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The World Trade Model: Revised Estimates

Author(s):
International Monetary Fund. Research Dept.
Published Date:
January 1984
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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
Geographic DisaggregationCommodity Disaggregation1Endogenous VariablesExogenous Variables
industrial countriesSITC 0+1: AgriculturalImport volumes by commodityReal domestic demand for
Austriagoodsclass, by countrymanufactures, by country
Belgium-LuxembourgSITC 2 + 4: Raw materialsExport volumes by commodityReal personal consumption
CanadaSITC 3: Fuelsclass, by countryexpenditure, by country
DenmarkSITC 5-8: ManufacturesExport volumes of automobilesPotential output in manufacturing,
Francebetween theby country
Germany, Fed. Rep. ofUnited States and CanadaExchange rates, by country
ItalyImport unit values by commodityFuel prices
Japanclass (excluding fuels),Implicit GNP deflators, by
Netherlandsby countrycountry
NorwayExport unit values by commodityHourly earnings in manufacturing,
Swedenclass (excluding fuels),by country
Switzerlandby countryOutput per man-hour in manufacturing,
United KingdomDomestic wholesale prices ofby country
United Statesmanufactures, by countryPotential man-hours of employment
Domestic wholesale prices ofin manufacturing,
Regionsraw materials, by countryby country
Developed primary producingTotal import volumes, bySpot prices for 35 non-oil
countriesregioncommodities
Major oil exporting countriesTotal export volumes, by
Centrally planned economiesregion
Non-oil developing countriesTotal import unit values, by
region
Total export unit values, by
region

According to Standard International Trade Classification.

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)
(1)ΔlnXPMi=a1ΔlnPRMi+a2ΔlnNULCi+a3Δln(POILLCDi)+a4Δln(PFXiLCDi)+a5ln(NULCi/ULCi)
Restrictions:(1.1)a1+a2+a3+a4=1(1.2)a1=ri1a2(1.3)a3=ri2a2
(1a)lnPFXi=ΣjsmxijΣkismmkj1smmijln(XPMk/LCDk)
(2)ΔlnMPMi=b1Δln(PFMDiLCDi)
Restriction: (2.1) b1 = 1
(2a)lnPFMDi=Σjsmmjiln(XPMj/LCDj)
(3)ΔlnPMi=c1ΔlnMPMi+c2ΔlnPRMi+c3ΔlnNULCic4Δln(POILLCDi)+c5ΔlnXPMi+c6Δln(PMi)1
Restriction: (3.1) C1 + C2 + C3 + C4 + C5 + C6 = 1
Definition of Variables1
Variables endogenous to the price equations
XPMiIndex of export unit values of manufactured goods from country i, expressed in the currency of country i, 1970 = 100.
PFXiDouble-weighted index reflecting an average of competitor countries’ export prices for manufactures in U.S. dollars.
MPMiIndex of import unit values of manufactures in country i, expressed in the currency of country i, 1970 = 100.
PFMDiAverage of partner-country export unit value indices for manufactures in U.S. dollars.
PMiIndex of wholesale price of manufactures in country i, in the currency of country i, 1970 = 100.
Variables exogenous to the price equations
(Variables exogenous to the manufacturing price block but endogenous to the model are indicated by an asterisk.)
LCDiExchange rate variable for country i, calculated as the number of currency units of country i per U.S. dollar, expressed in index form, 1970 = 100.
NOMHiNormal output per man-hour in manufacturing, in country i.
NULCiNormal unit labor costs in manufacturing, WMi/NOMHi, in country i, expressed in the currency of country i, 1970 = 100.
OMHiOutput per man-hour in manufacturing, in country i.
POILAverage oil export unit value of the oil exporting countries, in U.S. dollars, 1980 = 100.
PRMi*Index of domestic costs of raw materials in country i, in the currency of country i, 1970 = 100.
ri1Ratio of raw material to labor inputs in gross manufacturing output, in country i, based on 1970 input-output weights.
ri2Ratio of fuel to labor inputs in gross manufacturing output, in country i, based on 1970 input-output weights.
smmijShare of manufactured imports from industrial countries in market j originating in country i, in value terms, in 1970.
smxijShare of manufactured exports of country i going to market j, in value terms, in 1970.
ULCiUnit labor costs in manufacturing, WMi/OMHi, in country i, in the currency of country i, 1970 = 100.
WMiIndex of compensation per man-hour in manufacturing in country i, expressed in the currency of country i, 1970 = 100.

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

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)
(4)lnMVMi=a0+a1ln(AVGi/QMTi)+a2lnQMTi+a3(RMPMi)
Restriction: a2 = 1
(5)ln XVMi=b0+b1lnFMi+b2lnRQMTi+b3lnRXPMi+b4lnRXCUi
Restriction: b2 = 1
(5a)FMi=ΣjsmmijMVMjMj
Definition of Variables1
Variables endogenous to the volume equations
MVMiImport volume of manufactures for country i.
XVMiExport volume of manufactures for country i.
FMiForeign market variable for manufactured exports from country i.
Variables exogenous to the volume equations
(Variables exogenous to the volume equations but endogenous to the model are marked with an asterisk.)
AVGi*Weighted average of output in manufacturing (QMi) and real final domestic demand for manufactures (DVMt) both in index form, 1970 = 100, with the weights reflecting the share of manufactured imports going to intermediate and final demand, respectively.
AVGi = (1 − SHi) · QMi + SHi · DVMi
MiShare of country i’s imports of manufactured goods coming from the industrial countries, in value terms, in 1970.
MPMi*Index of import unit values of manufactures in country i, expressed in the currency of country i, 1970 = 100 (cf. equation (2) in Table 2).
PMi*Index of wholesale price of manufactures in country i, in the currency of country i, 1970 = 100 (cf. equation (3) of Table 2).
QMiIndex of real value added in manufacturing in country i, 1970 = 100.
QMTiIndex of potential output in manufacturing in country i.
RMPMi*Index of domestic prices of manufactures relative to import price of manufactures. This index is calculated as
RMPMi = PMi/MPMi
RQMTiIndex of potential output in manufacturing in country i relative to competitors’ potential output in manufacturing.
lnRQMTi=lnQMTiΣjsmxijΣksmmkjlnQMTk
RXCUi*Average measure of capacity utilization in countries importing from country i, calculated as
RXCUi=ΣjsmxijXiQMj/QMTj
where Xi is the share of country i’s exports going to industrial countries, in value terms, in 1970.
RMPMi*Index of export unit values of manufactures in country i relative to competitors’ price index.
ln(RXPMi)=ln(XPMi/LCDi)Σjsmxijln(PFMDj)
smmijShare of manufactured imports from industrial countries in market j originating in country i, in value terms, in 1970.
smxijShare of manufactured exports from country i to market j, in value terms, in 1970.

