Chapter

14 A Dynamic Error-Correction Model of the U.S. Current Account

Author(s):
Yusuke Horiguchi
Published Date:
January 1992
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Author(s)
ELLEN M. NEDDE

Conventional models of the U.S. current account, which express trade flows as functions of activity variables and relative prices, have recently been criticized on the grounds that they fail to reflect fully supply-side effects and, as a result, generate medium-term projections that may be overly pessimistic. These criticisms were partly fueled by the inability of many modelers to forecast accurately the turning point in U.S. trade and current account developments since 1987 and the degree of more recent improvements.1

The inability of models to forecast accurately short-term movements in net flows should not be surprising. Net flows that are based on much larger underlying gross flows are inherently difficult to predict. A prediction error in the trade balance in 1989 equal to 3 percent of underlying gross flows (current dollar merchandise imports plus exports) would have implied an error of $25 billion, or 22 percent of the actual trade balance. While it is possible for short-run prediction errors to indicate more fundamental problems with a model’s predictive power, one should test directly for structural breaks in the equations rather than examine the model’s ability to track actual developments in net flows over a short horizon.

This paper outlines a quarterly model of the U.S. current account that was recently estimated by the IMF’s North American Division for use in projections associated with the World Economic Outlook. The model contains 40 estimated equations which describe the behavior of volumes and prices for trade in goods and services, payments and receipts of investment income, and gross flows in the capital account. To the extent possible, foreign demand and price variables were taken from the “global economic environment” for the United States provided as part of the World Economic Outlook exercise.

While some researchers have focused on additional variables that might capture missing supply effects, another possible source of misspecification is the assumed lag structure. The specification of the current model combines some conventional features of trade models with an error correction methodology. This methodology, combined with a general-to-specific testing-down procedure, permits the data to identify a more general lag structure and demand and supply specification than those contained in most existing models of the U.S. current account, and thus may be better able to capture longer-run supply effects.

To evaluate the model’s ability to capture supply effects, particularly since the decline of the dollar beginning in 1985, several diagnostic tests are performed to check for the presence of white noise residuals. In addition, a subsample of the data is reserved to test for structural breaks in the equations. Ex post simulation and forecast properties are then examined, revealing the model’s overall ability to predict out of sample. Experiments with alternative assumptions for some key exogenous variables reveal further the model’s simulation properties.

The paper is organized as follows. Section I describes the general methodology of the paper, including the error correction methodology and general-to-specific testing-down procedure used and the degree of disaggregation of the current account for purposes of estimation. Section II contains descriptions of long-run equilibrium and short-run error correction equations for merchandise trade volumes and prices. Equations for trade in services are discussed in Section III, while Section IV contains equations for investment income and the capital account. The predictive performance of the model is examined in Section V of the paper. Section VI describes the response of the current account and its components to changes in assumptions regarding domestic and foreign growth and the value of the dollar. Concluding remarks are contained in Section VII. Estimated equations, associated test statistics, and tabulations of alternative estimates are presented in Annexes I and II.

I. Methodology

For purposes of estimation, real trade flows are disaggregated into oil and non-oil imports and agricultural and nonagricultural exports. Implicit deflators for all but oil imports and fixed-weight prices for non-oil imports and nonagricultural exports are also estimated. In the services account, equations are estimated for real payments and receipts of total services and their deflators. In the investment account, nominal direct investment income payments and receipts are estimated, as are implicit rates of return on private and government portfolio investments and stocks of direct investment and portfolio assets and liabilities. The stock of private portfolio liabilities is solved residually to ensure that external financing is consistent with the estimated current account balance.

The model is estimated using the two-step procedure as developed by Granger and Engle.2 This procedure involves the estimation of a long-run equilibrium relationship among levels of variables in the first stage. In the second stage, first-differences of variables and lagged residuals from the long-run equation (deviations from equilibrium) are used to estimate a short-run error correction equation which models short-run dynamics.

In both the first and second stages of the estimation, a general-to-specific methodology was followed. In the first stage, alternative sets of variables (that were consistent with perfect and imperfect competition) were tested for cointegration with the dependent variable. In addition, volume equations were tested for cointegration with alternative activity variables, such as gross national product and total domestic demand, and for the importance of trend terms that might signal supply effects not fully reflected in prices. Prices were specified generally to allow the United States to be either a price setter or price taker in export and import markets. In the second stage, Granger causality tests were performed to test for exogeneity of possible independent variables. The lag structure specified in the error correction equations was a general one, with four lags in the dependent and independent variables included. Nested F tests were then used to test for a more parsimonious representation. All estimated equations, test statistics, and definitions of the tests performed are contained in Annex I; the results of these tests are not discussed in detail except for those cases in which they indicate a possible specification error.

II. Merchandise Trade

As disaggregated here, the major components of U.S. merchandise trade are non-oil imports and nonagricultural exports. Demand for imports is modeled assuming that imported goods are imperfect substitutes for domestic goods; empirically, supply is best represented as a variable price markup over cost. While foreign exporters seem to exhibit some strategic pricing behavior, the U.S. market for exports is best represented by perfect competition, with exports being viewed as imperfect substitutes for foreign goods on the demand side. Oil imports and agricultural exports are modeled separately because of the unique behavior of these components; both models contain elements of the perfect substitutes model under perfect competition.3

Model of Non-Oil Imports and Nonagricultural Exports

Imports are modeled as imperfect substitutes for domestic goods so that the volume of non-oil imports demanded depends positively on a domestic scale variable and negatively on the price of imports relative to the domestic price level. On the supply side, the presence of product differentiation or other market imperfections is assumed to give foreign suppliers some degree of control over the price they charge. The price of imports is therefore not determined in the U.S. market, but is determined by a variable price markup relative to foreign costs, where suppliers adjust the markup in response to changes in competitive pressures in the U.S. market.4 In level terms, the foreign export price (PX*) is equal to the markup, δ, times foreign unit labor costs (ULC*), where the markup is a function of U.S. export prices adjusted for exchange rates (PXER) relative to foreign costs. The exchange rate is expressed in units of foreign currency per U.S. dollar.

Taking logs and assuming U.S. import prices are approximately equal to foreign export prices adjusted for exchange rates yields the following foreign export price and domestic import price equations.5

The price of non-oil imports is thus a weighted average of the domestic export price and foreign unit labor costs adjusted for exchange rates.

Nonagricultural exports are modeled according to perfect competition, assuming that foreigners view exports as imperfect substitutes for their own domestic production. The volume of exports demanded (xnad) is therefore a positive function of a foreign scale variable (y*) and a negative function of the price of exports (pxna) relative to foreign export prices adjusted for exchange rates (px$* = px* - er). The supply of exports is a positive function of the price of exports relative to domestic costs.

Setting export demand equal to export supply and solving for the equilibrium quantity yields a volume equation in which exports are a positive function of the foreign scale variable and a negative function of U.S. unit labor costs relative to the dollar price of foreign exports.

The price of exports then becomes a positive function of foreign demand and a weighted average of domestic unit labor costs and foreign export prices, adjusted for exchange rates.

Finally, combining equations (2) and (7) allows U.S. and foreign export prices and the U.S. import price to be written as weighted averages of domestic and foreign unit labor costs.6

Non-Oil Imports and Nonagricultural Exports in the Long Run

In the long run, the volume of non-oil imports was found to depend upon real U.S. total domestic demand and the relative price of imports adjusted by the average tariff rate.7 The estimated demand elasticity is equal to 2.3 in the long run, a value that is in line with other estimates.8 Others have included real GNP as the activity variable to account for the intermediate goods that the United States imports. An alternative long-run equation using real GNP was therefore tested; while the elasticity was little changed, the R2 and cointegration statistics declined. A long-run price elasticity of –0.9 was estimated using a fixed-weight price index for non-oil imports; when the relative price term was constructed using the implicit deflator, this elasticity was slightly smaller in absolute value.

