Article

The Behavior of Export Prices for Manufactures

Author(s):
International Monetary Fund. Research Dept.
Published Date:
January 1974
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Price theory, until recently, was concerned mainly with the determination of an equilibrium price, abstracting from existing environmental constraints such as uncertainty about the future and the need to gather costly information. Development of the “new” microeconomics has changed this situation.1 Work in the field of microeconomics has rapidly extended the understanding of short-run price dynamics and has led to the construction of more operational models. However, empirical tests of these models are lacking. The focus of this paper is to develop such a model in a form suitable for estimation and to test its performance in the explanation of a country’s export price index for manufactures.

Section I derives the specification of an export price equation for manufactures from a formal economic theory that combines the traditional long-run equilibrium price theory with the recent analyses of short-run optimal pricing decisions. This approach makes it possible to focus the empirical analysis on the short-run dynamic pricing mechanism as it is consistent with the implications of the long-run equilibrium theory of price determination. The export price equation, in turn, explains contract prices in local currency. A separate equation relates export unit values in local currency to contract prices in local currency, taking into account delivery lags and denomination of certain export contracts in foreign exchange. Section II presents the results of econometric estimation of the parameters of these equations for five industrial countries from semiannual observations during 1958–72. Emphasis is given to the magnitude and timing of exchange rate effects on export contract prices and unit value indices implied by these results.

I. The Model

The behavior of export prices is analyzed here within the context of the theory of the firm. The firm considered is a profit-maximizing firm confronted by two relatively isolated markets—the home and export markets—in each of which it is selling a product differentiated to some extent from products sold by competitors. It operates under various environmental constraints that influence its optimal pricing decision in the short run but can be ignored in the long run.

The analysis proceeds in four steps. The first three steps deal with the export contract price, hereinafter referred to simply as the export price; and the last step relates the export unit value to this export price. First, the long-run target export price is expressed as a function of the expected average labor compensation, the cost of intermediate inputs, and the output per man-hour by using the long-run equilibrium price theory. Expected values are derived from adaptive expectation functions. Second, the optimal adjustment path for the actual export price is determined, taking into account short-run environmental constraints. Third, short-run and long-run analyses are integrated to obtain an equation explaining the behavior of the export price. Last, the export unit value is related to the export price by taking into account delivery lags and denomination of certain contracts in foreign exchange. The analysis is then extended to the whole manufacturing sector, involving various aggregation problems which are then considered.

The long-run target export price PX* can be derived directly from the profit maximization condition, which relates the expected average compensation of labor to the value of its expected marginal product:

where W = average hourly labor compensation,

Y = total production (for home and export markets),

L = labor (man-hours) paid,

T = tax, or subsidy rates if T has a negative value, in proportionate terms.

The asterisk indicates that the expected long-run optimal value of a variable is considered. The superscript e refers to the expected average value of a variable. This condition takes into account discriminatory price practices between home and export markets and the existence of finite and constant price elasticities of export demand (ηxx) and labor supply (ηt). The assumption of a constant demand elasticity, which does not depend on income or prices of competing products, is somewhat restrictive. It is consistent with monopolistically competitive, monopolistic, or perfectly competitive market structures, but it may not be a valid assumption if the market structure is oligopolistic with few sellers. Price determination in such a market is not considered here.

The specific form of equation (1) depends on the characteristics of the production process, which are represented by a system of two equations:

Equation (2) expresses the value added by the firm (VA) as a function of the capital in place (K) and the amount of labor paid (L). The slack variable (U) indicates the short-run departures from optimal use of K and L. The relation is a factor-augmenting CES (constant elasticity of substitution) production function with constant returns to scale. The trend t represents technical progress, and the parameter σ is the elasticity of substitution between labor and capital. Equation (3) indicates that the value added (VA) and the raw materials and other intermediate inputs (M) are combined in fixed proportions. The parameter v indicates the proportion of the value added in the total production (Y).

The slack variable (U) can be set at zero in the present long-run equilibrium analysis. Evaluating (dY/dL)* in equation (1) by using the production functions (2) and (3), under the assumption that there will be an unlimited supply of intermediate inputs (M) at the expected market price (PMe), and converting to natural logarithms yield 2

whereA = v[ln(1 + 1/ηl) – ln(1 + 1/ηxx) – ln(b0)]
andr = (1/σ – 1)vb1.

Price and labor compensation variables in equation (4) are expressed in local currency.

