I. Recent Developments in Trade Prices

After declining at an annual rate of about l½ percent from mid-1982 to the first quarter of 1985, the price of nonagricultural exports, as measured by the implicit deflator in the national income accounts, fell at a rate of 1 percent a year through the first quarter of 1988. The decline in the earlier period occurred in the face of the rapid appreciation of the dollar, which might have been expected to squeeze the profit margins of U.S. exporters. The continued fall in export prices, however, was a generally unexpected development because a depreciation might have been expected to enable exporters not only to pass on cost increases but also to expand profit margins.² Standard equations based on production costs and competitors’ prices adjusted for exchange rate changes have tended to overpredict the level of the implicit deflator for U.S. nonagricultural exports by an increasing amount during 1985–87.

Major factors behind the unexpected behavior of the implicit deflator for nonagricultural exports are the movements of export prices of business machines and commodities, as well as the growing importance of business machines in U.S. exports. Export prices of business machines dropped at an average annual rate of 12 percent from the first quarter of 1985 to the first quarter of 1988; prices of commodities also declined sharply from the first quarter of 1985 to the end of 1986, before recovering in 1987. At the same time, the share of business machines in nonagricultural exports rose from 14 percent in the first quarter of 1985 to 21 percent in the first quarter of 1988.³

To take account of the influences of these factors on the implicit deflator, a fixed-weighted price index of U.S. manufactured exports excluding business machines was constructed.⁴ From the first quarter of 1985 to the first quarter of 1988, this index rose at an average annual rate of 2¼ percent (compared with the 1 percent a year fall for the implicit deflator noted above), while unit labor costs in the manufacturing sector declined at a 1 percent annual rate and producer prices of intermediate inputs remained flat (Figure 1).

After declining by 2 percent a year from mid-1981 to early 1985, the price of non-oil imports, as measured by the national income accounts’ implicit deflator, began to pick up in late 1985. This rise, however, has been relatively modest, given the extent of the dollar’s depreciation. From the first quarter of 1985 to the first quarter of 1988, the price of non-oil imports increased at an annual rate of only 3 percent, while the nominal effective value of the dollar (multilateral exchange rate model (MERM) weights) declined at an annual rate of about 15 percent. Indeed, standard equations for the implicit deflator for non-oil imports, which had performed quite well historically, overpredicted the actual rise in import prices during 1985–87 by a substantial margin.

United States: Expon Prices, 1979–87

(1980 = 100)

Citation: IMF Staff Papers 1989, 004; 10.5089/9781451930757.024.A007

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United States: Expon Prices, 1979–87

(1980 = 100)

Citation: IMF Staff Papers 1989, 004; 10.5089/9781451930757.024.A007

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United States: Expon Prices, 1979–87

(1980 = 100)

Citation: IMF Staff Papers 1989, 004; 10.5089/9781451930757.024.A007

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The unexpectedly modest rise in the implicit deflator for non-oil imports also may be partially explained by the movements of the prices of business machines and commodities and the increasing weight of business machines in total non-oil imports. Import prices of commodities have exhibited wide swings over the past few years, and their level in the first quarter of 1988 was only modestly above that prevailing in the first quarter of 1985. As regards business machines, the deflator for imports used in the official statistics is the same as the deflator for exports, which, as noted above, has decreased substantially in recent years.⁵ Moreover, the impact of this decline on the implicit (current-weighted) import deflators is again magnified by the pronounced rise in the share of business machines in total non-oil imports (from 3 percent in 1982 to almost 8 percent in the first quarter of 1985 and to 15 percent in the first quarter of 1988). To adjust for the influence of these factors, a fixed-weighted deflator for manufactured imports excluding business machines was developed.⁶ This index shows an annual rate of increase of 7½ percent since early 1985, after having remained roughly constant in the first half of the 1980s. (See Figure 2.)

Even with these adjustments, import prices still appear to have risen less than might have been expected, given the size of the dollar’s depreciation. The remaining discrepancy can be explained largely by the following two factors.

