The Global Forest Products Model (GFPM) is an economic model of production, consumption, and trade in forest products at the global level. It was developed as part of FAO's on-going work on forestry sector outlook studies. The GFPM is one of a series of spatial equilibrium forest sector models that have developed from the work of Gilless and Buongiorno (1987). Other international applications of the same modelling framework include ITTO (1993, 1995), FAO (1997), and Zhang et al. (1997).
The GFPM uses historical information and exogenous assumptions in a market equilibrium model to produce forecasts of global forest products market developments to 2010. The model is calibrated using 1994 as its base year and allows for the projection of consumption, production, capacity, prices and trade in forest products for 180 countries and territories and 14 different forest products categories. The purpose of this guide is to provide potential users with the information necessary to apply the model, to perform sensitivity analyses by altering the model's assumptions, to update the input data and to understand how changes can be made to the model's structure.
Implementation of the model requires three basic sets of data:
· data on prices and quantities produced, consumed, imported, exported for each product and country in the base year;
· estimates of production capacity for each product and country in the base year; and
· estimates of future economic growth rates and technology changes for each product and country.
The parameters used in the model include: demand elasticities for final products; supply elasticities for industrial roundwood; manufacturing costs; production capacity parameters; wastepaper recovery rates; and trade inertia coefficients. Each of these parameters are defined below.
The GFPM is based on price endogenous linear programming. This is a method of combining and utilizing regional information on supply and demand curves, manufacturing technologies and transportation costs in spatial sector models. Variants of this method have previously been used to model a number of agricultural and energy-related sectors (see, for example: Kennedy 1974; McCarl and Spreen 1980) as well as the forest sector (Adams and Haynes 1980; Kallio et al. 1987; Zhang et al. 1996).
The GFPM has both static and dynamic phases. In the static phase, it computes the quantities and prices that match demand and supply of all commodities in all countries in a given year. In the dynamic phase, it predicts the evolution of this spatial equilibrium from year to year. The dynamic phase predicts how production, consumption, trade and prices adjust gradually to changes in exogenous variables, such as economic growth.
The static phase of the GFPM solves a generalized version of Samuelson's (1952) spatial equilibrium problem to find the production and trade flows that match demand and supply in different regions and the corresponding market clearing prices.
the GFPM generalizes this problem to represent the production, transport, transformation, and consumption of 14 commodities (i.e. forest products) in 180 countries and territories in the world, referred to as regions1 in the model. A commodity may be either a primary raw material (such as industrial roundwood), a manufactured commodity (such as wood pulp) or a consumed commodity (such as newsprint). Fuelwood and "other industrial roundwood" are both primary raw materials and consumed commodities since they are consumed without further processing. The product flows in the GFPM are described in Appendix A.
In the GFPM, there are 181 demand regions and supply regions, in which the demand (supply) of a commodity is described by an equation that gives quantity demanded (supplied) as a function of price. These regions correspond to the 180 countries and territories used in the model and the world region. All countries and territories export to the world region and import from it.
The GFPM also has manufacturing regions, where the production of a commodity is modelled as a process described by activity analysis (as in Takayama and Judge 1964). Each process has a limited capacity. Within a process, a commodity is made with a particular input mix, defined by manufacturing coefficients (also called input-output coefficients) which specify the amount of each input needed per unit of output. Each input mix has a corresponding unit manufacturing cost.
The solution of the static phase of the GFPM is obtained by price endogenous linear programming (Hazell and Norton 1986). Figure 1 gives a simple example of how the model arrives at equilibrium prices and quantities of production, consumption, and trade for one commodity and two countries only. In countries A and B, the competitive market solution is the price-quantity combination that maximizes the value of the product to consumers minus the cost of supplying it (i.e. the area under the demand curve less the area under the supply curve). Without trade, in country A, this solution is the price Pa and quantity Qa2, while in country B the corresponding solution is price Pb and quantity Qb2. These are the competitive market solutions in the absence of trade. However, given the opportunity for trade, producers in country B can obtain a higher price in country A, while consumers in country A can buy more cheaply from country B. Trade will therefore have the effect of driving prices in both countries towards each other. The resultant global equilibrium price will be the one that maximizes the value of the product for consumers in both A and B, minus the cost of production for producers in A and B. If, for example, this price turns out to be Pc, then the associated equilibrium quantities supplied and consumed in country A would be Qa1 and Qa3, with the difference between these two amounts being imports from country B to A. Similarly, in country B, the equilibrium quantities supplied and consumed would be Qb3 and Qb1, and the difference between these two amounts would be exports from B to A.