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

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
Explanatory

Variable2
AustriaBelgium-LuxembourgCanadaDenmarkFranceFed. Rep. of

Germany
ItalyJapanNetherlandsNorwaySwedenSwitzerlandUnited

Kingdom
United

States
Domestic raw0.0290.0520.0320.0660.0690.0690.0290.0340.0900.0170.0130.0930.0330.023
material prices(1.42)(2.89)(2.27)(4.48)(8.03)(5.36)(2.85)(5.62)(5.71)(2.11)(5.19)(6.51)(3.60)(7.86)
Normal unit0.1150.2890.2430.4630.2670.2570.3530.4010.2780.3480.1310.665
labor costs(1.42)(2.89)(2.27)(4.48)(8.03)(5.36)(2.85)(5.62)(2.11)(6.51)(3.60)(7.86)
Normal unit0.4050.329
labor costs (−1)(5.71)(5.19)
Energy price0.0300.0630.0260.0680.1600.0670.0520.0810.051
(1.42)(2.89)(1.88)(5.36)(5.62)(2.94)(2.11)(5.19)(2.62)
Energy price (−1)0.0530.0330.1040.0450.0410.0960.0520.056
(2.27)(2.36)(8.03)(2.85)(2.19)(6.51)(3.60)(2.85)
Competitor prices0.2180.2250.6720.4130.5610.2120.2450.4050.3970.3070.4640.4390.204
(1.02)(1.01)(4.66)(3.15)(10.24)(2.10)(2.23)(3.83)(3.76)(3.50)(5.63)(3.32)(2.02)
Competitor0.6080.3710.3940.3290.6530.2710.346
prices (−1)(3.80)(2.20)(6.22)(2.91)(3.97)(3.41)(6.81)
Cyclical unit−0.248
labor costs(1.51)
Seasonal dummy−0.013−0.010
(2.25)(2.27)
Rho0.2860.3350.698
(1.68)(1.94)(5.10)
SEE0.0250.0190.0260.0140.0160.0130.0220.0270.0170.0310.0140.0220.0130.017
R¯230.280.240.110.340.640.650.590.470.460.090.640.550.810.63
D-W2.482.001.892.241.891.722.151.871.461.871.901.691.811.86

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.

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
Explanatory Variable2AustriaBelgium-LuxembourgCanadaDenmarkFranceFed. Rep. of GermanyItalyJapanNetherlandsNorwaySwedenSwitzerlandUnited KingdomUnited States
Partner-country0.8411.0160.6511.01.00.8620.7880.8830.5180.7400.8840.8030.8940.733
export prices(6.62)(8.86)(7.59)(9.62)(12.02)(9.12)(3.72)(5.64)(11.77)(12.59)(11.51)(7.86)
Partner-country0.1590.3490.1380.2120.1170.4820.260.1160.1970.1060.267
export prices (−1)(1.25)(4.07)(1.54)(3.24)(1.21)(3.46)(1.98)(1.55)(3.09)(1.36)(2.87)
Dummies3
D74.1−0.084
(4.43)
D74.2−0.071−0.128
(3.81)(3.78)
D75.1−0.043−0.039
(3.39)(2.14)
D75.2−0.039−0.039
(2.83)(2.90)
DUMW40.041
(5.01)
Rho−0.2830.2700.2320.4590.280
(1.59)(1.45)(1.29)(2.77)(1.59)
SEE0.0140.0210.0170.0130.0180.0190.0190.0340.0190.0140.0130.0160.0200.017
R¯250.380.580.330.250.100.320.480.310.290.330.420.580.110.18
D-W1.882.132.001.582.181.612.051.831.961.941.731.941.942.08

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.

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
Explanatory Variable2AustriaBelgium-LuxembourgCanadaDenmarkFranceFed. Rep. of GermanyItalyJapanNetherlandsNorway3SwedenSwitzerlandUnited KingdomUnited States
Export price of0.4360.5980.3760.169
manufactures(6.81)(10.32)(2.82)(3.11)
Export price of0.320
manufactures (−1)(2.74)
Import price of0.6380.2830.3190.4560.0990.1160.3060.7340.091
manufactures(8.44)(5.01)(4.38)(3.90)(2.01)(1.93)(3.74)(3.13)(1.62)
Import price of0.2490.153
manufactures (−1)(3.78)(2.65)
Normal unit0.4680.2050.5440.0970.1800.2160.2820.5480.6100.3040.582
labor costs(6.19)(5.06)(4.65)(2.66)(1.24)(3.80)(3.82)(6.28)(18.23)(2.94)(3.03)
Normal unit0.2770.411
labor costs (−1)(2.38)(3.51)
Domestic raw0.2130.4090.0790.3420.1460.4020.3750.064
material prices(7.74)(7.04)(3.80)(11.67)(2.49)(6.94)(12.04)(3.31)
Domestic raw0.047
material prices (−1)(2.27)
Energy price0.0270.0150.047
(2.59)(3.27)(4.82)
Domestic wholesale price0.3620.2630.5000.266
of manufactures (−1)(4.78)(3.07)(3.67)(1.13)
SEE0.0120.0100.0070.0190.0090.0100.0110.0130.0130.0240.0090.0050.0140.007
R¯20.320.610.820.300.740.590.830.890.410.260.760.840.570.82
D-W1.671.371.731.891.821.951.491.621.871.461.422.211.791.65

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.