First, the dollar’s depreciation against the currencies of some countries that are important suppliers to the United States has been much less than that against the currencies of the major industrial countries. An average exchange rate index of 11 principal exporters to the United States that incorporates their currencies shows an annual rate of decline in the value of the dollar since early 1985 of 10 percent, compared with a 15 percent rate of decline in the MERM index.⁷

Second, foreign export prices have been held down to some extent by the decline in energy prices, the effects of currency appreciation on prices of imported raw materials and intermediate inputs, and modest increases in unit labor costs. A weighted average of manufactured export prices of the major U.S. suppliers included in the alternative exchange rate index remained roughly constant in foreign-currency terms during 1985–87, owing largely to a ½ of 1 percent annual average drop in input prices. Over this period, foreign export prices and production costs in manufacturing thus moved broadly in tandem, suggesting that foreign exporters have not reduced their profit margins substantially in response to the appreciations of their currencies.⁸

United States: Import Prices, 1979–87

(1980 = 100)

Citation: IMF Staff Papers 1989, 004; 10.5089/9781451930757.024.A007

^aWeighted by shares in U.S. imports of manufactured goods in 1980.

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United States: Import Prices, 1979–87

(1980 = 100)

Citation: IMF Staff Papers 1989, 004; 10.5089/9781451930757.024.A007

^aWeighted by shares in U.S. imports of manufactured goods in 1980.

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United States: Import Prices, 1979–87

(1980 = 100)

Citation: IMF Staff Papers 1989, 004; 10.5089/9781451930757.024.A007

^aWeighted by shares in U.S. imports of manufactured goods in 1980.

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As a final point in this section, it may be noted that since early 1985, the price of total exports of manufactured goods of partner countries (including certain major developing countries) expressed in U.S. dollars has moved broadly in line with the U.S. import prices of manufactured goods excluding business machines. This is in contrast to the first half of the 1980s, when foreign export prices in dollar terms fell significantly relative to U.S. import prices. While this could suggest that profit margins on exports to the United States had been built up relative to those prevailing in other export markets during those years, it seems clear that there has been no further change in relative profit margins across markets since early 1985.⁹

II. The Trade Price Model

This section presents a simple model that may be used to analyze the movements of U.S. trade prices. A behavioral equation is developed for both U.S. export prices (in dollars) and foreign export prices (in foreign currency). U.S. import prices are then specified as a function of foreign export prices expressed in dollars.

The pricing of exports is analyzed assuming a producer that discriminates between its export and domestic markets. The analysis proceeds in the following two steps. An optimal export price for the producer can be specified as one that maximizes profits subject to a short-run production function. The path of actual export prices can then be derived by incorporating certain additional considerations that might cause export prices to deviate from their strictly profit-maximizing levels.

Assuming a short-run Cobb-Douglas production function with constant returns to scale with respect to variable inputs of labor and intermediate inputs, and with producers facing a downward-sloping demand curve having constant price elasticity,¹⁰ the profit-maximizing export price (PX*) may be written as

where ULC denotes the cost of labor per unit of output and PI the price of intermediate inputs (and raw materials), with lowercase letters denoting logarithms.

The actual path of export prices may deviate from their profit-maximizing levels because prices may be sticky owing to information costs or uncertainty about the demand response to price changes. In addition, exporters may desire to keep their prices in line with those of their competitors, at least in the short run, in order to protect their market shares. Actual export prices are assumed to be set so as to achieve the best possible compromise between the objective of maximizing profits and these additional considerations. Since all three objectives would not be attainable at the same time, the actual export price (px) at time t can be determined by minimizing the total cost from not meeting all targets simultaneously. The total cost may be specified according to the following quadratic loss function:¹¹

where L denotes the total loss subjectively perceived by suppliers. The coefficient l¹, denotes the loss associated with deviating from the short-run optimum. The coefficient l₂ denotes the loss associated with not maintaining stable prices. The loss related to deviations from the prices charged by foreign competitors in domestic-currency terms (pc) is split into two elements: (1) the coefficient l₃ denotes the cost of not staying in line with competing prices in the long run and is a function of the relative price level; and (2) the coefficient l₄ denotes the loss associated with short-run deviations from foreign prices and is a function of the relative price change.