Helkie and Hooper9 have attributed what is viewed as a high income (or demand) elasticity to the failure of trade equations to adequately capture longer-term supply effects. To capture these effects, they include the ratio of foreign to domestic capital stocks in their trade volume equations. One might expect U.S. exports to be a negative function and imports to be a positive function of this upward-trending variable. Various versions of the Helkie-Hooper model have produced mixed results on the importance of these effects, however; while the terms enter with the correct sign, they have not always entered significantly. When a trend term was added to the non-oil import volume equation in the present model, its estimated coefficient was negative and caused a significant increase in the estimated elasticity of demand.

The fixed-weight price index for non-oil imports was found to be cointegrated with domestic unit labor costs and foreign unit labor costs, adjusted for exchange rates. The equation satisfies homogeneity since the sum of the coefficients on domestic costs and foreign costs adjusted for the exchange rate is approximately unity.10 The equation also satisfies equal pass-through of foreign costs and exchange rates—a result that is expected from theory, but not always accepted by the data. In particular, one may not want to impose this equality in the short run since suppliers may respond differently to changes in exchange rates (which may be viewed as temporary) and changes in foreign costs (which may be viewed as more permanent). The importance of domestic unit labor costs in import prices (a weight of 0.5) indicates that foreign suppliers pay considerable attention to U.S. cost conditions even in the long run.11 If the United States were a price taker (setter) in the import market, one would expect a coefficient of unity (zero) on foreign costs adjusted for the exchange rate and a coefficient of zero (unity) on domestic costs.

Others have noted the difficulties of estimating implicit deflators for non-oil imports (and nonagricultural exports).12 Largely because prices of computers have been falling rapidly in recent years and because computers represent a growing share of U.S. trade, implicit deflators for U.S. exports and imports do not appear to reflect changing costs and exchange rates in a stable way. In particular, long-run cointegrating relationships for implicit trade deflators are difficult to find without including the price of computers explicitly and permitting somewhat large deviations from homogeneity. However, even if fixed-weight indices are used in the relative price terms of volume equations, implicit trade deflators need to be estimated in order to convert from volumes to values of merchandise trade. Implicit deflators were therefore estimated as functions of domestic costs, foreign export prices, the exchange rate, and the price of business machinery in the long run, even though homogeneity and equal pass-through of foreign prices and exchange rate changes would not be satisfied.13 The long-run relationship estimated for the implicit deflator for non-oil imports includes the foreign export price, the exchange rate, the price of business machinery, and a trend term.14

The volume of nonagricultural exports in the long run was found to depend positively on real foreign domestic demand and negatively on U.S. unit labor costs relative to foreign export prices adjusted for exchange rates. The addition of a deterministic trend was required to achieve cointegration. This term, entering with a negative estimated coefficient, is not inconsistent with the supply variable proposed by Helkie and Hooper, but given the mixed results associated with their relative capital stock term, it is not certain what the source of this unexplained time trend might be. The estimated long-run demand elasticity, at 2.1, is slightly less than the import demand elasticity, retaining the gap that is typically found between these elasticities. The price elasticity, at -0.5, is at the low end of other estimates.15

The fixed-weight index for prices of nonagricultural exports was found to be determined primarily by domestic costs in the long run. The equation approximately satisfies homogeneity since the sum of the cost coefficients is close to unity. Demand did not enter the long-run equation, but as seen below, does influence price in the short run. The implicit deflator for nonagricultural exports was found to be cointegrated with domestic unit labor costs, foreign export prices, the exchange rate, and the price of business machinery.16

Non-Oil Imports and Nonagricultural Exports in the Short Run

The short-run error correction equation for non-oil imports contains the independent variables of the long-run equation (but expressed in difference form) and the error correction term, which is equal to the residuals from the long-run equation lagged one period. The short-run demand elasticity of 1.4 is less than its long-run value, but the coefficient on the error correction term, at -0.5, implies relatively fast adjustment to equilibrium values.

In contrast, the fixed-weight price of non-oil imports adjusts relatively slowly to its long-run equilibrium. All short-run coefficients are less than their long-run values, implying a gradual increase over time of the impact of changes in domestic and foreign costs and the exchange rate. The implicit deflator also adjusts slowly to equilibrium, with a coefficient on the error correction term of –0.2. Short-run movements in the fixed-weight index improve the fit of the equation for the deflator significantly; these movements are the principal determinants of the implicit deflator in the short run, while foreign export prices, the exchange rate, and computer prices are its long-run determinants.

As in the import volume equation, the short-run elasticities in the equation for nonagricultural exports are less than their long-run values. Changes in relative prices enter only after a two-period lag with an elasticity of –0.4. In the price equations, changes in the fixed-weight price index depend primarily on its own lagged values and lagged changes in demand. While differences in domestic and foreign costs enter the short-run equation, the exchange rate enters only through the error correction term. The implicit deflator depends on first differences of its long-run explanatory variables; it does not contain the demand effects that enter the fixed-weight price equation.

Model of Oil Imports and Agricultural Exports

Oil imports are assumed to be perfect substitutes for domestic oil and are calculated as the residual from domestic consumption, production, exports, and stock changes. The latter three variables are not estimated. Consumption (in thousands of barrels a day) is modeled as a positive function of a domestic scale variable and a negative function of the price of oil imports relative to the domestic price level. The dollar a barrel price of imports is then used to translate to the dollar value of petroleum imports.

The presence of subsidies and trade restrictions in the U.S. market for agricultural products makes agricultural exports difficult to estimate. The supply of agricultural exports in the United States seems to be best described by the perfect substitutes model, in which exports are the difference between supply and demand for agricultural goods. Domestic supply (as) is a positive function of the price of agricultural goods (pxa) relative to the domestic price level (or costs), while domestic demand for agricultural goods depends negatively on the relative price of agricultural goods and positively on a domestic scale variable. The supply of exports—which is equal to the difference between domestic supply and domestic demand—is therefore a negative function of the scale variable and a positive function of the relative price.

The demand for agricultural exports abroad is a positive function of a foreign scale variable and a negative function of the price of agricultural exports relative to foreign export prices, adjusted for exchange rates. Equating demand and supply yields agricultural exports as a positive function of the foreign scale variable and the relative price of agricultural goods domestically and a negative function of the domestic scale variable and the relative price of exports abroad. The export price depends positively on domestic and foreign scale variables and prices.

Oil Imports and Agricultural Exports in the Long Run

A long-run cointegrating relationship could not be found for the consumption of oil so that an error correction representation was not used for this equation. The short-run dynamic equation for oil and its long-run implications are discussed below.

The volume of agricultural exports was found to be cointegrated with the expected demand and relative price terms, with the exception of domestic demand, which did not enter the equation significantly. While the model described above appears appropriate for the volume of trade, domestic and foreign costs and demand were poor explanatory variables for the export price and a long-run cointegrating relationship among these variables could not be found. The agricultural export price deflator moves closely with the commodity price index in the IMF’s International Financial Statistics (IFS), but these two series also were not cointegrated. Because of the importance of the medium-term simulation properties of the model, a long-run relationship was imposed that implied proportionality between the agricultural export price and the IFS commodity price index, with a more general specification in the short run.