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
Explanatory Variable2AustriaBelgium-LuxembourgCanadaDenmarkFranceFed. Rep. of Germany3ItalyJapan3NetherlandsNorwaySwedenSwitzerlandUnited KingdomUnited States3
Demand relative to1.410.941.181.692.261.641.942.171.642.231.961.471.701.22
potential output(5.45)(4.87)(6.28)(10.52)(8.99)(7.29)(9.05)(11.29)(5.96)(10.25)(11.16)(6.18)(5.04)
Potential output1.01.01.01.01.01.01.01.01.01.01.01.01.01.0
Relative price40.971.151.140.670.521.151.020.820.530.650.690.140.561.57
(1.47)(6.36)(6.88)(0.95)(3.89)(3.85)(3.79)(3.03)(3.45)(1.98)(3.16)(0.89)(4.07)(4.78)
Constant6.657.707.997.067.898.427.457.798.026.417.307.077.548.11
(39.41)(207.32)(317.94)(59.45)(163.19)(56.30)(172.68)(200.19)(280.87)(62.82)(246.71)(183.68)(140.86)(69.56)
Seasonal dummy0.015−0.041−0.058−0.035−0.078−0.024−0.016−0.047−0.044
(1.98)(6.64)(5.30)(2.92)(12.83)(2.87)(2.13)(4.31)(3.22)
Time trend0.0160.0160.0100.0070.0230.0190.0240.0100.0190.0160.0210.0320.033
(2.90)(15.12)(13.25)(1.92)(15.13)(4.04)(18.71)(9.85)(7.21)(17.13)(17.35)(17.10)(7.06)
Dummy 10.0780.120−0.0810.1200.0840.076−0.1700.0400.031
(4.44)(4.28)(3.30)(1.88)(3.39)(4.35)(7.76)(2.60)(3.16)
Dummy 2−0.048−0.700−0.049−0.0480.095
(1.83)(4.97)(3.47)(1.51)(2.21)
Rho0.500.420.580.600.770.640.580.490.33
(3.12)(2.52)(4.11)(4.20)(10.80)(5.26)(4.43)(5.26)(2.18)
SEE0.0300.0240.0310.0490.0250.0260.0630.0540.0240.0340.0310.0230.0380.047
R¯20.9780.9780.9470.8140.9890.9930.9260.9000.9210.8920.9390.9720.9830.973
D-W1.671.541.562.111.792.021.332.031.921.791.892.171.391.89

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.

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
Time Delay in Six-Month UnitsAustriaBelgium-LuxembourgCanadaDenmarkFranceFed. Rep. of GermanyItalyJapanNetherlandsNorwaySwedenSwitzerlandUnited KingdomUnited States
t0.101.140.531.020.280.530.080.140.56
t−10.390.220.521.150.610.301.56
t−20.391.15−0.08−0.070.270.69
t−30.09
Sum of weights20.971.151.140.670.521.151.020.820.530.650.690.140.561.56
(1.47)(6.36)(6.88)(0.95)(3.89)(3.85)(3.79)(3.03)(3.45)(1.98)(3.16)(0.89)(4.07)(4.78)
Average lag length31.4820.57110.911.321
Degree of polynomial42122

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.

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
Explanatory Variable2AustriaBelgium-LuxembourgCanadaDenmarkFranceFed. Rep. of

Germany
ItalyJapanNetherlandsNorwaySwedenSwitzerland3United Kingdom 4United States
Foreign demand0.6110.9080.3691.5210.5321.0750.9100.8061.3331.1010.7461.1380.8460.655
(5.92)(5.79)(4.31)(12.06)(4.37)(54.95)(9.35)(4.65)(7.28)(5.28)(3.81)(4.43)(54.15)(7.32)
Foreign demand (−1)0.2750.3180.4020.4670.518
(1.81)(3.53)(3.36)(2.54)(2.96)
Potential output
relative to
competitors1.01.01.01.01.01.01.01.01.01.01.01.01.01.0
Relative price5−1.372−1.552−0.708−1.133−1.245−1.411−0.638−1.608−0.885−1.485−1.594−0.727−0.306−1.669
(6.28)(3.09)(2.75)(7.49)(3.82)(3.23)(0.81)(6.46)(1.79)(5.22)(5.01)(1.25)(1.52)(8.07)
Capacity utilization
relative to
competitors0.649
(2.62)
Constant1.925−0.9582.250−2.9120.510−0.8320.633−2.246−2.102−0.810−2.182−1.2771.2282.908
(3.05)(1.16)(2.47)(4.08)(4.50)(4.37)(0.73)(2.08)(1.67)(0.71)(2.93)(0.62)(8.46)(4.00)
Seasonal dummy0.038−0.039−0.025−0.0680.0150.087−0.0270.029−0.044−0.032
(5.77)(4.23)(4.04)(10.91)(2.09)(6.29)(2.80)(7.30)(3.32)(5.40)
Time trend0.020−0.021−0.003−0.0250.0296−0.018−0.019−0.006−0.0040.004
(4.74)(4.02)(0.41)(4.82)(1.12)(2.85)(2.31)(0.70)(0.65)(0.83)
Dummy 10.0370.0160.0990.0550.068−0.213
(4.23)(2.04)(4.29)(2.65)(5.83)(7.30)
Dummy 20.088−0.047
(3.82)(2.75)
Rho0.3140.3130.6640.3140.2630.774−0.2080.256
(1.93)(2.12)(7.50)(1.79)(1.60)(7.75)(1.16)(1.54)
SEE0.0220.0260.0280.0360.0210.0190.0410.0380.0360.0470.0270.0330.0290.021
R¯21.000.990.940.991.001.000.890.990.990.981.000.980.990.99
D-W1.582.031.761.791.591.792.461.902.101.941.662.011.982.11

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.

