sorted out many subtle points in GAMS. Earlier
work with GTAP was supported by the World Bank in collaborative work
with David Tarr and Glenn Harrison. Renger van Nieuwkoop, Randy
Wigle, Joseph Francois and Jesper Jensen provided some very helpful
editorial suggestions on an earlier draft. The usual disclaimers
units assures better numerical precision in equilibrium
extensions of the core static model, the GTAPinGAMS framework can be
readily employed to study adjustment paths, but a description of
these techniques lies beyond the scope of the present paper. See
Rutherford, Lau and Pahlke  for a pedagogic introduction to
dynamic general equilibrium analysis within the GAMS framework.
- These tools have been implemented with the assistance
of Ken Pearson using modified versions of his SEEHAR.EXE and
- Under a maintained assumption of perfect
competition, Mathiesen may characterize technology as CRTS without
loss of generality. Decreasing returns are accommodated through
introduction of a specific factor, while increasing returns are
inconsistent with the assumption of perfect competition. In this
environment zero excess profit is consistent with free entry for
atomistic firms producing an identical product.
- Model files in the GTAPinGAMS distribution
accomodate an infinite elasticity of transformation between domestic
and export markets as they are treated in the GTAP implementation in
GEMPACK. For simplicity, my algebraic exposition in this paper
focuses on the case in which the elasticity of transformation is
- For the sake of brevity, I
present functional forms explicitly but represent unit demand and
supply functions in reduced form, e.g. airD(pirD,
pirX). The next section of the paper presents detailed specific
functions in the GAMS/MCP implementation.
- There is no
reason that this functional form should be employed in every study.
For example, when we use the GTAP dataset to study energy and
environmental issues, it is important to account for the nature of
substitution possibilities among energy carriers as well as between
energy and non-energy inputs to production; so in those applications
a nested CES function is employed in which energy trades off against
value-added with a non-zero elasticity of substitution.
- There are some simplifications here. For example,
the regional composition of transportation services is identical
across all bilateral trade flows. Furthermore, while the dataset
incorporates explicit trade and transport margins on international
trade flows, wholesale and retail margins on domestic sales are
ignored in the dataset, so there is some asymmetry in the database's
- The model formulation assumes that the export
tax applies on the fob price (net of transport margins), while the
import tariff applies on the cif price, gross of export tax and
- Within the dataset investment inputs flow to the
cgd sector, and demand for cgd sectoral output
appears as the sole non-zero in the Iir vector for each region
- When the elasticity of
transformation between goods produced for the domestic and export
markets is infinte, the market clearance conditions for Dir and
Xir are merged, i.e.
and prices pirD and pirX are replaced throughout the model
by a single price index, pirY.
- The distribution files
provide representations of the core model as a constrained nonlinear
system (CNS) and a square system of nonlinear constraints within a
conventional nonlinear program (NLP).
- Users can define
their own aggregations of the GTAP data and use any labels to
describe regions. For technical reasons, if a GTAP dataset is to be
used with MPSGE, then regional identifiers can have at most 4
- I have omitted exception operators
from the variable and function declarations to make the code easier
to read. In most aggregations of the dataset, the model shown here
is operational. In highly disaggregate models, however, not all
goods are produced in all regions, and it is necessary to specify,
for example, Y(i,r)$(vdm(i,r)+vxm(i,r)).
- The output tax is defined on a gross basis.
For example, the value of sales in the domestic market gross of tax
equals vdm(i,r) of which (1-ty(i,r))*vdm(i,r) is
returned to producers and ty(i,r)*vdm(i,r) is paid to the
is a nesting idetifier. These names are arbitary and may have from one to
four characters. Two reserved names are "s:" which
represents the elasticity of substitution at the root of the inputs
tree and "T:" which represents the elasticity of
transformation at the root of the output tree.
- Readers unfamiliar with the MPSGE model
representation may wish to refer back to the algebraic equilibrium
conditions. The specification of the $PROD:Y(I,R) block
automatically generates a zero profit condition for Yir. It
also generates terms in the market clearance equations for all
associated inputs and outputs. In this function the affected markets
include the domestic output market, the market for export of good i
from region r, markets for Armington composites entering
intermediate demand, and primary factors markets. For this reason
the tabular format is very compact - in essence, the user only needs
to specify the dual (zero-profit) conditions and the modeling
language automatically generates the primal (market clearance)
- Note that export taxes on
sales from region s in region r are accrue to the
representative agent in region s (A:RA(s)) while
import tariffs are paid to the representative agent in region
- A .tl suffix alerts MPSGE that a
set of nests are being declared. When an input is to be associated
with one of these nests, the set label flag must be specified on the
- In terms of
compuational complexity, the cost of solving a system of equations
increases somewhere between the square and the cube of the number of
dimensions, although in large-scale implementations such as the
GAMS/MCP solver PATH or MILES, computational complexity depends on
both the number of equations and their density.
- Of course it is mathematically equivalent to use the
cost function or an expression for cost based on the unit demand
functions, i.e. if:
then c(p) = SUMi pi xi*(p) where
xi*(p) is the unit demand function.
- There is a subtle
but important point with regard to the complex system of taxes in
GTAP. Users should not assume that because the dataset has a tax
instrument the associated tax rates have a strong
empirical basis. The research work in putting together GTAP has
tended to focus on trade taxes (import tariffs and export taxes), and
all other tax rates come directly from the national input-output
tables. If you undertake an analysis in which the structure of the
domestic tax system plays an important role, it is highly recommended
to collect and update the benchmark tax rates. For an example of how
a domestic tax system may be introduced in a GTAP model, see
Harrison, Rutherford and Tarr .
- In the MPSGE model a single entry in the import
activity introduces both the import and export taxes, and given a
description of taxes applying to the producer, the modelling language
automatically generates the appropriate income entries, greatly
reducing the likelihood of an accounting error.
programs should work with GAMS 2.25.089 or later, but the matrix
balancing relies on some significant improvements in robustness which
Michael Ferris and his students have achieved with the latest release
of PATH. If you are running GAMS with version 2.25 and encounter
problems with the rebalancing routine, you could try unzipping a
newer version of PATH into the GAMS system directory, first
renaming your existing GAMS2PTH.EXE to GAMS2PTH.BAK.
- Note that sectoral and regional
identifiers in these models are all three characters in length. If
you are planning to use the GAMS/MPSGE version of the GTAPinGAMS
model, then regional identifiers are limited to at most four
characters and sectoral set labels may have at most 10 characters.
- This dataset is compatible with the GTAP-E
satelite energy tables which represent all energy-related
transactions in physical units. A subsequent paper will describe how
GTAP-E data can be introduced into the GTAPinGAMS model.
- N.B. The BUILD script only works
properly with the distribution header array file for the full GTAP
database, GSDDAT.HAR. This program is not designed to work
with aggregated GTAP datasets which have been constructed in GEMPACK.
- If you are using GAMS/MPSGE, you need to
restrict regional identifiers to 4 or fewer characters. Commodity
and factor names may have at most 10 characters.
- The mapping file is copied if
one can be found. This is done to assure that it is always possible
to trace the aggregation definitions for any dataset.
- The first calculation which is
performed is a benchmark replication check in which a solver
may report "INFEASIBLE". This simply means that there is some
imprecision in the data, as is subsequently reported in the listing
as "Benchmark tolerance". Any number on the order of 1.e-4
or smaller indicates a reasonably precise dataset.
- See CONVERT.GMS for details on
conversion from har to zip format, and see GAMS2HAR.GMS and
HAR2GAMS.GMS in the INCLIB directory for
general-purpose tools for data transfers between GAMS and header
October 23, 1998