The entrepreneur is assumed to revise his estimate of the expected long-run optimal value of the output per man-hour (Y/L)* as a function of the evolution of the actual output per man-hour rather than as a function of the expected rental price of capital and other production and demand conditions. More precisely, expectations are assumed to be formed on the basis of the actual (trend corrected) output per man-hour:

where 0 < λ0 < 1 and where λ1 is added to permit an anticipated trend in output per man-hour. The notation u represents a random error term.

This derivation of the long-run target export price has two advantages over the alternative method of expressing the optimal price directly as a function of all expected factor prices: (1) it does not introduce the rental price of capital in the export price equation; and (2) it does not assume that the capital stock is adjusted to its optimal level. The rental price of capital is at best a fuzzy concept, because most capital equipment is owned by the firms rather than rented. Since the adjustment of the actual capital stock to its optimal level may require an extremely long time, the corresponding optimal export price is not likely to have much bearing on actual pricing decisions. The present approach is based on what seems to be a more realistic view of the behavior of the entrepreneur.

To complete the long-run pricing model, it is necessary to specify how expectations are formed for the price of intermediate inputs and the average labor compensation. These expectations could be postulated to follow simple adaptive schemes similar to equation (5). However, such an assumption may be somewhat unrealistic, particularly when a change in the exchange rate is involved. It seems likely that entrepreneurs would revise their expectations as to the future price of intermediate inputs and the average labor compensation when an exchange rate occurred even before observing any exchange rate effects on the actual variables. The following adaptive schemes are somewhat less restrictive, although they are more complex. It is postulated that changes in expectations, not directly caused by an exchange rate adjustment, are based on the trend-corrected evolution of the actual values of the variables adjusted for expected exchange rate effects. In addition, expectations can be directly influenced by an adjustment of the exchange rate. The expectation schemes are specified as

where E is the value of one SDR in terms of local currency relative to its value in a base year.3

The parameters τn and τn are the fractions of exchange rate effects on average labor compensation and intermediate input prices, respectively, that entrepreneurs expect to observe in the nth period after the exchange rate adjustment. The parameters λ2 and λ2 are elasticities which indicate the magnitude of the direct exchange rate effects on expected average labor compensation and intermediate input prices, respectively. The first two factors in equations (6) and (7) depict changes in expectations not directly caused by an exchange rate adjustment while the third one describes direct exchange rate effects on expectations. The schemes depicted by equations (6) and (7) are identical to the simple adaptive scheme represented by equation (5) if the parameters λ2 and λ2 are nil.

The adjustment of the actual price to the long-run desired level does not necessarily follow a gradual and smooth adjustment path.4 Uncertainty as to future developments by itself might slow down the adjustment in the likely case of a risk-adverse firm.5 Other factors, such as changes in competitors’ prices or the appearance of unused labor and capital within the firm, might push the actual export price further away from the long-run target price. It will be assumed here that the dynamic adjustment process results from the fact that in any given short-run (semiannual) period, the entrepreneur tries to reach the following four independent targets: (1) the actual price is equal to a certain fraction of long-run optimal price, which depends on the anticipated trend in price; (2) the actual price stays the same as in the previous period; (3) there is no change in the actual price relative to competitors’ prices; and (4) the actual price is such as to allow for an actual level of production equal to the long-run optimal level corresponding to the factors of production employed by the firm.

Failure to meet any one of the four targets results in real costs to entrepreneurs. The nature of such costs has been discussed at length in the literature and needs to be reviewed only briefly here.6 The first target is self-explanatory. The second target is dependent upon the costs inherent in the process of changing a given price because of the administrative work involved, the uncertainty as to the effect of this change, and the loss of good will which may not be fully compensated by a reversal at a later stage. The third expresses the view that in the short run entrepreneurs keep their prices in line with competitors’ prices so as to avoid sudden changes in their exports, because these would result in sharp variations in their production rates or in the allocation of their production among export and home markets. This effect is likely to be important mainly for relatively homogeneous products for which a change in relative prices would rapidly lead to a large change in market shares. Finally, it may be in the interest of entrepreneurs to modify their export selling price temporarily in order to reduce the proportion of their labor and capital that is under-employed or over-employed by expanding or contracting their sales.

Obviously, all four of these targets are not normally attainable, and entrepreneurs have to fix their export selling price so as to minimize the total costs arising from not meeting one or more of them. The problem can be depicted as the search for the minimum value of the following loss function, which is assumed to be quadratic both for the purpose of economic realism and mathematical convenience:

where LX is the loss (costs), subjectively perceived, which results when entrepreneurs do not have an export selling price which meets all four targets; PXC is the price of competitors’ products expressed in SDRs; Y*f is the long-run optimal level of production, corresponding to the factors of production employed by the firm; and k is added to permit anticipated trends in the export price.