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
Time Delay in Six-Month UnitsAustriaBelgium-Luxembourg CanadaDenmarkFranceFed. Rep. of GermanyItalyJapanNetherlandsNorwaySwedenSwitzerlandUnited KingdomUnited States
t−0.549−0.177−0.075−0.820−0.204−0.318−0.594−0.242−0.401−0.272−0.263−0.183
t−1−0.384−0.417−0.327−0.313−0.274−0.088−0.192−0.418−0.249−0.339−0.454−0.198−0.296
t−2−0.247−0.484−0.303−0.297−0.155−0.096−0.276−0.216−0.278−0.477−0.139−0.353
t−3−0.137−0.377−0.003−0.271−0.201−0.032−0.169−0.144−0.217−0.342−0.087−0.354
t−4−0.055−0.097−0.198−0.226−0.095−0.033−0.155−0.049−0.040−0.009−0.298
t−5−0.231−0.056−0.094−0.047−0.185
t−6−0.214−0.069
t−7−0.177−0.075
t−8−0.119−0.066
t−9−0.041
Sum of weights2−1.372−1.552−0.708−1.133−1.245−1.411−0.638−1.608−0.885−1.485−1.594−0.727−0.306−1.669
(6.28)(3.09)(2.75)(7.49)(3.82)(3.23)(0.81)(6.46)(1.79)(5.22)(5.01)(1.25)(1.52)(8.07)
Average lag length31.101.871.330.281.994.630.751.331.411.781.651.236.872.50
Degree of polynomial22212222212222
End-point zero restrictions4farnonenonenonenonenearfarnonenonenonenonefarfarnone
Chi-squared test of5.220.00.23.318.78*1.7812.5*3.818.2*0.20.781.21.6
polynomial restrictions5r=3r=2r=1r=2r=6r=2r=3r=2r=4r=2r=3r=4r=3

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.

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.

Table 11.Fourteen Industrial Countries: World Trade Model—Relative Price Elasticities for Trade in Manufactures1
ImportsExports
ImpactShort-runLong-runImpactShort-runLong-run
Countryelasticityelasticityelasticityelasticityelasticityelasticity
Austria0.100.490.97−0.55−0.93−1.37
(2.14)(1.47)(2.44)(6.28)
Belgium1.15−0.18−0.59−1.55
(6.36)(0.75)(3.09)
Canada1.141.141.14−0.08−0.40−0.71
(6.88)(6.88)(0.36)(2.75)
Denmark0.530.750.67−0.82−1.13−1.13
(1.48)(0.95)(3.04)(7.49)
France0.520.52−0.20−0.48−1.25
(3.89)(1.11)(3.82)
Germany, Fed. Rep. of1.151.15−0.09−1.41
(3.85)(3.23)
Italy1.021.021.02−0.32−0.51−0.64
(3.79)(3.79)(0.41)(0.81)
Japan0.280.890.82−0.59−1.01−1.61
(1.20)(3.03)(3.69)(6.46)
Netherlands0.530.530.53−0.24−0.49−0.89
(3.45)(3.45)(0.92)(1.79)
Norway0.080.380.65−0.40−0.74−1.49
(2.62)(1.98)(5.00)(5.22)
Sweden0.69−0.27−0.73−1.59
(3.16)(1.42)(5.01)
Switzerland0.140.140.14−0.26−0.46−0.73
(0.89)(0.89)(1.65)(1.25)
United Kingdom0.560.560.56−0.31
(4.07)(4.07)(1.52)
United States1.561.56−0.18−0.48−1.67
(4.78)(1.00)(8.07)

The impact elasticity gives the response in the current semester; the short-run elasticity gives the response after two semesters (one year); and the long-run elasticity gives the total response. The t-values are given in parentheses. The tabulated estimates may differ slightly from the parameters used in the current forecasting version of the model.

The impact elasticity gives the response in the current semester; the short-run elasticity gives the response after two semesters (one year); and the long-run elasticity gives the total response. The t-values are given in parentheses. The tabulated estimates may differ slightly from the parameters used in the current forecasting version of the model.

I. Price Equations for Industrial Countries

Trade prices for manufactures, raw materials, and agricultural goods are all determined in a general two-step procedure. First, export prices are determined for each exporting country as a function of domestic costs and export prices of competitor countries. Import prices are then determined as functions of weighted averages of trading partners’ export prices. For raw materials and agricultural goods, weighted indices of world commodity prices also enter into both export and import price equations.6

While the essential structure of the price equations for manufactures is carried over from the previous version of the model, a number of important changes are introduced here, including a new equation to explain the domestic wholesale price of manufactures, the use of restrictions requiring homogeneity in both export and import unit value equations, and a fuller treatment of the effects of raw material and energy costs on export prices. A comparison of the coefficient estimates of export and import unit value equations in the previous and current versions of the model7 reveals some significant differences, particularly in those equations where the previous parameter estimates clearly did not exhibit suitable homogeneity properties.

For each of the 14 industrial countries included in the model, export unit values for manufactures are determined within the set of simultaneous equations described by equations (1) and (la) in Table 2. Equation (1) gives the percentage rate of change8 in the export unit value for country i as a function of the rates of change of three categories of domestic input costs (raw materials, labor, and energy), the rate of change of competitor country export prices converted into country i currency, and a variable representing cyclical movements in unit labor costs. Equation (1a) then expresses the index of export prices of country i’s competitors as an appropriately weighted index of the (U.S. dollar) export prices of countries other than i. On the right-hand side of equation (1a), all of the industrial country export prices are weighted up to give separate price indices for each of country i’s export markets, j, and these indices are then weighted by the shares of country i’s total manufactured exports going to each market. The share matrices used here and elsewhere in the model are based on 1970 trade flows.9

