Our development of a multiple equation model of demand and supply is motivated by two objectives: (1) to improve the explanatory power of demand models, and (2) to explain product supply. For the demand equations, the multiple equation approach allows us to explore the board question of substitution. Aspects of this question were examined briefly in ETTS IV, where the inquiry focused on the role of the price of substitute materials in the demand for wood products. For a number of reasons, including the high degree of aggregation and weak data on prices of substitutes, this approach was not successful.
Our approach to the analysis of substitution differs from that in ETTS IV. In many respects, the simplest type of substitution is in choosing alternative sources of supply or in directing production to alternative markets.5 If this type of substitution takes place, and it is significant, there are a number of implications for both demand and supply modeling. First, the general model for consumption and production must be expanded to include more than one price. Consumption, for example, will be determined by prices of the broad alternatives sources of products: the domestic market and imports. Similarly, total production may be determined by prices in both the domestic market, and the export market.
That is,
| CONSUMPTION | = fn (Pd, Pm, X); and | (1) |
| PRODUCTION | = fn (Pd, Px, Z), | (2) |
where Pd is the price of domestically-produced goods, Pm is the price of imports, Px is the price of exports, X is additional factors that determine demand (demand shifters), and Z is additional factors that determine supply (supply shifters).
However, in order to explore the broad hypotheses of substitution described above, we must further modify equations (1) and (2). In particular, we must divide consumption and production into their respective components. Total consumption consists of consumption from imports, and consumption of domestically produced commodities; total production consists of production for domestic markets, and production for export markets.
Expanding equations (1) and (2) to reflect the components of consumption and production yields the following set of equations:
| QDD = f(Pd, Pm, DD); | (3) |
5 Other types of substitution include material-for-material, and technology-for-material; ETTS IV examined material-for- material substitution. See Brooks (1993) for further discussion of substitution issues in forest products markets.
| QM = f(Pd, Pm, DM); | (4) |
| QDS = f(Pd, Px, SD); and | (5) |
| QX = f(Pd, Px, SX), | (6) |
where QDD is demand for domestically-produced products, QM is import demand, QDS is production (supply) for domestic markets (QDS = QDD), QX is production for export markets, Pd is the price in domestic markets, Pm is import price, Px is export price, DD are demand shifters for the domestic market, DM are demand shifters for import demand, SD are supply shifters for the domestic market, and SX are supply shifters for the export market.
Using equations (3) – (6) as an analytical framework differs from previous approaches to both demand and supply modeling. Although the factors used to explain supply and demand are not an innovation, and there are numerous examples of import demand and export supply models for forest products, the framework itself is the departure. Equations (3) and (4) are demand equations separated by the origin of supply; equation (3) is demand from domestic production, equation (4) is import demand. The specification of both equations is consistent with demand models such as those in previous TTS, and those found in the general literature. However, the notable difference here is that multiple prices are used in place of a single price to explain demand.
In equation (3), domestic price (Pd) is the “own price” and is expected to have a negative sign, as is standard for a demand equation; the sign on import price can be either positive (indicating substitution) or negative (indicating that imports are a complement). Similar expectations hold for the signs on prices in equation (4); import price should have a negative sign, and domestic price may have either a positive or a negative sign.
The demand shifters in equations (3) and (4) may vary, but we use identical specifications for the two equations based on the assumption that domestic production and imports are generally homogenous and, for most products and countries, have similar end uses. In specifying and estimating equations (3) and (4) for solid wood products, we use the end-use elasticity approach that was initially developed by Baudin and Lundberg6, and used by Lundbäck in ETTS IV. In this approach to identifying demand shifters, a composite index is constructed in order to take into account information from a variety of end use sectors. The construction of the index is described in more detail below. For paper and paperboard products, gross domestic product (GDP) is used to shift the two demand equations.
6 Anders Baudin and Lars Lundberg, ‘Analysis of the demand for forest products; a preliminary survey of objectives, methods, and data,’ manuscript prepared in the framework of the FAO Programme in Outlook Studies for Supply and Demand of Forest Products, Rome, Italy.
The formulation for supply equations (5) and (6) parallels the structure of the demand equations: domestic markets and export markets are alternative destinations for production: producers may treat these markets as substitutes. Therefore, total production (QDS + QX) will adjust in response to prices in both domestic markets and export markets. Here, negative cross-price elasticities will indicate substitution, as the expected sign for price in a supply equation is positive. In equations (5) and (6), supply shifters include manufacturing costs and raw material costs.