The loss function (8) can be minimized with respect to PX by taking into account the short-run elasticity of the total production (home plus export demand) with respect to the export price (ηyx). The short-run optimal export supply price is

Substituting equation (4) for PX* in equation (9), rearranging terms, and adding an error term v yield:

where C = B + ΦA.

The optimal production level Y*f can be derived from the production functions (2) and (3) after having set the slack dummy variable U to zero. The model—composed of the price equation (9) and the expectation functions (5), (6), and (7)—possesses the necessary equilibrium properties of having the direct long-run elasticities of the export price equal to v with respect to the average hourly labor compensation, –(v/σ) with respect to the output per man-hour, 1 –v with respect to the price of intermediate inputs, and zero with respect to the exchange rate and competitor prices. The exchange rate effects considered here are the direct effects on entrepreneurs’ expectations and relative export prices, rather than the indirect effects through a change in actual input prices and the output per man-hour.

Equation (10) explains the export contract price expressed in local currency. The explanation of the price at the time of the delivery, hereafter referred to as the export unit value, must take into account the delivery delay and the practice of stipulating some contract prices in foreign exchange, mainly in U. S. dollars. If π is the delivery delay, c the proportion of contracts in U.S. dollars, and (1–c) the proportion of contracts in local currency, the average export unit value in local currency (PXD) is equal to

where E$ is the value of one U.S. dollar in local currency π periods before delivery.

Application of the export price model—composed of equations (5), (6), (7), (10), and (11)—to the explanation of manufactured export prices raises problems related to aggregation procedures and stability of the parameters. The export price equations (10) and (11) are derived for an individual firm producing one product for two markets. These equations can readily be extended by analogy to an industry producing a specific product for two markets. Aggregation of the micro- economic relationships (10) into a macroeconomic relationship describing the behavior of a country’s export price index for manufactures is a more complex task; in an empirical analysis, it must be dealt with on a somewhat ad hoc basis because a lack of microeconomic data prevents a rigorous construction of relevant microeconomic variables.7

Equation (10) is employed as a basis for the empirical analysis of export prices for manufactures. The index of competitors’ prices for country l is calculated by taking into account the commodity composition and the geographical structure of its exports:

where PXij = export price for the product i exported by country j in SDRs

Sgij = market share of country j in the market for product i in country g

Zgil = share of product i exported by country l to country g in the total exports of manufactures by country l.

Published aggregate series for manufactures are used for production, man-hours, and average hourly compensation, although these series are based on weighting schemes that reflect the relative importance of each industry in the total production of manufactures rather than the production for exports.

Equation (11) is rewritten as follows to take into account the different delivery delays of various manufactured products and an error term (v’):

A weakness of the present pricing model is that some of its structural parameters cannot really be assumed to remain constant over long periods of time. Changes in expectation behavior, in the proportion of export contracts in U.S. dollars, and in the commodity pattern of exports would lead to a change in the values of corresponding parameters. Longer “queues” for foreign orders may influence the lag parameters in the relationship between contract prices and delivery prices. The parameters of the model are estimated only from the most recent observations, so as to minimize these difficulties and to obtain results that are meaningful in analyzing the present export pricing behavior of entrepreneurs. Obviously, one is limited in this direction by the need to have a sufficient number of observations with a certain degree of variation to obtain reliable estimates. Ultimately, the estimates must be interpreted as estimates of average values of the parameters over a given period of observation and only extrapolated to present and future periods with great caution.

II. The Empirical Analysis

The model represented by equations (5), (6), (7), (10), and (13) was employed to study empirically the export pricing behavior of the manufacturing industries of France, Germany, Japan, the United Kingdom, and the United States. The parameters of the model were estimated by least-squares multiple regression or from a priori information. The period of observation was 1958–72, where data were available. The sources of the data are presented in the Appendix. There were three stages: first, the parameters of equation (13), which relates the export unit value to the export (contract) price, were estimated; then, the parameters of the export price equation (10) and the expectation functions (5), (6), and (7) were estimated simultaneously; and finally, the complete export price model was used to simulate the effects of changes in exchange rates and other exogenous variables on export prices for manufactures.

