The World Trade Model: Revised Estimates
Author: GRANT SPENCER

This paper gives a general description of the revised version of the world trade model that is currently in use in the Research Department of the International Monetary Fund, both in research applications and as an input into the world economic outlook forecasting exercise.1 The paper describes the economic structure of the model and emphasizes the revisions that have been made since the previous description of the model.2 The discussion concentrates on the price and volume equations for trade in manufactures between the 14 industrial countries. It is this group of equations that dominates the overall behavior of the model, and it is here that the most significant revisions have been made.3

Abstract

This paper gives a general description of the revised version of the world trade model that is currently in use in the Research Department of the International Monetary Fund, both in research applications and as an input into the world economic outlook forecasting exercise.1 The paper describes the economic structure of the model and emphasizes the revisions that have been made since the previous description of the model.2 The discussion concentrates on the price and volume equations for trade in manufactures between the 14 industrial countries. It is this group of equations that dominates the overall behavior of the model, and it is here that the most significant revisions have been made.3

Introduction

This paper gives a general description of the revised version of the world trade model that is currently in use in the Research Department of the International Monetary Fund, both in research applications and as an input into the world economic outlook forecasting exercise.1 The paper describes the economic structure of the model and emphasizes the revisions that have been made since the previous description of the model.2 The discussion concentrates on the price and volume equations for trade in manufactures between the 14 industrial countries. It is this group of equations that dominates the overall behavior of the model, and it is here that the most significant revisions have been made.3

The world trade model attempts to explain the volumes and unit values of merchandise exports and imports for the 14 largest industrial countries and for 4 aggregate regions making up the rest of the world (Table 1). The model is not a world macromodel along the lines of that developed under Project LINK.4 In particular, it does not attempt to explain the major national macro-economic aggregates; rather, it takes rates of domestic inflation and real domestic demand growth as given and attempts to generate a set of aggregate trade flows, both in value and volume terms, that are consistent with these domestic variables.

Table 1.

Summary of Model Specification

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According to Standard International Trade Classification.

As shown in Table 1, the main exogenous inputs into the model include, for each industrial country, the major components of real domestic demand, hourly earnings in manufacturing, the gross national product deflator, the nominal exchange rate, and potential output and employment (in terms of man-hours) in manufacturing. The U.S. dollar prices of petroleum products and a wide range of other primary commodities also enter the model exogenously. Taking these variables as given, the model then generates estimates of the trade volume and unit value variables on a semiannual basis for each country and for four broad commodity classifications. In a forecasting context, these estimates are bench-marked on alternative sets of historical data to give projected levels of volumes and values of total merchandise trade on both a customs and a balance of payments basis. Disaggregated trade flows under the four commodity classifications are provided solely on a customs basis.

The sets of endogenous and exogenous variables in the present version of the model, as shown in Table 1, are not identical to those described in the Deppler-Ripley paper (p. 150). For example, the previous model contained equations that attempted to explain the volume of fuel exports of industrial countries; some obvious difficulties in this area led to the elimination of these equations, and fuel exports are now taken as exogenous.5 On the other hand, a number of variables that were previously assumed exogenous are now determined within the model. These include domestic wholesale prices for both manufactures and raw materials in the industrial countries and the volume of trade in automobiles between Canada and the United States. The inclusion of equations to determine domestic wholesale prices allows the set of variables exogenous to the industrial country prices block to be reduced to only unit labor cost and commodity price variables, while the U.S.-Canada auto trade equations contribute to an improvement in the model’s explanation of the aggregate levels of U.S. and Canadian exports and imports of manufactures.

After the various structural modifications were introduced, all of the equations of the model were re-estimated on a sample of semiannual data extending from the beginning of 1962 through the second half of 1979. This involved a seven-semester extension of the sample used in the previous version of the model, introducing data for the three and a half years from the second half of 1976 through the second half of 1979. Extension of the sample to cover this period brought in observations representing an additional cyclical expansion of demand in industrial countries and a corresponding expansion in the volume of world trade. Furthermore, the extension of the sample provides additional quantitative information on the longer-term effects of the first oil shock and of the initial impact of the second oil shock, thus offering scope for more precise estimation of the model’s trade price elasticities. The equations of the new version of the model were estimated singly, using either ordinary least squares or instrumental variable techniques. In several equations, coefficients were estimated subject to a priori linear restrictions. In particular, compared with the previous version of the model, greater use was made of prior information in the equations specifying the behavior of export and import unit values for manufactures. Finally, in estimating the lagged effects of relative prices on trade volumes, a more flexible scheme of distributed lag restrictions was adopted.

The discussion of the model is divided into two sections, corresponding to the two main blocks of equations: industrial country price equations and industrial country volume equations. The general functional forms of the equations for trade in manufactures in each block are presented in Tables 2 and 3, while country-by-country coefficient estimates are set out separately in Tables 4 through 11. For each block, both the general descriptions and the algebraic functional forms describe structural equations for a single country (i), with foreign variables constructed using the partner-country index (j). Detailed descriptions are not given for equations explaining unit values and trade volumes of nonmanufactured commodities, nor for equations explaining the total trade of the four regions. These equations are not substantially different from those adopted by Deppler and Ripley; details of functional forms and updated estimates are given in Spencer (1984).