Oil Imports and Agricultural Exports in the Short Run

The short-run dynamic equation for oil consumption was estimated in both level and difference form. Coefficients were very similar and both equations performed satisfactorily in terms of diagnostic tests, but the equation in level terms performed better in dynamic simulations (the in-sample mean absolute error was reduced significantly). Oil consumption was found to depend on its own lagged values (up to five quarters) with the coefficients approximately summing to unity. Short-run demand and price elasticities for oil consumption were estimated at 0.8 and -0.1, respectively.

The short-run dynamic equation for agricultural exports was estimated using a general specification that included differences (contemporaneous and lagged) of the relative price terms and demand terms, as well as lagged values of the dependent variable. However, sequential testing down reduced the equation to one with rather sparse dynamics, with only the dock strike dummy and the error correction term entering significantly, although none of the diagnostic tests rejected white noise residuals.17 In the short run, first differences in the agricultural export price are a function of its own lagged values and lagged differences of the IFS commodity price index. In the long run, the price is constrained to move with world commodity prices. The coefficient on the error correction terms was low (-0.13), but significantly different from zero (t = -3.9).

III. Trade in Services

Model of Service Payments and Receipts

Trade in services includes travel, passenger fares, other transportation (freight and port services), royalties and license fees, and other private services such as education and business services. These services were aggregated and estimated in real terms using deflators for “other service” imports and exports from the national income and product accounts.18

Real service payments are expressed as a function of a domestic scale variable, the price of service payments relative to the domestic price level, and the volume of merchandise imports and exports to capture the effects on freight and port services of growing international trade. Real service receipts are expressed analogously. Reflecting the prices used to deflate individual components of service payments and receipts in the national accounts, the deflator for service payments is expressed as a weighted average of the U.S. GNP deflator and the foreign consumer price index adjusted for exchange rates, and the deflator for services receipts is expressed as a weighted average of the U.S. GNP deflator and the U.S. consumer price index.

Service Payments and Receipts in the Long Run

Service payments and receipts were each found to be cointegrated with total domestic demand, relative prices, and merchandise trade volumes. Both long-run equations also contain several dummy variables to reflect recent revisions to the data.19 The demand elasticity in the payments equation was estimated to be relatively low at 0.4, compared with an elasticity in the receipts equation of 1.0. This divergence offsets somewhat the effects of a higher elasticity of demand in the merchandise import equation relative to that of the export equation. However, since service flows are smaller than merchandise flows and because service payments respond more strongly to growth in merchandise trade than do receipts, the model still has the property that the current account gradually deteriorates under assumptions of equal U.S. and foreign growth and unchanged real exchange rates.

The deflator for service receipts was found to be cointegrated with the U.S. consumer price index and the GNP deflator as expected. However, the deflator for service payments was not cointegrated with the expected price series, although the estimated coefficients were consistent with theory and approximately satisfied homogeneity. Including the fixed-weight price index for GNP rather than the implicit deflator had no effect on the estimated coefficients or the results of the tests for cointegration. However, as in the case of the agricultural export price, the medium-term simulation properties of the model were given precedence over its statistical properties, and the dynamic equation was estimated including this error correction term.20

Service Payments and Receipts in the Short Run

Real service payments and receipts both respond strongly to deviations from equilibrium in the short run, with coefficients on the error correction terms of -0.7 and -0.5, respectively. Payments respond more strongly to changes in demand in the short run (0.7) than in the long run (0.4); in contrast, service receipts do not respond to short-run changes in demand except through the error correction term.

The deflators for payments and receipts of services both depend on their own lagged values in the short run, as well as on lagged price levels and the error correction terms. Despite the poor performance in cointegration tests of the long-run equation for the payments deflator, the error correction term enters significantly (t = –3.3), although with a relatively low coefficient (–0.1).

IV. Investment Account

Model of Investment Income

Investment income includes direct investment income, interest income on private portfolio assets, and interest income on government portfolio assets. Data on direct investment income payments and receipts are collected, while interest income is estimated by the Bureau of Commerce by applying an imputed interest rate to estimated stocks of assets and liabilities. The estimation method employed here mimics these techniques by calculating an implicit rate of return on private and government portfolio assets and liabilities and estimating the rate of return as a function of the U.S. Treasury bill rate.21

For direct investment, income payments and receipts are estimated directly as functions of the relevant (book value) stocks, capacity utilization in the countries where the investments are located, and quarterly seasonal dummies. The receipts equation also includes the price of oil since a significant portion of U.S. direct investment abroad is in the petroleum industry.22

Estimated asset and liability stocks are required to forecast investment income payments and receipts. The error correction methodology was not used for these equations, rather stocks were estimated as functions of their own past values, time trends, and quarterly dummy variables.

Estimated Investment Income

The implicit rates of return on private portfolio liabilities and assets were found to be cointegrated with the U.S. Treasury bill rate (with long-run coefficients of 0.7 and 0.9, respectively). Long-run cointegrating relationships did not exist between the implicit rates of return on government portfolio assets and liabilities and the U.S. Treasury bill rate. In the short run, all four implicit returns depended on their own lagged values and contemporaneous and lagged values of the U.S. Treasury bill rate.23

With the exception of the price of oil, which was found to influence direct investment income receipts only in the short run, cointegration tests confirmed the long-run relationships for direct investment income payments and receipts described above. Capacity utilization effects enter strongly in both the long run and the short run. The estimated coefficient on the asset stock was close to unity in the long run (1.1), which is somewhat surprising given the large discrepancy between this book value measure and the market value of foreign direct investment assets; the coefficient on the liability stock was estimated at 0.7. As found by others, estimated standard errors are high for these equations.

In the capital account, estimated equations for asset and liability stocks imply estimated gross capital flows, which are unlikely to match the estimated current account. Rather than place all discrepancies between estimates of the current account and capital flows in the statistical discrepancy, the inflow of private portfolio investment is taken as a residual to ensure that estimated net capital flows are consistent with the required financing of the estimated current account balance. In other words, the inflow of private portfolio investment (LPNET) is taken as the residual from private portfolio investment outflows (APNET), the balance on the current account (BCUR), net inflows of foreign direct investment (LDNET - ADNET) and government portfolio investment (LGNET - ADNET), the statistical discrepancy (SD), and the allocation of SDRs (SDRA). (The statistical discrepancy and allocation of SDRs are taken as exogenous to the model.)

The stock of private portfolio liabilities (LP) is then calculated using cumulated gross flows.

While only the net flows need satisfy this balance of payments identity, the distribution of the gross flows are important for forecasting investment income since the United States receives and pays a wide range of implicit rates of return on its assets and liabilities. Almost all assets and liabilities depend on a trend term in addition to their own lagged values. Diagnostic tests indicated that residuals from the equations for official assets and liabilities suffered from heteroscedasticity, possibly a result of increased intervention in the 1980s.

V. Predictive Performance of the Model

This section discusses the performance of the model in static and dynamic simulations.24 The equations were estimated over the period 1969:1–1987:2, retaining 1987:3–1989:2 for out-of-sample forecasts. Root mean square percent errors for both periods for the major components of the current account are given in Table 1.