In specifying costs for the supply equations we focus on raw material costs for two reasons. First, data on all elements of manufacturing costs for each sector of the forest products industry in each country were not available. However, log prices, chip prices, and pulp prices generally were available. Second, we emphasize raw material costs because these permit explicit consideration of the effects of timber availability on domestic production and export supply in scenario development.7
Additional factors must be incorporated in equation (6) to adequately explain export supply. These additional factors include an indicator of the real exchange value of a country's currency, and the level of demand in export markets. Export price (Px) reflects prices received by producers for exported products; prices paid by consumers in overseas markets are in local currencies, and competitiveness in these markets--and therefore the level of exports--depends in part on changes in the exchange value of the country's currency. The ideal indicator would be a broadly-based, trade-weighted index of a country's exchange value. However, where such an index was not available, the bilateral exchange rate with a major currency (such as the United States dollar) was used as a proxy for the broader measure of a country's currency value.
The level of demand in external markets also is an important factor in determining a given country's exports. In fact, an ideal approach would explicitly consider demand and supply factors in all markets. This more complex system of equations would incorporate factors influencing demand in external markets, and competition from other suppliers in these markets. For this study, however, more complete specification and estimation of trade relationships was not possible. We incorporate export market activity by using a population-weighted index of real GDP in the four largest European countries (France, Germany, Italy, and the United Kingdom) in each of the export supply equations. Because this is a demand indicator used as an explanatory factor in what is nominally a supply equation, we treat equation (6) as the reduced-form of the more complex system of equations.
This multiple equation approach offers a number of theoretical and practical advantages for modeling demand and supply. First, factors important in domestic markets can be separated from factors important in external markets. Second, an important aspect of (potential) substitution behavior can be directly examined. However, having specified a “fully-developed” multiple-equation framework, we were almost immediately forced to make modifications to account for differences observed across the countries we analyzed. In some countries, one or more equations cannot be estimated because the quantity is negligible. For example, Sweden, Finland, and Norway import negligible quantities of coniferous and non-coniferous sawn wood. An effort to estimate import demand equations for these countries and products was unlikely to be successful. Similarly, exports of some products from some countries also are small and irregular; successful models are unlikely here, too.
In addition, all four equations represent an over-identified system for projection purposes: along with import demand and export supply (if both trade flows occur), only one equation must be estimated for the domestic market to fully-define production and consumption. In developing projections of demand and supply for countries in Group I we estimated more than 100 demand equations, and nearly 40 export supply equations.8 For most countries and products we estimated the domestic market quantity as a demand equation (equation 3) for projection purposes. Data for demand prices and demand shifters were better than the corresponding data necessary to estimate and project supply equations.
For both demand and supply equations, each country was analyzed separately. Previous TTS, and other large-scale studies such as the FAO Outlook Studies (FAO 1986, 1991) have employed a cross-section, time series approach. Although this approach offers benefits in terms of the degrees of freedom for model estimation, the approach also imposes some restrictions on elasticities estimates. Typically, consumption in countries with similar income levels is assumed to respond identically to changes in prices and income (that is, these countries are assumed to have identical price and income elasticities). We felt that there was greater benefit from estimating these relationships using prices and costs specified in domestic currencies, and that there was an advantage to an approach that allowed model specification and estimated elasticities to vary across countries. Our single-country approach also permitted use of simultaneous equation estimation methods, where this approach yielded statistically-superior results. Although the simultaneous equation approach to estimating the parameters of equations 3–6 did not produce parameter estimates substantially different from parameters estimated using single-equation estimation methods, our results do vary across countries.
An exception to the single-country approach (for the countries in Group I) was used to estimated models of paper and paperboard exports for the Nordic countries. The single-equation approach to estimating export supply for paper and board products for the Nordic countries (Finland, Norway, and Sweden) produced results that were not satisfactory. Although the overall fit of the equations was good, and coefficients were generally significant, the signs on price coefficients were consistently unexpected (negative), and elasticities were quite high. These initial results would have produced unreasonable projections. Therefore, we estimated export supply models for these countries with a time-series, cross-section approach. In order to minimize the effect on elasticity estimates caused by differing scales of currency units, prices and costs were converted to a constant currency basis (for each country) and then converted to an index. Similarly, quantities were converted to an index to adjust for differences in scale of exports.
