VII International Trade

Hamid Faruqee, Douglas Laxton, Bart Turtelboom, Peter Isard, and Eswar Prasad
Published Date:
May 1998
  • ShareShare
Show Summary Details

This section describes the equations that MULTIMOD uses to explain international trade in countries' main composite goods.116 The disaggregation of trade flows in the Mark III model remains essentially the same as in Mark II. Imports and exports of goods and nonfactor services are measured according to the national income accounts definition. Imports of oil and non-oil primary commodities, and exports of oil, are then excluded to obtain measures of imports and exports of the main composite goods. A novel feature of Mark III is the use of information from input-output tables (compiled by the OECD) to calculate separate import propensities for consumption, investment, government purchases, and exports. For most countries, the different components of domestic absorption have substantially different import contents. Allowing for these differences enhances MULTIMOD's analysis of the macroeconomic effects, especially on external sector variables, of changes in government expenditure and a variety of other shocks.


To allow for differences in import propensities for different components of domestic absorption, separate import propensities for each category of absorption (private consumption, private fixed investment, and government purchases) and for exports were calculated using data from the most recent input-output matrices for each country.117 These import propensities were then used to create weighted measures of aggregate activity (ACT) for each country as follows:

Figure 7 plots, for each of the major industrial countries and for the block of small industrial countries, the volume of imports as a share of these activity variables, as well as the inverse of the relative price of imports. This figure suggests that, over the last three decades, the trend increase in imports relative to the weighted activity variable has been associated with declines in the price of imports (relative to the price deflator for non-oil GNP). This pattern appears to hold in all cases except for the United States, where import prices rose relatively sharply in the early 1970s.

Figure 7.Import-Activity Ratios and Relative Import Prices

Table 11 presents estimates of a parsimonious error-correction specification for the import volume equations. This specification reflects the view (supported by Figure 7) that the activity variable and the relative price of imports are likely to be the main determinants of the trend in imports. The parameter γm2 captures the speed of adjustment to the long-run equilibrium relationship. The long-run elasticity of import volumes with respect to the relative price of imports is denoted by the parameter γm3. The specification also includes changes in the relative price of imports. The parameter γm1 represents the short-run price elasticity of imports. In addition, for countries other than the United States, the regression includes a term specified as the difference between domestic potential output growth and U.S. potential output growth.118 This term, F(x), allows for the possibility that, in the process of convergence of productivity levels across countries, countries with relatively low productivity levels may have required a transfer of technology in the form of imported investment goods. This term could also reflect the expansion (by foreign producers) of distribution networks for imports, spurred by the expansion of productive capacity abroad.119

Table 11.Volume Equations for Imports
Δlog (MGSLOCt) − Δlog (ACTt) = γm0 + γm1 ΔPMRELt + γm2 [log(MGSLOCt−1) γm3PMRELt−1 − log ACTt−1] + F(x)
MGSLOC: imports of goods and nonfactor services, excluding oil and non-oil commodities.
ACT: weighted activity variable based on import propensities from input-output tables.
F(x): contribution of variables included to control for variation in imports not accounted for by weighted domestic activity and relative prices.1
PMREL: relative price of imports in logs.
Estimation period: 1972–96
Canada0.01 (0.01)−0.33** (0.04)0.06 (0.07)−0.99** (0.12)0.560.045
France0.00 (0.01)−0.33** (0.04)0.14** (0.05)−0.99** (0.12)0.690.037
Germany0.01* (0.01)−0.33** (0.04)0.13** (0.05)−0.99** (0.12)0.600.028
Italy−0.02 (0.02)−0.33** (0.04)0.34** (0.07)−0.99** (0.12)0.660.048
Japan−0.07** (0.03)−0.33** (0.04)0.35** (0.07)−0.99** (0.12)0.560.077
United Kingdom−0.00 (0.01)−0.33** (0.04)0.25** (0.05)−0.99** (0.12)0.640.034
United States0.03** (0.01)−0.33** (0.04)0.06** (0.03)−0.99** (0.12)0.730.046
Note: Standard errors reported in parentheses.