Table 1.Root Mean Square Percent Errors1
1971:4–1987:21987:3–1989:2
StaticDynamicStaticDynamic
Non-oil import volume2.64.01.72.3
Fixed-weight price1.32.80.20.4
Implicit deflator1.12.60.81.7
Oil import volume5.819.74.74.2
Nonagricultural export volume2.53.73.26.1
Fixed-weight price0.92.40.50,5
Implicit deflator0.81.30.61.3
Agricultural export volume7.010.76.68.2
Implicit deflator1.94.42.27.5
Real service payments2.02.92.22.7
Implicit deflator1.02.40.92.2
Real service receipts2.02.31.32.0
Implicit deflator1.12.80.92.5
Trade balance1.63.71.31.6
Net services1.31.31.62.7
Net direct investment income3.55.52.54.2
Net portfolio income1.97.31.84.7
Balance on services and investment income1.92.61.41.5
Current account1.42.91.00.9

The larger components of merchandise trade, non-oil imports and nonagricultural exports, tended to perform better than the smaller, more volatile, components of oil imports and agricultural exports both in and out of sample (Figures 1 and 2). The nonagricultural export equation began to underpredict post sample in the dynamic simulation, but otherwise the major components of trade volumes tracked the data closely. One marked difference among the four volume equations was the absence of an error correction term in the oil import equation and its tendency to miss some major turning points in the data.25 The direction of the trade volume errors post sample tends to be somewhat offsetting, with small underpredictions of the major components and small overpredictions of agricultural exports and oil imports.

Figure 1.United States: Actual and Predicted Import Volumes

Figure 2.United States: Actual and Predicted Export Volumes

Figures 3 and 4 contain simulations of implicit deflators and fixed-weight price indices for merchandise trade. Again, the smaller, more volatile components of trade produced larger percent errors than the two major components. As others have found, the import deflator increased by less than predicted during 1985–86, but these prediction errors were eliminated by mid-1987. In the post-sample period, the model began to overpredict the deflator for agricultural exports, but tracked closely both fixed-weight prices and implicit deflators for non-oil imports and nonagricultural exports.

Figure 3.United States: Actual and Predicted Trade Deflators

Figure 4.United States: Actual and Predicted Fixed-Weight Trade Prices

The portion of the model describing services performed relatively well in sample, with root mean square percent errors under 3 percent for both dynamic and static simulations (Figures 5 and 6). This ability to track the data closely continued in the post-sample period, with nearly all of the root mean square percent errors declining in value. Recall that tests for cointegration did not support the long-run equation for the service payments deflator, yet the dynamic equation for that deflator performs slightly better than the deflator for service receipts both in and out of sample.

Figure 5.United States: Actual and Predicted Real Services

Figure 6.United States: Actual and Predicted Service Deflators

Figures 79 contain simulation results for the balances on portfolio income, total investment income (excluding capital gains and losses), the combined service and income account, the trade account, and the current account. Root mean square errors are calculated as percentages of the underlying gross flows relevant to the balance.26

Figure 7.United States: Actual and Predicted Balances on Services and Income

1 Excluding capital gains and losses.

Figure 8.United States: Actual and Predicted Merchandise Trade Balance

Figure 9.United States: Actual and Predicted Current Account Balance

Simulation errors for the balances on trade and the current account are presented in two forms in Figures 8 and 9. The bottom part of each figure shows the forecast error of each balance expressed as a percentage of underlying gross flows. The maximum percent error for the trade balance is 4 percent for the static simulation and 10 percent for the dynamic simulation. The maximum percent error for the current account balance is 3½ percent for the static simulation and 7½ percent for the dynamic simulation.27 The mean percent error for both balances is approximately zero for the static simulation, both in and out of sample. However, the dynamic simulations produce in-sample mean percent errors of 2.2 and 2.1 percent for the trade and current account balances, respectively. The corresponding post-sample errors are smaller in absolute value at –1.1 and –0.3 percent.

VI. The U.S. Current Account in the Face of Exogenous Shocks

This section examines alternative assumptions about the paths of variables that have been taken as exogenous to the model: domestic demand, foreign demand, and the value of the dollar. In general, the response of trade or current account balances to alternative paths of these variables depends upon the underlying reasons for changes in what are essentially endogenous variables. A partial equilibrium model cannot distinguish among these underlying changes, but an exercise such as this still can be useful in illustrating further the simulation properties of the model.

Table 2 contains estimates of changes over 12 quarters in components of the current account in response to a permanent increase in real U.S. total domestic demand. An increase in real domestic demand by 1 percent in the first quarter causes the volume of non-oil imports to increase by 1.4 percent on impact, rising almost completely to a long-run value of 2.3 percent of baseline imports by the second quarter. The response of oil imports is greater in the short run than in the long run—the first quarter increase of 2.4 percent of baseline declines to 1.2 percent by the end of the third year. Import prices and export volumes and prices are unaffected by changes in U.S. demand. The trade balance therefore deteriorates in the first quarter by 0.8 percent of gross flows (0.1 percent of GNP) and by the twelfth quarter has deteriorated by 1.1 percent of gross flows (0.2 percent of GNP).

Table 2.The U.S. Current Account: Response to a 1 Percent Increase in U.S. Domestic Demand(In percent)
Quarter
1246812
Non-oil imports
Volume1.42.22.42.42.32.3
Fixed-weight price
Implicit deflator
Value1.42.22.42.42.32.3
Oil imports
Volume2.41.60.81.51.11.2
Value2.41.60.81.51.11.2
Nonagricultural exports
Volume
Fixed-weight price
Implicit deflator
Value
Agricultural exports
Volume
Implicit deflator
Value
Trade balance1-0.8-1.0-1.0-1.1-1.0-1.1
(As percent of GNP)-0.1-0.1-0.1-0.1-0.1-0.2
Service payments
Volume1.00.91.00.90.90.9
Implicit deflator
Value1.00.91.00.90.90.9
Service receipts
Volume
Implicit deflator
Value
Net services1-0.4-0.4-0.4-0.5-0.4-0.4
Net direct investment income1-0.2-0.3-0.6-0.6-0.6
Net portfolio income1-0.1-0.2-0.6-0.9-1.1-1.8
Current account1-0.6-0.8-0.8-0.9-0.9-1.0
(As percent of GNP)-0.1-0.1-0.1-0.2-0.2-0.2

The components of the balance on services and income that are affected by the change in demand include service imports, direct investment income payments (responding to the higher capacity utilization in the United States and higher merchandise imports), and the balance on portfolio income (arising from the response of capital inflows to the lower current account balance). Service payments rise immediately to a long-run value of about 1 percent above baseline. The balance on direct investment income as a percent of baseline gross flows falls gradually to 0.9 percent below baseline by the end of the third year. The balance on portfolio income as a percentage of gross flows also declines gradually; the balance is down by 0.6 percent relative to baseline at the end of the first year and down by 1.8 percent at the end of the third year. Correspondingly, the balance on the current account deteriorates by 0.6 percent of gross flows (0.1 percent of GNP) during the first quarter and by 1.0 percent of gross flows by the twelfth quarter (0.2 percent of GNP).

The effects of an equivalent change in foreign total domestic demand are contained in Table 3. The effects on trade include increases in both nonagricultural and agricultural exports, with both deviations from baseline gradually rising to their respective long-run values of 2.1 percent and 1.3 percent. Although there are short-run demand effects on the fixed-weight nonagricultural price index, these effects are not present in the implicit deflator, causing the value of exports to rise by the same percentage as volume. The effects on the trade balance are a 0.6 percent increase relative to baseline (as a percentage of gross flows) during the first quarter, rising to a long-run value of 0.9 percent by the end of the first year (0.1 percent of GNP).