Figure 1. Equilibrium price and quantities between two countries in the GFPM
The GFPM calculates global equilibrium prices and quantities for all countries and commodities simultaneously, by maximizing the difference between the value of products to consumers and the cost of production for suppliers throughout the world. The solution to this calculation is obtained using a linear programming algorithm which solves the multi-country, multi-commodity problem given in Appendix B.
The demand equations of the GFPM express consumption in a region as a function of gross domestic product (GDP) and price. These were estimated econometrically from international data, supplemented with other information. Industrial roundwood supply is represented in the GFPM as an upward-sloping curve, the price elasticity of which was selected with reference to the academic literature on this subject and expert opinion. Supply of other raw materials (fuelwood, other industrial roundwood, non-wood fibre, and waste paper) is represented as perfectly elastic up to an upper bound. For some countries upper bounds are also placed on the supply of industrial roundwood, to reflect physical or legal limits on production.
The input-output coefficients used in the GFPM (e.g., the amount of roundwood needed to produce one unit of sawnwood) were based on the academic literature on this subject and expert opinion. Manufacturing costs were then derived from roundwood and product prices using the input-output coefficients (see Appendix C). All costs and prices are expressed in the GFPM in US$ at 1994 prices and exchange rates. Estimates of manufacturing capacity were based on production data, available capacity data and expert opinion.
The above is a complete list of the information necessary to calculate equilibrium prices and quantities of production, consumption, and trade in the base year. The model, was calibrated by calculating the global market equilibrium for the base year and checking the model's results against the input data. The model's output was close to the input data for 1994. However, data limitations and inconsistencies make discrepancies inevitable, particularly for smaller countries.
The dynamic phase of the GFPM is a succession of static phases, one for each year in the forecast. The calculation of the short-term equilibrium in each year depends on the position of the demand, supply and cost curves and capacity availability in each year. Each year is linked to the next years by exogenous and endogenous variables. Exogenous trends include changes in manufacturing technologies, waste paper recovery rates and shifts in demand and supply curves (which are, in turn, driven by exogenous changes in GDP and timber availability, respectively). The GFPM simulates the rational behaviour of sub-optimizing agents who forecast the future imperfectly, based on past information. This approach is different to the assumption of inter-temporal optimization used in some other studies (see, for example: Sedjo and Lyon, 1990).
Global manufacturing capacity is projected in the GFPM as a function of past production and thus, past demand and prices. The share of global capacity increase going to each country depends on each country's shadow price of capacity. The shadow price is the increase in profit that producers in each country would get by increasing their capacity. If country A has a higher shadow price of capacity than country B, new capacity is more profitable in A than in B and, therefore, the GFPM projects that a greater share of the global increase in capacity would go to A than to B. Appendix B presents the mathematical formulation of the static and dynamic phases of the GFPM, including the capacity change equations used in the model.
The GFPM consists of one WORLD model, which is solved first, and four regional sub-models (Figure 2). The WORLD model has the same commodity detail as the regional models, but only four demand and supply regions: Africa, America, Asia, and Europe. The four regional models include country-level detail, with constraints to ensure that aggregate exports and imports of the region are equal to those predicted by the WORLD model.
The WORLD model must be solved first, to give projections of regional production, consumption, imports, exports and prices. These WORLD model results, which can be obtained quickly, have inherent interest, as they quickly give projections of aggregate global trends and can be used to explore the effects of different assumptions.
The WORLD model produces an essential input to the regional models in that export and import flows calculated in the WORLD model determine the aggregate trade flows in each of the regional models. For example, the aggregate Asian exports in the ASIA model must be equal to exports from Asia in the WORLD model. Similarly, total imports by Asian countries in the ASIA model must be equal to the WORLD model projections of Asian imports. This
insures that the projections of trade for each country in Asia are consistent with demand and supply in the rest of the world.
Figure 2. Structure of the WORLD Model
In practice, this consistency is accomplished by having separate entries in the regional models for world demand (i.e. exports from the region to the world) and for world supply (i.e. imports from the world to the region). Within the regional models then, the levels of total regional exports and imports change exogenously, according to the projections given in the WORLD model.
The countries and territories and commodities used in the GFPM are listed in Appendix A. Major data sources used in the GFPM (mostly from FAO databases) are shown in Table 1.
Table 1. Data sources for the GFPM
Data Type |
Source |
Production, Exports, Imports, Unit Values (used to calibrate the base year) Estimates of timer supply potential (used to shift the industrial roundwood supply curve between years) GDP growth rate estimates (used to shift the product demand curves between years) |
FAO Forest Products Yearbooks and FAO Forestry Statistics FAO background papers FAO projections |
1 Terms in italics are defined in the glossary.