Minimizing the loss function (2) with respect to px yields

where

and

The equation determining the actual export price may now be obtained through substitution by using equation (1) for the optimal short-run price

The import price faced by a country can be expressed as a simple function of the foreign export price converted into domestic currency (px^$), with lagged terms to account for delays between order and delivery

III. Empirical Tests¹²

Equation (4) was used to estimate equations for the fixed-weighted price index for U.S. exports of manufactured goods excluding business machines and the weighted average of foreign export prices discussed above. Equation (5) was used to estimate the relationship between foreign export prices and the fixed-weighted price index for U.S. imports of manufactured goods excluding business machines. The equations were estimated using quarterly data over the sample period, which extended from the first quarter of 1974 to the fourth quarter of 1984. These equations then were predicted over the period extending from the first quarter of 1985 to the fourth quarter of 1987 in order to test whether the behavior of trade prices had changed significantly during that period, when there was a sharp decline in the value of the dollar.

Estimation Results

The fixed-weighted price index for U.S. exports of manufactured goods excluding business machines (px^us) was estimated as a function of unit labor costs and intermediate import prices in the U.S. manufacturing sector, and a weighted average of the export prices of competing foreign suppliers in major U.S. export markets expressed in U.S. dollars (pcx). Because of strong multicollinearity between unit labor costs and intermediate input prices, they were combined into a single variable-cost term (vc) using weights obtained from the 1977 U.S. input-output table. The regression results on the equation, corrected for serial correlation, are presented below (with t-statistics in parentheses below the coefficients): ¹³

$$\begin{gathered} p{x}^{us}=0.092+0.246vc+0.002pcx \\ \left(1.18\right)\left(2.73\right)\left(0.05\right) \\ +0.070(pcx-pc{x}_{-1}+p{x}_{-1}^{us})+0.667p{x}_{-1}^{us} \\ (1.27)\left(7.67\right) \\ \overline{R^2}=0.993SEE=0.011\hat{\rho }=0.458 \\ \left(3.18\right)\mathrm{.} \end{gathered}$$

(SEE denotes the standard error of estimate.)

The estimation results suggest that during 1974–84, the prices of U.S. exports were determined by domestic costs in both the short run and the long run. The coefficient on the export prices of foreign competitors (pcx) was not significant and was almost equal to zero, implying full pass-through in the long run of changes in domestic costs and no long-run impact of changes in exchange rates on U.S. export prices.¹⁴ The coefficient on the term representing the influence of relative price changes $(pcx-{pcx}_{-1}+{px}_{-1}^{us})$ was positive but small and not very significant, suggesting a limited short-run response of U.S. export prices to changes in the export prices of foreign competitors measured in U.S. dollars. Table 1 illustrates this result.

Table 1.

Cumulative Effects of a 1 Percent Rise in Foreign Prices

(In percent)

Table 1.

Cumulative Effects of a 1 Percent Rise in Foreign Prices

(In percent)

Quarterly Period	U.S. Export Price
0	0.042
1	0.033
2	0.027
3	0.022
4	0.019
8	0.011
12	0.009
∞	0.007

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Table 1.

Cumulative Effects of a 1 Percent Rise in Foreign Prices

(In percent)

Quarterly Period	U.S. Export Price
0	0.042
1	0.033
2	0.027
3	0.022
4	0.019
8	0.011
12	0.009
∞	0.007

Foreign export prices (pxf) in foreign-currency terms were estimated as a function of foreign unit labor costs and intermediate input prices in the manufacturing sector,¹⁵ and competing U.S. producer prices of manufacturing goods expressed in foreign currency (pc). As in the case of the U.S. export price equation, a foreign variable-cost term (vcf) was constructed according to appropriate input-output weights to handle multi-collinearity between foreign unit labor costs and intermediate input prices. The regression results are presented below (with t-statistics in parentheses below the coefficients).