Table 3.The U.S. Current Account: Response to a 1 Percent Increase in Foreign Domestic Demand(In percent)
Quarter
1246812
Non-oil imports
Volume
Fixed-weight price
Implicit deflator
Value
Oil imports
Volume
Value
Nonagricultural exports
Volume1.61.71.92.02.12.1
Fixed-weight price0.50.50.3
Implicit deflator
Value1.61.71.92.02.12.1
Agricultural exports
Volume0.30.81.01.21.3
Implicit deflator
Value0.30.81.01.21.3
Trade balance10.60.80.90.90.90.9
(As percent of GNP)0.10.10.10.10.10.1
Service payments
Volume0.20.20.30.30.30.3
Implicit deflator
Value0.20.20.30.30.30.3
Service receipts
Volume0.20.81.31.51.51.6
Implicit deflator
Value0.20.81.31.51.51.6
Net services10.30.60.60.70.7
Net direct investment income14.08.06.25.45.34.9
Net portfolio income10.10.30.71.11.52.3
Current account10.71.01.11.21.21.2
(As percent of GNP)0.10.20.20.20.20.2

On the services side, both payments and receipts of services rise in response to the larger volume of real merchandise exports and its effect on freight and port services. The effect on receipts exceeds that on payments, causing the balance on services to rise by 0.7 percent of gross flows by the eighth quarter. Responding to the new current account path, the balance on portfolio income improves by 2.3 percent of gross flows by the end of the third year. The current account improves gradually from 0.7 percent of gross flows during the first quarter to 1.2 percent at the end of the third year. As a percentage of GNP, the improvement is 0.2 percent.

These simulations imply that the medium-term projections produced by the model under assumptions of constant real exchange rates and similar growth rates at home and abroad will be characterized by a widening trade deficit because of the remaining asymmetry with respect to income elasticities in the trade volume equations and the fact the similar growth rates of imports and exports imply larger absolute increases in imports since they start from a larger base. In the current account, a gradual deterioration in the balance on portfolio income reinforces the worsening trade performance.

Changes in exchange rate assumptions have more widespread effects on the current account than do changes in demand. Table 4 shows these effects for a 10 percent effective depreciation of the dollar. On the trade account, the volume of non-oil imports responds immediately, declining by 1.7 percent of its baseline value; that response gradually increases, reaching 3.3 percent by the end of the second year and 5.2 percent by the end of the third year. The high degree of exchange rate pass-through in the implicit price deflator, combined with a somewhat low price elasticity in the volume equation, implies that the value of imports increases relative to baseline, although by less than the increase in exports so that the trade balance improves as expected.

Table 4.The U.S. Current Account: Response to a 10 Percent Depreciation of the U.S. Dollar(In percent)
Quarter
1246812
Non-oil imports
Volume-1.7-2.0-3.3-4.5-5.0-5.2
Fixed-weight price2.33.85.35.96.16.2
Implicit deflator3.46.29.510.210.09.3
Value1.74.25.85.34.53.6
Oil imports
Volume
Value
Nonagricultural exports
Volume1.66.86.25.95.7
Fixed-weight price0.31.11.61.92.1
Implicit deflator3.53.43.23.23.13.1
Value3.55.110.29.69.29.0
Agricultural exports
Volume1.43.44.55.25.8
Implicit deflator
Value1.43.44.55.25.8
Trade balance10.80.82.42.42.42.3
(As percent of GNP)(1.10.10.30.30.30.3
Service payments
Volume-1.4-2.0-3.1-3.9-4.0-4.2
Implicit deflator1.72.75.05.85.96.0
Value0.20.61.81.71.61.5
Service receipts
Volume1.92.03.13.23.23.2
Implicit deflator
Value1.92.03.13.23.23.2
Net services10.90.80.80.90.90.9
Net direct investment income1
Net portfolio income10.10.20.91.62.23.6
Current account10.70.71.91.92.02.0
(As percent of GNP)0.10.10.30.30.40.4

With respect to exports, the volumes of nonagricultural and agricultural exports do not respond on impact to the depreciation of the dollar. By the second quarter, however, both rise by over 1 percent of baseline, and by the end of the third year nonagricultural exports are up by 5.7 percent relative to baseline and agricultural exports are up by 5.8 percent. The nonagricultural export price rises by 3.5 percent in the first quarter; the increase then dampens to 3.1 percent by the twelfth quarter. The fixed-weight price index shows slightly smaller pass-through, rising by only 0.3 percent in the second quarter, and up to 2.1 percent after three years. With these price and volume effects, the value of nonagricultural exports rises by as much as 10.2 percent during the first year, but by 9.0 percent in the long run. Agricultural exports rise by 5.8 percent in value terms. The effects on the trade balance are an improvement during the first quarter by 0.8 percent of gross flows (0.1 percent of GNP), implying the absence of a J-curve. This effect rises to 2.3 percent of gross flows and 0.3 percent of GNP by the fourth quarter.

In the services and income accounts, real service payments decline relative to baseline in response to an increase in the relative price, as the implicit deflator absorbs over half of the exchange rate change. The deflator for receipts does not respond to an exchange rate change, but volumes increase by 2.0 percent during the first half year, and 3.2 percent after three years in response to improved competitiveness. No exchange rate effects are present in the direct investment equation, but the balance on portfolio income improves as net inflows decline and the current account improves. Relative to gross flows, the current account improvement is 0.7 percent initially, rising to 2.0 percent; relative to GNP, the improvement is 0.1 percent, rising to 0.4 percent by the third year.

VII. Concluding Remarks

This paper has described a model of the U.S. current account that combines some conventional features with an error correction methodology. This methodology permits a more general lag structure than that contained in most existing models of the U.S. current account, and thus may be better able to permit the short-term disequilibria associated with the large exchange rate changes of the 1980s and to capture longer-run supply effects.

To evaluate the model’s ability to capture supply effects, particularly since the decline of the dollar beginning in 1985, several tests were performed. First, a number of diagnostic tests indicated that the equations captured most of the systematic movements in trade volumes and prices during the sample period. Second, a subsample of the data was reserved to perform tests for structural breaks in the equations with the results confirming stability of the estimated parameters. Ex post simulation and forecast properties were then examined, revealing that the model’s overall ability to predict does not deteriorate during the latter part of the 1980s. Alternative assumptions for some key exogenous variables further revealed the model’s simulation properties. In particular, simulations involving alternative paths of domestic and foreign demand confirmed that in the face of unchanged real exchange rates and policies and similar rates of growth at home and abroad, the U.S. current account is likely to resume a modest deterioration.

ANNEX I

Estimated Equations of the Model

Tests for cointegration in the long-run equations were performed using critical values developed by Sargan and Bhargava for the Durbin-Watson statistic, Dickey-Fuller tests, and augmented Dickey-Fuller tests.28 Standard errors are not reported for the long-run equilibrium equations since the coefficients, while consistent, do not have asymptotic normal distributions and because the equation residuals, while I(0), are autocorrelated, producing biased standard errors. For the short-run error correction equations, several diagnostic tests were performed to ensure well-behaved residuals. These included tests for residual autocorrelation, conditional heteroscedasticity, normality, and unconditional heteroscedasticity.29 In addition, the period 1987:3–1989:2 was reserved for out-of-sample forecasts and the results of Chow tests for parameter constancy are reported (followed in brackets by the probability of the null hypothesis of parameter constancy).30 Absolute values of t-statistics are reported below each estimated coefficient.