Each equation of the form of equation (1) is estimated subject to three linear restrictions. The first (1.1) is a restriction requiring homogeneity; it requires that the sum of the elasticities for all domestic costs and competitor prices be equal to unity, thus ensuring that a common proportionate increase in all cost variables (across countries) results in an equiproportionate rise in the index of manufactured export prices for each country. Recalling that export unit values represent the prices of gross outputs rather than value-added deflators, such a restriction can be derived at the microeconomic level for the pricing behavior of a firm that maximizes profit subject to decreasing returns to scale, perfect competition in factor markets, and less than perfect competition in its product market (Deppler and Ripley, pp. 151, 153). In this context, the ratio of the total weight on the cost variables to the weight on the index of competitor prices is equal to 1/αη, where a is the elasticity of domestic marginal cost with respect to output and η is the absolute value of the price elasticity of foreign demand. The ratio can be interpreted as a measure of the effective degree of monopoly power exerted by the home country in the world market for manufactures, becoming larger as the price elasticity of demand decreases and/or as the price elasticity of export supply (i.e., 1/α) increases. In the coefficient estimates in Table 4, the weight on the variable representing competitor prices is smallest for the United States (0.204), implying the greatest effective monopoly power, and largest for Austria (0.826), implying the least effective monopoly power. Most of the weights appear to lie in the range of 0.4 to 0.6, with the one notable exception being the United Kingdom, where the estimated weight of 0.785 implies a relatively low degree of effective monopoly power and therefore, given the large scale of U.K. manufactured exports, a relatively low export supply-price elasticity.

The second and third restrictions (1.2) and (1.3) in equation (1) require that the relative weights on the three cost variables reflect the relative contributions of the three factors of production in total (gross) manufacturing output. The relative factor contributions are represented by the ratios ri1 and ri2 which, for the base year 1970, give the relative values of raw material inputs to labor inputs and of energy to labor inputs, respectively. The previous version of the model employed neither the homogeneity restriction nor these restrictions on the relative size of parameters in its equations for manufactured export prices.10 Comparing the current estimates shown in Table 4 with the previous set of estimates (Deppler and Ripley, p. 168), there are no consistent differences in the relative contributions of explanatory variables. However, there is much less cross-country variation in the relative contributions of the explanatory variables.

The two relative-cost restrictions and the restriction requiring homogeneity were tested as a group for each country using a Chi-squared log likelihood test,11 and it was found that 5 of the 14 sets of restrictions were not consistent with the data at the 1 percent level. While there was thus an indication that special factors had not been adequately accounted for in these 5 sets, the full set of restrictions was nevertheless retained in the current version of the model in order to ensure that the prices block as a whole would exhibit the desired behavioral properties.

The proportional change (as measured by the first difference of the logarithm) in the import price of manufactures is determined in a straightforward manner by the percentage rate of change in a geometrically weighted average of partner countries’ manufactured export prices (equations (2) and (2a) of Table 2). While it would appear that restriction (1.2) completely determines the parameters of equation (2), the actual model equations (cf. Table 5) include current and lagged values of the weighted export price index and a number of dummy variables. Consequently, it is necessary to estimate the parameters of this equation subject to the restriction requiring that the total elasticity with respect to the weighted export price index be equal to one. The estimates displayed in Table 5 show that, in the majority of equations, at least 70 percent of the total effect of this variable is felt in the current semester. The unity restriction applied here was not used in the previous version of the model although most of the estimated coefficients on the partner-country export price variables were close to one. Two exceptions were Canada and the Federal Republic of Germany, where these coefficients were significantly smaller than one (Deppler and Ripley, p. 170).

The domestic wholesale prices of manufactures that are used in the relative price terms affecting import volumes are determined in equation (3) of Table 2 as functions of domestic cost variables and of both export and import unit values. The rationale underlying this specification is as follows. The wholesale price of manufactures reflects prices of both imported and domestically produced goods. In turn, the price of domestically produced manufactures is influenced both by the prices prevailing in the export market and by domestic costs. Restrictions requiring homogeneity are once again imposed across the coefficients of the equation for each country in order that proportionate increases in all domestic costs and import and competing prices of manufactures (in local currency) should yield the same proportionate increase in the dependent variable. Where a lagged dependent variable enters as an explanatory variable, long-run homogeneity is achieved by including its coefficient in the unity summation restriction (3.1).

The equations explaining wholesale and import prices of manufactures were estimated using ordinary least squares, while the equations for the export prices of manufactures were estimated using a modified two-stage least-squares procedure. The modification to the standard two-stage least-squares procedure involves the set of first-stage regressions, where the competitor country export price variables are regressed on weighted averages of competing country labor, energy, and raw material costs, rather than on the whole set of competing country cost variables.

While the structural equations for agricultural and raw material prices are more similar to their counterparts in the previous version of the world trade model than are the price equations for manufactures, there are nevertheless a number of modifications: the equations of the present version are in log first difference rather than log level form, a separate energy cost term is included in the export price equations of the current version, and an equation is now included for the domestic wholesale price of raw materials. As previously, all of the nonmanufacturing price equations are estimated by ordinary least squares. For details of the nonmanufacturing equations, see Spencer (1984).

II. Export and Import Volume Equations for Industrial Countries

The structure of the equations explaining export and import volumes of manufactures for each industrial country, and definitions of the dependent and explanatory variables, are given in Table 3. Coefficient estimates for this set of equations are set out in Tables 7 through 10; a summary of the price elasticities of demand for imports and exports of manufactures is given in Table 11. For detailed descriptions of the revised volume equations for trade in raw materials, agricultural goods, and fuels, see Spencer (1984).

Retaining the same basic structure adopted by Deppler and Ripley, each country’s demand for imports of manufactures (equation (4) of Table 3) is given as a function of potential output in manufacturing,12 relative prices, and a cyclical excess demand variable that measures the logarithm of the ratio of potential output to a weighted average of final domestic demand for manufactures and the level of value added in manufacturing. The weights used in the averaged demand variable are intended to reflect the relative shares of final and intermediate products, respectively, in total imports. The most important innovations in this block of the current version of the model include the use of more general lag structures on the relative price variables and the use of unity restrictions on the elasticities of imports with respect to potential output. In the Deppler-Ripley model, the lag distributions on relative price terms were restricted to conform to simple-step functions through the use of two averaged relative price terms, giving one constant weight for effects lagged one and two semesters and a further constant weight for effects lagged from three to seven semesters. In the current model, the two averaged price terms are replaced by polynomial distributed lag structures, which allow a far greater flexibility in both the length and pattern of lagged responses.