$$\begin{gathered} pxf=0.631+0.423vcf+0.001pc \\ \left(3.09\right)\left(6.05\right)\left(0.01\right) \\ +0.221(pc-p{c}_{-1}+px{f}_{-1})+0.221px{f}_{-1} \\ (4.64)\left(2.67\right) \\ \overline{R^2}=0.951SEE=0.007\hat{\rho }=0.843 \\ \left(9.28\right)\mathrm{.} \end{gathered}$$

The estimation results suggest that costs of production are the major long-run determinant of foreign export prices. The coefficient on the competing U.S. producer-price term (pc) is not significantly different from zero, suggesting that foreign export prices do not respond to movements in competing prices or the exchange rate in the long run. The positive and significant coefficient on the term representing the effect of relative price changes $(pc-{pc}_{-1}+{pxf}_{-1})$ suggests, however, that in the short run the pricing behavior of foreign exporters can be influenced substantially by movements in exchange rates or by the pricing behavior of U.S. producers. The estimated elasticity of foreign export prices with respect to competing U.S. prices in foreign-currency terms is shown in Table 2. The results suggest that, on average, foreign exporters initially absorb roughly one fifth of the loss in their competitiveness by lowering profit margins. Prices adjust quickly thereafter toward their long-run levels; after two or three quarters, almost all of the initial impact of a change in exchange rates or in U.S. prices on foreign export prices (expressed in foreign currency) would be reversed.

Table 2.

Cumulative Effects of a 1 Percent Fall in Competing Prices

(In percent)

Table 2.

Cumulative Effects of a 1 Percent Fall in Competing Prices

(In percent)

Quarterly Period	Foreign Export Price	U.S. Import Price
0	–0.219	0.220
1	–0.096	0.557
2	–0.042	0.878
3	–0.018	0.947
4	–0.007	0.977
8	0.001	1.000
∞	0.001	1.001

View Table

Table 2.

Cumulative Effects of a 1 Percent Fall in Competing Prices

(In percent)

Quarterly Period	Foreign Export Price	U.S. Import Price
0	–0.219	0.220
1	–0.096	0.557
2	–0.042	0.878
3	–0.018	0.947
4	–0.007	0.977
8	0.001	1.000
∞	0.001	1.001

Finally, the fixed-weighted price index for U.S. imports of manufactured goods excluding business machines was estimated as a distributed lag of current and previous foreign export prices expressed in U.S. dollars (pxf^$). Regression results, with the equation corrected for serial correlation using the standard Cochrane-Orcutt procedure, are presented below (with t-statistics in parentheses below the coefficients):¹⁶

$$\begin{gathered} pxf=0.324px{f}^{\$}+0.380px{f}_{-1}^{\$}+0.329px{f}_{-2}^{\$} \\ \left(2.28\right)\left(2.24\right)\left(2.32\right) \\ \overline{R^2}=0.992SEE=0.018\hat{\rho }=0.963D-W=1.27 \\ \left(19.07\right)\mathrm{.} \end{gathered}$$

(D-W denotes the Durbin-Watson statistic.)

The results suggest that changes in foreign export prices are fully translated into changes in U.S. import prices after three quarters; the sum of the lag coefficients on foreign export prices is equal to 1.03 and is not significantly different from l.¹⁷ Thus, as the last column of Table 2 illustrates, changes in exchange rates are fully passed through to U.S. import prices in the long run. In the short run, however, the impact of changes in competitiveness on the pricing behavior of foreign exporters, combined with the lag with which changes in foreign export prices in local-currency terms are reflected in changes in U.S. import prices, implies significantly less than full pass-through over several quarters.

Predictive Performance

In order to examine the extent to which the recent behavior of U.S. trade prices may have deviated from what would have been expected on the basis of historical experience, the estimated equations presented above were forecast over the period extending from the first quarter of 1985 to the fourth quarter of 1987.¹⁸ The in-sample (from the first quarter of 1974 through the fourth quarter of 1984) and post-sample performances of the estimated equations are shown in Figures 3 and 4.