Non-Oil Import Volume

Long-Run Equilibrium

R2 = 0.991 DW = 0.75 DF = -4.35 ADF = -4.34

Short-Run Error Correction

R2 = 0.696 SE = 0.029

AR(1-5): F[5,57] = 1.54 ARCH(4): F[4,54] = 0.69

Normality: χ2 (2) = 0.73 Heteroscedasticity: F[12,49] = 1.19 Chow: F[8,62] = 0.32 [0.955]

Comparison of Alternative Estimates: Non-Oil Import Volume
Demand/IncomeRelative PriceCapacityRelative
LR (SR)LR (SR)UtilizationSupply
Present model2.3 (1.4)-0.9 (-0.7)
Dunaway (1988)2.7-1.1 (-0.6)
Helkie and Hooper (1988)2.1-1.2-0.3-0.8
Krugman and Baldwin (1987)2.9-0.9 (—)

Non-Oil Import Fixed-Weight Price

Long-Run Equilibrium

R2 = 0.992 DW = 0.35 DF = -2.76* ADF = -3.53

Short-Run Error Correction

R2 = 0.575 SE = 0.013

AR(1-5): F[5,56] = 0.60 ARCH(4): F[5,51] = 0.62

Normality: χ2(2) = 4.46 Heteroscedasticity: F[10,50] = 0.99

Chow: F[8,61] = 0.04 [1.00]

Non-Oil Import Deflator

Long-Run Equilibrium

R2 = 0.998 DW = 0.63 DF = -3.71 ADF= -4.01

Short-Run Error Correction

R2 = 0.955 SE = 0.005

AR(1-5): F[5,57] = 0.98 ARCH(4): F[4,54] = 0.80

Normality: χ2(2) = 2.02 Heteroscedasticity: F[ 12,49] = 1.17

Chow: F[8,62] = 1.74 [0.107]

Comparison of Alternative Estimates: Non-Oil Import Deflator
Domestic

Cost

LR (SR)
Domestic

Price

LR (SR)
Foreign

Cost

LR (SR)
Foreign

Price

LR (SR)
Exchange

Rate

LR (SR)
Computer

Prices
Present model (fixed weight)0.5 (0.4)0.6 (0.3)-0.6 (-0.2)
Present model1.0 (0.1)-0.8 (-0.2)0.1
Dunaway (1988)1.0 (0.6)-1.0 (-0.6)
Helkie and Hooper (1988)0.9-0.9
Krugman and Baldwin (1987)1.1 (0.3)-1.1 (-0.3)

Nonagricultural Export Volume

Long-Run Equilibrium

R2 = 0.981 DW = 0.48 DF = -3.46 ADF = -3.58

Short-Run Error Correction

R2 = 0.661 SE = 0.026

AR(1-5): F[5,61] = 0.25 ARCH(4): F[4,58] = 2.29

Normality: χ2(2) = 0.52 Heteroscedasticity: F[4,61] - 1.11

Chow: F[8,66] = 1.35 [0.233]

Comparison of Alternative Estimates: Nonagricultural Export Volume
Demand/Income

LR (SR)
Relative Price

LR (SR)
Log

Trend
Relative

Supply
Present model2.1 (1.6)-0.5 (-0.4)-0.1
Dunaway (1988)2.0-1.3 (-0.7)
Helkie and Hooper (1988)2.2-0.8-1.4
Krugman and Baldwin (1987)2.5-1.3 (-0.2)

Nonagricultural Export Fixed-Weight Price

Long-Run Equilibrium

R2 = 0.994 DW = 0.33 DF = -2.55* ADF = -4.17

Short-Run Error Correction

R2 = 0.694 SE = 0.010

AR(1-5): F[5,56] = 0.70 ARCH(4): F[4,53] = 1.66

Normality: χ2(2) = 2.69 Heteroscedasticily: F[10,50] = 1.59

Chow: F[8,61] = 0.21 [0.989]

Nonagricultural Export Deflator

Long-Run Equilibrium

R2 =0.999 DW = 0.57 DF = -3.51 ADF = -3.22

Short-Run Error Correction

R2 = 0.797 SE = 0.010

AR(1-5): F[5,55] = 0.33 ARCH(4): F[4,52] = 0.46

Normality: χ2(2) = 0.03 Heteroscedasticity: F[10,49] = 1.51

Chow: F[8,60] = 0.27 [0.972]

Comparison of Alternative Estimates; Nonagricultural Export Deflator
Domestic

Cost

LR (SR)
Domestic

Price

LR (SR)
Foreign

Cost

LR (SR)
Foreign

Price

LR (SR)
Exchange

Rate

LR (SR)
Computer

Prices
Present model (fixed weight)0.9 (0.3)0.2 (—)-0.2 (—)
Present model0.5 (0.4)0.7 (0.6)-0.3 (-0.3)0.1
Dunaway (1988)0.90.5-0.50.3
Helkie and Hooper (1988)1.10.2-0.2
Krugman and Baldwin (1987)0.5 (0.9)0.5 (0.1)-0.5 (-0.1)

Oil Consumption Volume

R2 = 0.926 SE = 0.025

AR(1-5): F[5,53] = 0.79 ARCH(4): F[4,50] - 0.74

Normality: x2(2) = 1.91 Heteroscedasticity: F[17,40] = 0.57

Chow: F[8,58] = 0.63 [0.747]

Agricultural Export Volume

Long-Run Equilibrium

R2 = 0.854 DW = 0.49 DF=-3.51 ADF=-2.16*

Short-Run Error Correction

R2 = 0.242 SE = 0.068

AR(1-5): F[5,61] - 0.65 ARCH(4): F[4,58] = 0.94

Normality: χ2(2) = 0.95 Heteroscedasticity: F[4,61] = 0.21

Chow: F[8,66] = 0.90 [0.521]

Agricultural Export Deflator

R2 = 0.854 SE = 0.021

AR(1-5): F[5,61] = 0.32 ARCH(4): F[4,58] = 0.40

Normality: χ2(2) = 0.02 Heteroscedasticity: F[4,61] = 1.88

Real Service Payments

Long-Run Equilibrium

R2 = 0.992 DW=1.62 DF=-7.34 ADF=-5.90

Short-Run Error Correction

R2 = 0.822 SE = 0.019

AR(1-5): F[5,56] = 0.66 ARCH(4): F[4,53] = 1.02

Normality: χ2(2) = 0.61 Heteroscedasticity: F[14,46] = 0.65

Chow: F[8,61] = 1.66 [0.126]

Real Service Receipts

Long-Run Equilibrium

R2 = 0.996 DW = 1.10 DF = -5.47 ADF = -3.43

Short-Run Error Correction

R2 = 0.709 SE = 0.020

AR(1-5): F[5,59] = 1.29 ARCH(4): F[4,56] = 1.85

Normality: χ2(2) = 0.62 Heteroscedasticity: F[9,54] = 0.81

Chow: F[8,64] = 0.39 [0.920]

Service Payments Deflator

Long-Run Equilibrium

R2 = 0.986 DW = 0.10* DF = 1.29* ADF = -2.00*

Short-Run Error Correction

R2 = 0.667 SE = 0.011

AR(1-5): F[5,57] = 1.30 ARCH(4): F[4,54] = 0.66

Normality: χ2(2) = 18.88* Heteroscedasticity: F[12,49] = 1.22

Chow: F[8,62] = 0.56 [0.805]

Service Receipts Deflator

Long-Run Equilibrium

R2 = 1.000 DW = 0.57 DF=-3.78 ADF = -4.31

Short-Run Error Correction

R2 = 0.691 SE = 0.005

AR(1-5): F[5,59] = 0.12 ARCH(4): F[4,56] = 1.15

Normality: χ2(2) = 1.43 Heteroscedasticity: F[8,55] = 2.10

Chow: F[8,64] = 0.35 [0.940]