In restricting the elasticity of imports with respect to potential output to equal 1.25 across all industrial countries, the objective in the Deppler-Ripley model was to keep trade balances in manufacturing neutral with respect to a general across-country shift in potential output. An average elasticity greater than one was required because levels of manufactured exports for industrial countries are generally greater than levels of manufactured imports. Subsequently, the elasticity restrictions were refined to more nearly guarantee the neutrality property,13 but this gave rise to the unsatisfactory situation whereby the (restricted) potential output elasticities were in some cases greater than the estimated excess demand elasticities. In such cases, a simulated increase in excess demand resulting from a reduction in potential output would give rise to a decline rather than an increase in manufactured imports. In the current version of the model, the potential output elasticities are all restricted to one and the estimated excess demand elasticities are nearly all greater than one,14 ensuring appropriate responses to fluctuations in the cyclical excess demand variable. Furthermore, with fixed unitary elasticities on the relative capacity terms in the export volume equations, the model now has the desirable property that, for each industrial country, an equiproportionate change in domestic demand and potential output gives rise to the same proportionate change in both imports and exports of manufactures.

Table 7 presents the new estimates for the volume of imports of manufactures. The estimated elasticities on the cyclical demand variable are all well determined and lie within the range of 0.9 to 2.3. The estimated relative price elasticities shown in Table 7 are generally less than one and usually lie between 0.5 and 1.2; these estimates are considerably more uniform than the elasticity estimates of Deppler and Ripley, which ranged from zero to over 3. The lag distributions on the relative price elasticities presented in Table 8 are made up, in all but one case, of three or fewer terms. The maximum lag length is three semesters (one and one half years) and the average lag, across all 14 industrial countries, is approximately one semester.

The volume of manufacturing exports supplied by each industrial country (equation (5) of Table 3) is linked to import volumes in trading partner countries through foreign market variables (FM). These variables are weighted averages, reflecting base year (1970) market shares, of volumes of manufactures imported by partner countries. The two other major explanatory variables in equation (5) are the price of domestic exports relative to a weighted index of the export prices of competitor countries and the level of potential output in the domestic manufacturing sector relative to potential output in competing countries. The elasticities on the latter variable are set equal to one for all countries included in the model on the assumption that, for given levels of foreign demand and relative prices, export market shares tend to shift proportionately with differential rates of manufacturing capacity growth in supplying countries. The fourth explanatory variable shown in equation (5) is an index of capacity utilization in importing partner countries. This variable does not play an important role in the overall model, as it is found to be a significant contributing factor to export volume growth only for the United States.

Estimates of the equations determining the volume of each country’s manufactured exports are presented in Table 9, with the full lag distributions on the relative price terms displayed in Table 10. By and large, the estimated elasticities on the foreign market variable are found to lie between 0.7 and 1.3. Such a dispersion about one is, of course, to be expected if a proportionate change in all import volumes is to result in a similar proportionate change in overall exports. Considering the estimated relative price elasticities, these are generally larger than the estimated import price elasticities, with 9 of the 14 total elasticities falling between −1.1 and −1.7. The remaining 5 elasticity estimates lie between −0.3 and −0.9. As with the import price elasticities, the export price elasticities are considerably less variable between countries than in Deppler and Ripley; also, the average elasticity across all countries is smaller, at −1.17 compared with −1.40. The estimated price elasticities for the volumes of both exports and imports of manufactures are summarized in Table 11. Figures given in the table measure the effects of a once-for-all relative price change after one semester, after two semesters, and in the long run, when the total effect is felt. If one compares the total price elasticities with trade price elasticities estimated in other recent empirical studies,15 there would appear to be a general consistency, with world trade model estimates lying well within the range of alternative estimates for almost every country.

The lag distributions of the response of export volumes to relative price movements are estimated to be considerably longer (Table 10) than the lags in the response of import demand to relative price changes (Table 8).16 In all but two of the export equations, the maximum lag on the relative price term is less than or equal to five semesters, but in the remaining two the maximum lags stretch out to eight and ten semesters.17 The average length of lag for the 14 industrial countries is approximately one year, compared with the one-semester lag found for import volume responses. In all of the export equations, the polynomial distributed lag structures are assumed to be of either the first or second degree; end-point restrictions are employed in 5 of the 14 countries.18 Chi-squared tests of all of the restrictions implicit in the lag structures (cf. Table 10) indicate that the restrictions can be accepted at the 5 percent level in all but three cases.19 In the import equations (cf. Table 8), only two of the lag structures involve binding restrictions, and these were found to be consistent with the data at the 5 percent level.

Components of trade in manufactures that are not included in the export and import volume aggregates determined by equations (4) and (5) (Table 3) include all exports and imports of ships and aircraft, which are treated as exogenous, and the trade in automotive products between the United States and Canada, which is determined by two separate behavioral equations. Items relating to ships and aircraft are taken out, as these tend to be lumpy flows, while U.S.-Canadian auto trade is treated separately in an attempt to allow for the major impact of the 1965 U.S. Canadian automotive agreement. The two auto trade equations are described in detail in Spencer (1984).

Estimates of the equations for the volume of total manufactured imports are obtained by the instrumental variables method, while the equations for each country’s total manufactured exports are estimated by ordinary least squares. The instrumental variables method is required for the import equations because of the simultaneity between the volume of imports, MVMi, and the demand variable, AVGi. The latter variable is directly related to value added in manufacturing, QMi, which in turn is defined as the domestic demand for manufactures, DVMi, plus a fixed proportion of the excess of exports over imports of manufactures. Export volumes, on the other hand, are primarily determined as functions of the foreign demand variables, and these are related only in a very indirect manner back to export volumes.