Note that the short-run elasticity of imports with respect to activity is constrained to be unity. This restriction, although not supported by the data, is necessary in order to obtain reasonable price elasticities. In the absence of this restriction, the trend in the level of imports would result in estimates of a large elasticity with respect to activity (which also has a trend) and, consequently, a small and often imprecise estimate of the price elasticity.

To minimize the global trade discrepancy (see discussion below), it is assumed that all countries have identical long-run price elasticities. The pooled estimate of this price elasticity (γm3) is −0.99. The estimated parameters on the error-correction terms γm2 vary from a low of 0.06 for Canada and the United States to a high of about 0.35 for Italy and Japan. These parameter estimates are statistically significant for all countries, corroborating the evidence presented in Figure 7 that the upward trend in the volume of imports is associated with the decline in the relative price of imports. The coefficient on the contemporaneous change in relative import prices (γm1) is also restricted to be the same for all countries. The estimated coefficient is negative and statistically significant.

Import prices are determined in the model as weighted averages of other countries' export prices. The average price of imports of country i, denoted PIMi, is given by

where Sjidenotes the share of exports from country j to country i in the total exports to country i, PXMj is the price of exports of country j, and Eij is an index of the value of currency j in terms of currency i.


The econometric specification for the export equation is similar to that of the import equation.

The scale variable used in this equation is foreign activity, and the relative price variable is the real competitiveness index (RCI).

The foreign activity variable is constructed as a weighted sum of the import volumes of other countries. The weights are equal to the base period shares of the home country's exports accounted for by the foreign countries and are based on the pattern of trade flows in 1996; see Table 12.

Table 12.Bilateral Total Exports, 1996(In billions of U.S. dollars)
ExporterUnited StatesJapanGermanyCanadaFranceItalyUnited KingdomSmaller industrial countriesDeveloping countries
United States67.523.5132.614.48.830.973.6271.6
United Kingdom31.46.729.
Smaller industrial countries53.931.8183.57.6100.651.191.1240.9205.2
Developing countries365.2180.9103.120.656.150.165.7178.4716.7

The real competitiveness index (RCI) is defined as a weighted sum of the logarithms of export prices of a country's trading partners relative to home-country export prices. This competitiveness index is constructed in a manner consistent with the use of partner countries' imports as the foreign activity variable that enters into the export equations.120

Consider the following identity that relates the exports of a given country (Xi) to the imports of each of its trading partners (Mj), weighted by its share in each of their markets (Sij):

The base-period export share of country i to country j is denoted by

where the bar above a variable indicates the base-period value of that variable. It can then be shown that an appropriate set of weights for constructing country i' s competitiveness index is as follows:121

The weights wik indicate the sensitivity of the exports of country i to competition in third markets from country k. The weights are normalized to sum to one for each country. The foreign activity variable for country i is defined as follows:

where E¯ij denotes the base-period price of currency j in terms of currency i.

The export volume equation is specified in first differences but includes an error-correction term. The estimated export equations constrain the coefficients on the lagged level of the real exchange rate to be the same for all countries. Also, the short-run elasticity of exports with respect to foreign activity is constrained to be unity. This restriction is imposed since, as in the import equation, the elasticity of exports with respect to foreign activity would otherwise be dominated by the trends in these two variables and result in very low estimates of the price elasticity.

Estimates of the export volume equations are presented in Table 13. The long-run price elasticity of exports (γx3) is estimated to be −1.74. Short-run price elasticities (γx1) differ across countries and are lower than the long-run price elasticity, but are still quite large and statistically significant for all countries. The estimated parameters on the error-correction terms (γx2) are positive in all cases and statistically significant for all countries except Canada and France. This suggests that, in the long run, exports are generally closely tied to the foreign activity and real exchange rate variables. This is confirmed by Figure 8, which plots, for each country, the ratio of export volume to the foreign activity variable as well as the real competitiveness index.