Implicit Rate of Return on Private Portfolio Liabilities

Long-Run Equilibrium

R2 = 0.911 DW = 0.71 DF = -3.90 ADF = -3.77

Short-Run Error Correction

R2 = 0.789 SE = 0.091

AR(1-5): F[5,52] = 1.30 ARCH(4): F[4,49] = 0.74

Normality: x2(2) = 1.04 Heteroscedasticity: F[6,50] = 3.52*

Chow: F[8,57] = 0.68 [0.705]

Implicit Rate of Return on Private Portfolio Assets

Long-Run Equilibrium

R2 = 0.879 D W = 0.66 DF = -3.80 ADF = -3.06

Short-Run Error Correction

R2 = 0.794 SE = 0.102

AR(1-5): F[5,51] = 0.36 ARCH(4): F[4,48] = 0.61

Normality: χ2(2) = 1.22 Heteroscedasticity: F[8,47] = 0.50

Chow: F[8,56] = 1.03 [0.424]

Implicit Rate of Return on Government Portfolio Liabilities

R2 = 0.989 SE = 0.062

AR(1-5): F[5,52] = 0.80 ARCH(4): F[4,49] = 0.68

Normality: χ2 (2) = 0.67 Heteroscedasticity: F[6,50] = 1.34

Chow: F[8,57] = 0.75 [0.645]

Implicit Rate of Return on Government Portfolio Assets

R2 = 0.888 SE = 0.103

AR(1-5): F[5,60] = 3.62 ARCH(4): F[4,57] = 0.60

Normality: χ2(2) = 64.18* Heteroscedasticity: F[9,55] = 1.83

Foreign Direct Investment Income Payments

Long-Run Equilibrium

R2 = 0.860 DW = 0.70 DF = -3.95 ADF = -2.50*

Short-Run Error Correction

R2 = 0.368 SE = 0.249

AR(1-5): F[5,53] = 0.96 ARCH(4): F[4,50] = 0.89

Normality: χ2(2) = 1.69 Heteroscedasticity: F[5,52] = 1.90

Chow: F[8.S8] = 0.47 [0.870]

Foreign Direct Investment Income Receipts

Long-Run Equilibrium

R2 = 0.925 DW = 0.80 DF = -4.17 ADF = -3.44

Short-Run Error Correction

R2 = 0.549 SE = 0.099

AR(1-5): F[5.50] = 2.19 ARCH(4): F[4,47] = 0.46

Normality: χ2(2) = 1.10 Heteroscedasticity: F[1341] = 1.84

Chow: F[8,55] = 0.42 [0.906]

Stock of Foreign Direct Investment Liabilities

R2 = 1.000 SE = 0.022

AR(1-5): F[5,65] = 0.61 ARCH(4): F[4,62] - 1.09

Normality: χ2(2) = 5.68 Heteroscedasticity: F[6,63] = 0.97

Stock of Government Portfolio Liabilities

R2 = 0.991 SE = 0.050

AR(1-5): F[5,66] = 1.85 ARCH(4): F[4,63] = 2.86

Normality: χ2(2) = 29.93* Heteroscedasticity: F[4,66] = 14.97*

Stock of Private Portfolio Liabilities

R2 = 0.999 SE = 0.028

AR(1-5): F[5,66] = 1.46 ARCH(4): F[4,63] = 0.20

Normality: x2(2) = 0.99 Heteroscedasticity: F[4,66] = 0.37

Stock of Foreign Direct Investment Assets

R2 = 0.999 SE = 0.015

AR(1-5): F[5,66] - 1.17 ARCH(4): F[4,63] = 0.38

Normality: χ2(2) = 0.14 Heteroscedasticity: F[4,66] = 1.03

Stock of Government Portfolio Assets

R2 = 0.998 SE = 0.019

AR(1-5): F[5,65] = 2.50 ARCH(4): F[4,62] = 2.35

Normality: χ2(2) = 38.84* Heteroscedasticity: F[6,63] = 3.60*

Stock of Private Portfolio Assets

R2 = 0.999 SE = 0.030

AR(1-5): F[5,64] = 1.36 ARCH(4): F[4,61] = 1.29

Normality: χ2(2) = 2.54 Heteroscedasticity: F[5,63] = 0.61

ANNEX II

Variable Mnemonics31

mnoReal non-oil imports
pmnofwFixed-weight price index for non-oil imports
pmnoImplicit deflator for non-oil imports
tddReal U.S. total domestic demand
trAverage tariff rate, customs duties divided by non-oil imports
pgnpU.S. implicit GNP deflator
dsmDock strike dummy, imports
ulcU.S. unit labor costs in the nonfarm private business sector
ulcm*Foreign unit labor costs in manufacturing, industrial countries, import weighted (GEE)
ulcx*Foreign unit labor costs in manufacturing, industrial countries, export weighted (GEE)
erNominal effective value of the dollar, MERM weights
pxnm*Foreign export unit values, non-oil merchandise, non-oil exporting countries, import weighted (GEE)
pxx*Foreign export unit values, industrial countries, export weighted (GEE)
pbusU.S. price of business machinery
xnaReal nonagricultural exports
pxnafwFixed-weight price index for nonagricultural exports
pxnaImplicit deflator for nonagricultural exports
tdd*Real foreign total domestic demand, industrial countries, export weighted (GEE)
dsxDock strike dummy, exports
xaReal agricultural exports
pxaImplicit deflator for agricultural exports
pcomIFS (non-oil) commodity price index
ocU.S. consumption of oil, thousands of barrels a day, not seasonally adjusted
pmoImplicit deflator for oil imports
pmouvPrice of oil imports, dollars a barrel
msReal service payments
pmsImplicit deflator for service payments, national income accounts
pcpi*Foreign consumer price index, industrial countries, import weighted (GEE)
mgReal merchandise imports
xgReal merchandise exports
xsReal service receipts
pxsImplicit deflator for service receipts, national income accounts
pcpiU.S. consumer price index
pgnp*Foreign GNP deflator, industrial countries, import weighted (GEE)
RMYPImplicit rate of return on private portfolio liabilities
RXYPImplicit rate of return on private portfolio assets
RMYGImplicit rate of return on government portfolio liabilities
RXYGImplicit rate of return on government portfolio assets
RTBILLU.S. three-month Treasury bill rate
mydForeign direct investment income payments, excluding capital gains and losses, not seasonally adjusted
IdForeign direct investment liabilities, not seasonally adjusted
cugnpU.S. capacity utilization: deviations of real GNP from trend
xydForeign direct investment income receipts, excluding capital gains and losses, not seasonally adjusted
adForeign direct investment assets, not seasonally adjusted
cutdd*Foreign capacity utilization: deviations of real total domestic demand from trend, industrial countries, export weighted
lgGovernment portfolio liabilities, not seasonally adjusted
agGovernment portfolio assets, not seasonally adjusted
lpPrivate portfolio liabilities, not seasonally adjusted
apPrivate portfolio assets, not seasonally adjusted
Q1, Q2, Q3Quarterly seasonal dummy variables
TRENDDeterministic trend
trendLog trend
DUM883Drought dummy; 1 in 1988:3, 0 otherwise
DUM744Dummy for sharp rise in U.S. crop prices not fully reflected in IFS commodity price index; 1 in 1974:4, 0 otherwise
DUM80Break in services series; 1 in 1969:1–1980:4, 0 otherwise
DUM83Break in services series; 1 in 1969:1–1983:4, 0 otherwise
DUM85Break in services series; 1 in 1969:1–1985:4, 0 otherwise
DUM862Dummy for service payments to account for outlier introduced by new benchmark survey; 1 in 1986:2, 0 otherwise
DUM881Rescheduling of interest payments from Egypt; 1 in 1988:1, 0 otherwise
REFERENCES

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    Goldstein,Morris, andMohsinS. Khan,“Income and Price Effects in Foreign Trade,”in Handbook of International Economics,Vol. II, ed. byRonaldW. Jones andPeterB. Kenen (New York: North Holland, 1985).