The equations that determine the import and export volumes of raw materials and agricultural goods, and import volumes of fuels, are not discussed here in any detail. However, the logical structure of the import and export volume equations for nonmanufactured commodities is the same as that for the manufacturing block. Import volumes are explained as functions of domestic activity and import prices relative to domestic output prices. The activity variable entering the raw materials and fuel imports equations is real value added in manufacturing, while total domestic consumption is used in the agricultural imports equations; compared with raw materials and fuels, agricultural imports have a considerably greater component going directly to final demand. As in the manufactures block, the export volume equations for raw materials and agricultural goods are driven by foreign market variables, constructed as weighted averages20 of the imports of partner countries. The relative price variables are also formed in the same manner as for manufactures, with export unit values being compared with double-weighted indices of competing export prices.

Compared with the Deppler-Ripley model, changes in the non-manufacturing volume equations include (i) the wider use of relative price terms, which now enter all five equations in this block rather than just the agricultural imports equation, (ii) the inclusion of first differences of scale variables in the three import equations to allow for the acceleration effects of stock building, and (iii) the use of lagged dependent variables to allow for partial adjustment of import volumes to long-run equilibrium levels. In the fuels import equations, an effort was made to identify finite (polynomial) distributed lag structures on the relative price variables; consequently, it was not necessary to include lagged dependent variables in these equations.

All of the nonmanufacturing volume equations are estimated by ordinary least squares. In the imports of manufactures equations, there was clear simultaneity between the dependent variable and the right-hand side activity variable. However, in the import equations for nonmanufactures, neither of the activity variables—value added in manufacturing nor total final consumption—depends directly on the volume of imports of the commodities concerned.

III. Summary and Conclusions

The revised structural specification of the world trade model does not differ greatly from the Deppler-Ripley version of the model. Nevertheless, a number of significant structural modifications have been incorporated in the current version and, with the sample extended by seven semesters (three and a half years) to include the period from the second half of 1976 through the second half of 1979, there are many significant changes in coefficient estimates. The paper does not include descriptions of the non-manufacturing price and volume equations, as the main structural changes occur in the price and volume blocks for manufactures. In the price block, restrictions are imposed on the export unit value equations to ensure homogeneity under general shifts in the level of prices and to enforce actual base-year cost patterns on the relative cost contributions to changes in export unit values. Restrictions are imposed on the equations explaining import unit values of manufactures to ensure homogeneity under general shifts in all partner-country export prices. In the volume equations, more flexible (polynomial) structures are used to give an improved representation of both the overall size and timing of relative price effects. Some alterations have also been made to the nonmanufacturing volume and price equations. In particular, greater use is now made of relative price effects in export and import demand equations. While the current version of the world trade model has not been estimated over the sample of data reported in Deppler and Ripley for a direct comparison, it indeed appears that the extension of the sample to include the 1976–79 period has contributed to an improvement in the identification of relative price effects in a large proportion of both the nonmanufacturing and manufacturing volume equations.

Although the new relative price terms in the model have increased the responsiveness of trade flows in raw materials and agricultural goods to relative price movements, the average long-run price elasticities for exports and imports of manufactures are found to be slightly lower, at −1.17 and 0.83, respectively, than in Deppler and Ripley. The new estimates are also found to be considerably less variable across countries. No persistent differences are observed in estimated elasticities of trade volumes with respect to such scale variables as foreign demand in export equations and actual or potential output in import equations. However, the elasticities of manufactured imports with respect to potential output are now set uniformly at 1.0, compared with the 1.25 adopted in Deppler and Ripley. In the equations explaining export and import unit values, there are no persistent crosscountry differences between the estimated coefficients of the two versions of the model. As with the price elasticities in the volume equations, however, there is generally a greater consistency in the parameters of the price equations in the current version than in the Deppler-Ripley version.

Considering the effects that the new changes are likely to have on the performance of the current specified model, the restrictions on the unit value equations for manufactures and the greater degree of cross-country consistency in the relative contributions to export and import unit values should lead to more realistic responses in relative trade prices under shocks to the exogenous labor cost and commodity price variables. Furthermore, the more comprehensive treatment of relative price effects on trade volumes might be expected to improve the model’s predictions of how trade volumes respond to such relative price movements. In forecasting applications, it has indeed become apparent that the new version of the model tends to generate more consistent patterns of trade volumes and prices, in particular for manufactures.

APPENDIX: List of Dummy Variables

Most of the dummy variables used in the model have simple structures that may be conveyed through a system of mnemonics. The conventions of the system adopted are as follows:

DYSequals 1 in year Y semester S, zero elsewhere; for example, D197201.
DY1Y2equals 1 in second semester of year Y1, −1 in the first semester of year Y2; for example, D196768.
DY12equals 1 in first semester of year Y, −1 in second semester of year Y; for example, D196612.
CDYSequals 1 from year Y semester S onward, zero elsewhere; for example, CD196801.
SDY1Y2alternates between −1 and +1 from first semester of year Y1 to second semester of year Y2, and equals zero elsewhere; for example, SD196973.
Dummy Variable Definitions
austria
Manufactured imports
DUM1 =D197778. Advance purchases of manufactures caused by pre-announcement of value-added tax increases due in January 1978.
DUM2 =D197302 + D197401. Effects of trade liberalization between the European Communities and Austria.
Manufactured exports
DUM1 =2 in 197202, −1 in 197301 and 197302. Distortion resulting from the introduction of value-added tax.
DUM2 =D197401. Unusual increase in share of Eastern block and Organization of Petroleum Exporting Countries’ markets owing to particular commodity composition of Austrian manufactures.
belgium-luxembourg
Manufactured imports
DUM2 =D196612. Effects of U.K. shipping strike.
Manufactured exports
DUM1 =SD196973. Shift in seasonal pattern of exports.
france
Manufactured imports
DUM1 =CD196801. Effects of European Community tariff liberalization.
DUM2 =D197012. Anticipation of mid-1970 relaxation of tight monetary policies.
federal republic of germany
Manufactured imports
DUM1 =D197302 + D197401. Reduction in imports in response to restrictive domestic policies.
Manufactured exports
DUM1 =D196802. Anticipation of imposition of border tax.
DUM2 =D197001 + D197002. Effect of imposition of border tax.
italy
Manufactured imports
DUM1 =D197301. Acceleration of domestic demand coincided with a low level of inventories.
DUM2 =D196902 + D197001. Effects of strikes.
Manufactured exports
DUM1 =SD197779. Shift in seasonal pattern of exports.
japan
Manufactured imports
DUM1 =1 in 197202, 2 in 197301, 3 from 197302 onward, and zero elsewhere. Effects of trade liberalization.
netherlands
Manufactured imports
DUM1 =CD197401. Effects of enlargement of European Community.
DUM2 =D197301. Probable error in deflator, owing to wide exchange rate variations over period.
norway
Manufactured imports
DUM2 =D197201 + D197202. Unusual rundown in stocks reinforced by depressed level of fixed investment.
switzerland
Manufactured imports
DUM1 =D197502. Unusually low level of demand for capital goods relative to total domestic demand.
Manufactured exports
DUM1 =D197402. World recession and sudden lagged effect of 1973 devaluation.
united kingdom
Manufactured imports
DUM1 =1 in 197301 and 2 thereafter. Effects of entry into the European Community.
DUM2 =D197401. Fall in industrial production due to three-day workweek.
united states
Manufactured imports
DUM1 =zero up to 196702, increases from 1 to 7 from 196801 to 197101, and equals 7 thereafter. Effect of rapid increase in Japanese car imports.