Figure 8.Export-Activity Ratios and Real Competitiveness Indices

Table 13.Volume Equations for Exports
Δlog (XGSLOt) − Δlog (FACTt) = γX0 + γX1, Δlog (RCIt) + γX2[log (XGSLOt−1) − γX3 log (RCIt) − log (FACTt−1)
XGSLO: exports of goods and nonfactor services, excluding oil.
FACT: weighted sum of import volumes in other countries/regions.
RCI: real competitiveness index.
Estimation period: 1972–96
Canada−0.00 (0.01)−0.41** (0.10)0.01 (0.01)−1.74** (0.29)0.760.032
France0.00 (0.01)−0.48** (0.08)0.01 (0.03)−1.74** (0.29)0.640.028
Germany−0.00 (0.01)−0.40** (0.07)0.06* (0.03)−1.74** (0.29)0.570.033
Italy−0.02** (0.01)−0.38** (0.10)0.17** (0.06)−1.74** (0.29)0.500.035
Japan−0.02** (0.01)−0.45** (0.11)0.36** (0.09)−1.74** (0.29)0.460.044
United Kingdom0.00 (0.01)−0.45** (0.08)0.13** (0.03)−1.74** (0.29)0.720.025
United States0.03** (0.01)−0.42** (0.06)0.08** (0.02)−1.74** (0.29)0.770.026

Note: Standard errors reported in parentheses.

Export price equations were estimated for the major industrial countries. The rate of change of export prices is assumed to be linearly related to the rates of change of the price of domestic non-oil output and the prices of foreign non-oil exports, where foreign prices use the same weighting scheme as the real competitiveness index, reflecting competition in all export markets. In addition, the lagged logarithmic difference between domestic prices and home-country export prices is included in the specification, thereby forcing export prices to change in proportion to the change in domestic output prices over the long run. The coefficient on this term was restricted to be the same for all countries; this restriction was not rejected by the data. The estimates of the export price equations are reported in Table 14. The sensitivity of export prices to the rate of change of foreign prices is quite similar across the major industrial countries.

Table 14.Export Price Equations
Δlog(PXMt) = γpx0 + γpx1 Δlog (PGNPNOt) + (1-γpx1) Δlog(PFMt) + γpx2 log (PGNPNOt−1/PXMt−1)
PXM: export price of the composite good that excludes oil and primary commodities.
PGNPNO: non-oil GDP deflator.
PFM: a weighted average of competitors' prices in foreign markets.
Canada−0.01* (0.01)0.64** (0.05)0.03** (0.01)0.590.032
France−0.00 (0.00)0.71** (0.03)0.03** (0.01)0.920.016
Germany−0.00 (0.01)0.81** (0.10)0.03** (0.01)0.170.047
Italy0.00 (0.00)0.66** (0.05)0.03** (0.01)0.900.024
Japan−0.00 (0.01)0.65** (0.02)0.03** (0.01)0.920.028
United Kingdom−0.0 0 (0.00)0.63** (0.04)0.03** (0.01)0.870.019
United States−0.00 (0.01)0.64** (0.04)0.03** (0.01)0.540.034

Note: Standard errors reported in parentheses.

Adding Up of World Trade and Current Account Balances

The existence of a global trade discrepancy, which implies that exports and imports summed across all countries are not equal, is a well-known problem. The discrepancy is even larger when the current account, which includes factor incomes, is aggregated across all countries. Although such a discrepancy might exist in the baseline, it is desirable for the model to have the property that incremental exports and imports be equal.

The new weighting scheme used to construct the price and activity variables for the trade equations ensures that this discrepancy is very small, although not exactly zero. Adding up of world trade is, therefore, imposed by allocating real and nominal trade discrepancies to export volumes and import prices, respectively.122 Given the adding up of world trade, the adding up of current account balances across all countries is then imposed on the simulations by constructing estimates of net foreign asset positions that sum to zero globally and by assuming that all claims pay the same U.S. dollar interest rate.123

    Other Resources Citing This Publication