Figure 3 indicates that the estimated equation tends to underpredict the behavior of U.S. export prices by an increasing margin. About one half of the forecast errors are due to the fact that the predictions do not adjust for serially correlated errors; remaining errors are within two standard deviations of the mean U.S. export price over the forecast period. These results suggest that once adjustments are made for the prices of commodities and business machines and for changes in commodity composition, movements in U.S. export prices since early 1985 will be seen to have been in line with historical experience. If there had been a significant change in the pricing behavior of U.S. exporters and if, as a result, U.S. export prices had been restrained in the face of the depreciation of the dollar, the equation would have been expected to overpredict U.S. export prices in the post-sample period.

The top panel of Figure 4 shows the predictive performance of the foreign export price equation. This equation underpredicted foreign export prices in foreign-currency terms during 1985–87, with the extent of underprediction increasing through the first quarter of 1987, before declining over the rest of the forecast period. Thus, the results suggest that foreign exporters have not significantly changed their pricing behavior by absorbing a greater-than-normal proportion of the depreciation of the dollar.

The middle panel of Figure 4 shows the single-equation predictive performance of the U.S. import price equation. The bottom panel of the chart shows a forecast for U.S. import prices using predicted values of foreign export prices expressed in U.S. dollars. In both cases, the equation tends to underpredict in the early part of the forecast period, followed by small overpredictions that are not statistically significant toward the end of the forecast period. Thus, the results indicate that since early 1985 foreign exporters have not increasingly cut profit margins on their exports to the United States relative to those with other destinations in order to maintain their shares of the U.S. market.

United States: Actual and Predicted Prices of Exports of Manufactures, 1979–87

(1980 = 100)

Citation: IMF Staff Papers 1989, 004; 10.5089/9781451930757.024.A007

Note : Fixed-weighted price index of manufactured exports excluding business machines.^aRoot-mean-squared prediction error as a percentage of sample mean of actual value.

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United States: Actual and Predicted Prices of Exports of Manufactures, 1979–87

(1980 = 100)

Citation: IMF Staff Papers 1989, 004; 10.5089/9781451930757.024.A007

Note : Fixed-weighted price index of manufactured exports excluding business machines.^aRoot-mean-squared prediction error as a percentage of sample mean of actual value.

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United States: Actual and Predicted Prices of Exports of Manufactures, 1979–87

(1980 = 100)

Citation: IMF Staff Papers 1989, 004; 10.5089/9781451930757.024.A007

Note : Fixed-weighted price index of manufactured exports excluding business machines.^aRoot-mean-squared prediction error as a percentage of sample mean of actual value.

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Actual and Predicted Prices of Foreign Exports and U.S. Imports of Manufactures, 1979–87

(1980 = 100)

Citation: IMF Staff Papers 1989, 004; 10.5089/9781451930757.024.A007

^aRoot-mean-squared prediction as a percentage of sample mean of actual value.^bFixed-weighted price index of manufactured imports excluding business machines.^cBased on predicted values of foreign export prices.

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Actual and Predicted Prices of Foreign Exports and U.S. Imports of Manufactures, 1979–87

(1980 = 100)

Citation: IMF Staff Papers 1989, 004; 10.5089/9781451930757.024.A007

^aRoot-mean-squared prediction as a percentage of sample mean of actual value.^bFixed-weighted price index of manufactured imports excluding business machines.^cBased on predicted values of foreign export prices.

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Actual and Predicted Prices of Foreign Exports and U.S. Imports of Manufactures, 1979–87

(1980 = 100)

Citation: IMF Staff Papers 1989, 004; 10.5089/9781451930757.024.A007

^aRoot-mean-squared prediction as a percentage of sample mean of actual value.^bFixed-weighted price index of manufactured imports excluding business machines.^cBased on predicted values of foreign export prices.

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