Mr. Spencer, economist in the European Department, was a member of the External Adjustment Division of the Research Department when this paper was prepared. He is a graduate of Victoria University of Wellington and the London School of Economics and Political Science and is currently on leave of absence from the Reserve Bank of New Zealand.

The bulk of the estimation work on the model was completed in the summer of 1982 and reflects the data available in late 1981. Some of the parameter estimates used in the current forecasting version of the model are based on more recent revisions of the historical data set, but in general these do not differ significantly from the estimates reported here.

The Fund publishes in its Occasional Paper series reports on the world economic outlook. For the most recent report, see World Economic Outlook: A Survey by the Staff of the International Monetary Fund, Occasional Paper No. 27 (Washington, April 1984) and World Economic Outlook: Revised Projections by the Staff of the International Monetary Fund, Occasional Paper No. 32 (Washington, September 1984).

Michael C. Deppler and Duncan M. Ripley, “The World Trade Model: Merchandise Trade,” Staff Papers, International Monetary Fund (Washington), Vol. 25 (March 1978), pp. 147-206 (hereinafter referred to as Deppler and Ripley). See also, Duncan M. Ripley, “The World Model of Merchandise Trade: Simulation Applications,” Staff Papers, International Monetary Fund (Washington), Vol. 27 (June 1980), pp. 285-319.

The full set of revised parameter estimates is reported in Grant H. Spencer, “Revised Estimates for the World Trade Model” (unpublished, International Monetary Fund, April 30, 1984). (Hereinafter referred to as Spencer (1984).)

See, for example, R.J. Ball, ed., The International Linkage of National Economic Models (Amsterdam: North Holland, 1973).

In forecasting applications, import volumes of fuels for industrial countries and total import volumes for the regions are also determined exogenously.

Only those structural equations in the industrial country prices block relating to trade in manufactures, together with definitions of the variables, are set out in Table 2. Coefficient estimates for these price equations are presented in Tables 4 through 6. The tabulated estimates may differ slightly from the parameter estimates actually used in the current forecasting version of the model.

Tables 4 and 5 in the present paper compared with Tables 5 and 6 in Deppler and Ripley.

In the model, the percentage rate of change of each variable is expressed as the semiannual first difference of its natural logarithm.

In a behavioral model such as the world trade model, a fixed weighting system is necessary to avoid the spurious relative price movements that would arise if weights were adjusted within the sample period. However, in choosing a midsample (1970) base period with the aim of obtaining a representative set of elasticity estimates, it is inevitable that approximation errors will begin to have a significant impact on some of the weighted variables in the forecast period.

In the previous version, no separate energy price terms were included, and the weight on domestic raw material prices was set at 0.075 across all 14 industrial countries.

The test statistic used was 21n(L0/L1). This quantity is asymptotically distributed as χ2(3) where

L0 =the value of the likelihood function obtained from the unrestricted estimation of equation (1), and
L1 =the value of the likelihood function obtained from the estimation of equation (1) subject to restrictions (1.1), (1.2), and (1.3).

Potential output series are derived using the method described in Jacques R. Artus, “Measures of Potential Output in Manufacturing for Eight Industrial Countries, 1955–78,” Staff Papers, International Monetary Fund (Washington), Vol. 24 (March 1977), pp. 1-35.

These restrictions were incorporated in the model described by Spencer (1984).

The excess demand elasticity for manufactured imports in Belgium-Luxembourg is estimated at 0.94.

As summarized, for example, by Morris Goldstein and Mohsin S. Khan, “Income and Price Effects in World Trade,” Chap. 20 in Handbook of International Economics, ed. by Ronald W. Jones and Peter B. Kenen (Amsterdam: North-Holland, 1984).

The method adopted to determine the maximum length of lag was to successively reduce the lag length under a high-degree polynomial, choosing the lag length that minimized the estimated standard error of the equation.

As seen in Table 10, these are the Federal Republic of Germany and the United Kingdom. The diagnostic statistics given in Table 10 indicate that, in both of the equations concerned, the relative price lag distributions are not well determined. Furthermore, for the United Kingdom, the lag distribution is not very believable; the specification shown was chosen in preference to having no relative price effect at all.

End-point restrictions may be required to prevent U-shaped lag distributions. These may arise when the lag distribution is ill determined by the sample information, in which case end-point restrictions will tend not to be rejected by standard statistical tests, or when there is a misspecification, in which case end-point restrictions will tend to be rejected.

The test used here is the same likelihood ratio test described in Section I.

Using base year (1970) trade patterns to determine the weights.

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