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    Granger, C. W. J.,R.F.Engle,“Dynamic Model Specification with Equilibrium Constraints: Cointegration and Error Correction” (unpublished;San Diego: University of California, 1985).

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    Hendry,DavidF.,PC-GIVE: An Interactive Econometric Modelling System (Oxford: Institute of Economics and Statistics and Nuffield College, University of Oxford, 1989).

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    Hooper,Peter, andC.L.Mann,“Exchange Rate Pass-Through in the 1980’s: The Case of U.S. Imports of Manufactures,”Brookings Papers on Economic Activity: 1 (1989), Brookings Institution (Washington), pp. 297329.

    Isard,Peter,“Dock Strike Adjustment Factors for Major Categories of U.S. Imports and Exports, 1958–1974,”International Finance Discussion Paper No. 60 (Washington: Board of Governors of the Federal Reserve System, 1975).

    Jarque,CarlosM., andAnil K.Bera,“Efficient Tests for Normality, Homoscedasticity and Serial Independence of Regression Residuals,”Economics Letters, Vol. 6 (1980), pp. 25559.

    Krugman,PaulR., andRichardE. Baldwin,“The Persistence of the U.S. Trade Deficit,”Brookings Papers on Economic Activity: 1 (1987), Brookings Institution (Washington), pp. 143.

    Meade,EllenE.,“Computers and the Trade Deficit: The Case of the Falling Prices,”International Finance Discussion Paper No. 378 (Washington: Board of Governors of the Federal Reserve System, April1990).

    Melick, W.,“Single Equation Estimates of Exchange Rate Pass-Through” (unpublished;Washington: Board of Governors of the Federal Reserve System, 1990).

    Sargan,J. D., andA.Bhargava,“Testing Residuals from Least Squares Regression for Being Generated by the Gaussian Random Walk,”Econometrica, Vol. 51 (1983), pp. 15374.

    White,H.,“A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity,”Econometrica, Vol. 48 (1980), pp. 81738.

    Woo,WingT.,“Exchange Rates and the Prices of Nonfood, Nonfuel Products,”Brookings Papers on Economic Activity: 2 (1984), Brookings Institution (Washington), pp. 51136.

The author would like to thank Charles Adams, Liam Ebrill, and Yusuke Horiguchi for helpful comments and discussions and Fredesvinda Pham for research assistance.

See Hooper (1988) and Helkie and Hooper (1988).

Granger and Engle (1985). See also Hendry (1986) and Granger (1986). This procedure is appropriate for series that are integrated of order one (I(1)) and are part of a linear combination of variables that yield I(0) residuals, implying cointegration.

See Goldstein and Khan (1985) for a review of alternative trade equations.

See Hooper and Mann (1989) and Woo (1984) for similar models. Hooper and Mann also allow for the effects of demand pressures as measured by capacity utilization in both the home and foreign markets. These effects were not significant in the present model.

All lowercase variables are in logs.

Researchers are often interested in “pass-through” coefficients that describe the effects of exchange rates and foreign costs or prices on domestic trade prices. One should note that in the above model, for the same structural coefficients, the pass-through coefficients E2 and F2 for the effects of foreign costs on import and export prices are less than the coefficients (1 - b1) and D2 for the pass through of foreign export prices.

In addition to these I(1) variables, the dock strike dummy developed by Isard (1975) was included. Being an I(0) variable, its inclusion should not influence cointegration tests, but does assist in estimating unbiased long-run coefficients.

See the tabulation following equation (2) in Annex I for a comparison of alternative estimates. Sources are Dunaway (1988), Helkie and Hooper (1988), and Krugman and Baldwin (1987).

Helkie and Hooper (1988).

It is not possible to test this hypothesis statistically since the coefficients, while consistent, do not have an asymptotic normal distribution.

Melick (1990) estimates similar long-run coefficients for the price of manufactured imports.

An equation linking changes in the implicit deflator to changes in the fixed-weight price index performed poorly in dynamic simulations.

See the tabulation following equation (6) in Annex I for a comparison of alternative estimates.

See the tabulation following equation (8) in Annex I.

See the tabulation following equation (12) in Annex I for a comparison of alternative estimates.

Hendry (1989) refers to this dynamic model as the dead-start model, since the dependent variable depends only on lagged values of the independent variables.

The term “services” in this paper follows the new U.S. classification that excludes investment income. In contrast to Dunaway (1988), these aggregate equations were found to have smaller standard errors than individual equations for travel, transportation, and other services.

Trade in educational services was added beginning in 1981; a new survey for travel and passenger fares implies more complete coverage beginning in 1984; and other private services incorporate the results of a new benchmark survey beginning in 1986.

As will be discussed in Section V, this short-run equation performed well in both in- and out-of-sample in dynamic simulations.

The U.S. Treasury bill rate is used as the independent variable in all four equations since most of U.S. portfolio assets and liabilities are dollar denominated. This treatment follows Helkie and Stekler (1987).

Capital gains and losses are excluded from these income series for purposes of estimation. Realized capital gains and losses due to differences between the sale price and book value of an asset are difficult to estimate without knowing the timing of particular transactions. Unrealized capital gains and losses associated with exchange rate changes were not estimated since they are currently being removed from direct investment income. These adjustments will appear instead as valuation adjustments in the stocks of foreign direct investment assets and liabilities. These revisions are not incorporated in the data used by the model.

The return on government portfolio assets has been quite volatile since 1987. A dummy in the first quarter of 1988 was included to account for the rescheduling of interest receipts from Egypt; however, the Jarque-Bera (1980) test still rejected normal residuals.

Static simulations use actual data as lagged values, while dynamic simulations use values generated by the model. Both kinds of simulations are deterministic, in the sense that the estimated coefficients and error terms in the model are taken to equal their expected values.

Percent errors for oil imports appear large relative to the standard error of the estimated equation (2.5 percent) due to the translation from oil consumption to (the smaller volume of) oil imports. The root mean square percent errors for oil consumption are 2.3 and 2.0 for the static simulation and 8.3 and 1.8 for the dynamic simulation.

For example, errors in the balance on portfolio income are expressed relative to the sum of private and government portfolio income receipts and payments.

The maximum for each is 6 percent if two observations from the 1970s are excluded.

See Sargan and Bhargava (1983) and Dickey and Fuller (1979).

These are the Lagrange multiplier test for the rth order residual autocorrelation (tested for orders 1-5), the ARCH test (autoregressive conditional heteroscedasticity; tested for order 4), the Jarque-Bera (1980) test for normality, and the White (1980) test for heteroscedasticity.

Rejection of the null hypothesis for diagnostic tests at the 5 percent level of significance (failure to reject the null hypothesis of a cointegration test at the 10 percent level) is indicated by an asterisk. Test statistics reported for long-run equations include the R2, the Durbin-Watson statistic (DW), and the Dickey-Fuller (DF) and augmented Dickey-Fuller (ADF) statistics. Augmented Dickey-Fuller tests were performed using four lags of the dependent variable unless residual autocorrelation was present, in which case the number of lags was increased to eight.

All series are seasonally adjusted unless otherwise indicated; all lowercase variables are in logs; GEE refers to those variables that are part of the “global economic environment” from the World Economic Outlook; quarterly data for asset stocks were generated by adding quarterly capital flows and prorated annual valuation adjustments to end-of-year stocks.

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