Table 2.

World Trade Model: Specification of Price Equations for Trade in Manufactures by Countryi

(i = 1 to 14, and all summations are from 1 to 14)

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Endogenous variables are listed in order of appearance in the equation set; exogenous variables are listed alphabetically.

Table 3.

World Trade Model: Specification of Volume Equations for Trade in Manufactures for Countryi

(i = 1 to 14, and all summations are from 1 to 14)

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Variables endogenous to the volume equations are listed in order of appearance in the equation set; exogenous variables are listed alphabetically.

Table 4.

Fourteen Industrial Countries: Estimates of Export Unit Value Equations for Manufactures, Second Half 1962-Second Half 19791

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See Table 2, equation (1). The f-statistics are in parentheses. The tabulated estimates may differ slightly from the parameters used in the current forecasting version of the model.

The exact algebraic form of the equations and the variable definitions are given in Table 2. All variables are log first differences.

As a result of coefficient restrictions imposed on these equations, R¯2 gives the proportion of explained variation in the difference between the rate of change in XPM and the rate of change in competitor prices.

Table 5.

Fourteen Industrial Countries: Estimates of Import Unit Value Equations for Manufactures, First Half 1964-Second Half 19791

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See Table 2, equation (2). The r-statistics are in parentheses. The tabulated estimates may differ slightly from the parameters used in the current forecasting version of the model.

The exact algebraic form of the equations and the variable definitions are given in Table 2. All variables are log first differences (excluding dummies).

The four dummy variables D74.1, D74.2, D75.1, and D75.2 all equal one in the period given, and zero elsewhere. These variables attempt to capture the effects of structural shifts in the country composition of import baskets that occurred in the wake of the first oil shock. Increases in the level and cross-country variance of the prices of manufactures at that time caused switches in demand patterns which in turn led to a general reduction in the level of import prices relative to export price indices based on traditional trade patterns. Accordingly, all of these variables carry negative coefficients.

DUMW equals 1 in 78.1, 78.2 and −1 in 79.1, 79.2. This variable captures the effect of the lagged response of Swiss manufactured import prices to the rapid appreciation of the Swiss franc in 1978.

As a result of coefficient restrictions imposed on these equations, R¯2 gives the proportion of explained variation in the difference between the rate of change in MPM and the rate of change in PFMD.

Table 6.

Fourteen Industrial Countries: Estimates of Equations for Domestic Wholesale Price of Manufactures, First Half 1963–Second Half 19791

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See Table 2, equation (3). The r-statistics are in parentheses. The tabulated estimates may differ slightly from the parameters used in the current forecasting version of the model.

The exact algebraic form of the equations and the variable definitions are given in Table 2. All variables are log first differences.

First half 1966–second half 1979.

Table 7.

Fourteen Industrial Countries: Estimates of Volume Equations for Manufactured Imports, First Half 1964-Second Half 19791

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See Table 3 equation (4). The t-statistics are in parentheses. The tabulated estimates may differ slightly from the parameters used in the current forecasting version of the model

The exact algebraic forms of the equations and the variable definitions are given in Table 3. All nondummy variables are in log levels

Estimated over first half 1962-second half 1979.

Only total long-run elasticities and their t-values are given here. See Table 8 for the lag distribution of this effect.

Table 8.

Fourteen Industrial Countries: Relative Price Lag Distributions from Equations for Manufactured Imports1

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The tabulated estimates may differ slightly from the parameters used in the current forecasting version of the model.

Represents long-run elasticity. The t-values for total weights are given in parentheses.

Measured in six-month units.

No end-point restrictions are applied.

Table 9.

Fourteen Industrial Countries: Estimates of Volume Equations for Manufactured Exports, First Half 1963-Second Half 19791

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See Table 3, equation (5). The t-statistics are in parentheses. The tabulated estimates may differ slightly from the parameters used in the current forecasting version of the model.

The exact algebraic form of the equations and the variable definitions are given in Table 3. All variables are log levels excluding dummies.

Estimated over first half 1968-second half 1979.

Estimated over second half 1964-second half 1979.

Only total long-run elasticities and their t-values are given here. See Table 10 for lag distribution of this effect.

This coefficient corresponds not to a time trend but to a third dummy variable.

Table 10.

Fourteen Industrial Countries: Relative Price Lag Distributions from Equations for Manufactured Exports1

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The tabulated estimates may differ slightly from the parameters used in the current forecasting version of the model.

Represents long-run elasticity. The t-values for total weights are given in parentheses.

Measured in six-month units.

None: no restriction; far: far end-point restriction; near: near end-point restriction.

Test is 2ln(Lu/Lr) ~ χ2(r) where r=number of restrictions and Lu and Lr are unrestricted and restricted likelihood values, respectively. An asterisk indicates that the null hypothesis—that the polynomial restrictions are valid—can be rejected at the 5 percent significance level.