Footnotes

 

(1)

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 apply.  

(2)

Scaling units assures better numerical precision in equilibrium calculations.  

(3)

In 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 [1998] for a pedagogic introduction to dynamic general equilibrium analysis within the GAMS framework.  

(4)

These tools have been implemented with the assistance of Ken Pearson using modified versions of his SEEHAR.EXE and MODHAR.EXE programs.  

(5)

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.  

(6)

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 finite.  

(7)

For the sake of brevity, I present functional forms explicitly but represent unit demand and supply functions in reduced form, e.g. a_ir^D(p_ir^D, p_ir^X). The next section of the paper presents detailed specific functions in the GAMS/MCP implementation.  

(8)

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.  

(9)

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 price level.  

(10)

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 transport margin.  

(11)

Within the dataset investment inputs flow to the cgd sector, and demand for cgd sectoral output appears as the sole non-zero in the I_ir vector for each region r.  

(12)

When the elasticity of transformation between goods produced for the domestic and export markets is infinte, the market clearance conditions for D_ir and X_ir are merged, i.e. and prices p_ir^D and p_ir^X are replaced throughout the model by a single price index, p_ir^Y.

 

(13)

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).  

(14)

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 characters.  

(15)

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)).  

(16)

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 government.  

(17)

"va:" 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.  

(18)

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 Y_ir. 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) equations.  

(19)

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 r (A:RA(r)).  

(20)

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 input line.  

(21)

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.  

(22)

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) = SUM_i p_i x_i^*(p) where x_i^*(p) is the unit demand function.  

(23)

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 [1997].  

(24)

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.  

(25)

These 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.  

(26)

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.  

(27)

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.  

(28)

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.  

(29)

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.  

(30)

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.  

(31)

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.

 

(32)

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 array files.