Estimation of the parameters of the nonlinear equation (13) was difficult, mainly because of the lack of data. While data on the export unit values for manufactures are available for the five countries in the form of unit-value indices, indices of export contract prices for manufactures are available only for Germany and Japan. Parameters of equation (13) were estimated for those two countries from monthly observations by least-squares multiple regression.8 The period of observation is January 1963–April 1973. Since the unit-value indices are moving-weight indices, while the contract-price indices are based on a fixed-weight Laspeyres formula, the behavior of the indices may differ because of a change in the commodity pattern of exports.9 A trend variable was introduced in the regression equation to take these effects into account. For the same reason, the error terms can be expected to display a strong autocorrelation. It was postulated that the error terms obey a first-order autoregression scheme. Finally, the rate of change in the exchange rate was introduced in the regression equation to take into account customs lags in the compilation of export data (which may lead to spurious variation in unit values in local currency because of an incorrect conversion factor, whenever a change in the exchange rate occurs). No smoothing constraint was imposed on the distributed lag parameters (θπ), but these parameters were constrained to be positive. The estimation was made with and without the constraint that the sum of these coefficients is equal to one. Initially, the estimation was made with a large number of lags extending over three years by employing quarterly rather than monthly observations. Since the results showed that the lag between contract prices and export unit values was quite short, the estimation was confined to monthly observations and a relatively small number of lags.

The results of the statistical estimation of the parameters of equation (13) are presented in Table 1. The equation explains most of the variations in export unit-value indices, with R¯2 about 0.99 for Germany and 0.88 for Japan. The constraint that the sum of the lag parameters (θπ) is equal to unity is not statistically inconsistent with observations. The results corresponding to the constrained estimation are more consistent with a priori expectation and are therefore analyzed here. The estimates of the proportion of export contracts in U. S. dollars, about 18 per cent for Germany and 80 per cent for Japan, are consistent with a priori information. Estimates of delivery delays are more surprising. For both Japan and Germany, about 40 per cent of a variation in contract prices is reflected in the export unit-value index after a lag of only one month. Remaining effects are concentrated around a six-month lag, but available data on delivery delays would suggest longer lags. A likely explanation for this anomaly is that the composition of the contract price indices is biased in favor of manufactures with relatively small delivery delays. Estimates of the individual lag parameters have relatively large standard errors, primarily because of the autocorrelation present in the price series.10

Table 1.Regression Estimates: Export Unit Value for Manufactures as a Function of Contract Prices1(Monthly observations, January 1963–April 1973)
GermanyJapan
Unconstrained estimationConstrained estimationUnconstrained estimationConstrained estimation
Point

estimate
Standard

error
Point

estimate
Standard

error
Point

estimate
Standard

error
Point

estimate
Standard

error
Proportion of contracts in
U. S. dollars (c)0.1630.0580.1780.0610.8130.1200.8010.104
Delivery-lag parameters
θ10.3150.1650.4190.1620.4480.1440.4340.143
θ20.1890.1710.1780.169
θ30.220.2210.2430.2220.0970.2020.0680.199
θ40.0380.2230.0310.2070.0020.204
θ50.1470.1960.1150.192
θ60.2150.1700.3000.2050.3120.1970.2030.194
θ70.0060.194
Σπ = 07θπ0.7820.1551.0001.2300.2151.000
Trend coefficient–0.00102020.000128–0.00203220.0001290.0002860.0002950.0006780.000294
Coefficient of ln (E$/E$-1)0.0390.0670.0370.067–0.8480.082–0.8360.083
Rho30.3150.0850.3260.0870.5240.1050.5360.109
Goodness-of-fit statistics4
R¯20.9890.9870.8850.881
SE0.00810.00820.01230.0122
D-W1.982.012.212.22

Estimation of the parameters of the export price equation (10) and the expectation functions (5), (6), and (7) presented numerous difficulties.11 First, there is the lack of data on export contract prices for France, the United Kingdom, and the United States. Proxies for these variables were obtained by solving equation (13) for ln (PX):

Successive values of ln(PX) were derived from values of ln(PXD), ln{E$), and benchmark estimates of ln(PX). To obtain the benchmark estimates, it was postulated that contract prices in each of the first six months of 1955 were equal to unit values three months later. The values of the 0* parameters were chosen to reflect estimates of these parameters obtained for Germany and Japan: θ1 = 0.4, θ2 = θ3 = θ4 = θ5 = 0.1 and θ6 = 0.2. Based on exogenous information, the value of the proportion of contracts in U. S. dollars (c) was estimated to be 0.15 for France and the United Kingdom and 1.0 for the United States.

The expectation functions (5), (6), and (7) can be transformed to express expected values as weighted averages of past observations, with the weights declining geometrically. Substitution of these weighted averages in equation (10) and a succession of three Koyck transformations yield a rather complex equation which is overidentified.12 It would be quite inefficient (and probably not even feasible) to estimate all parameters by employing nonlinear estimation methods without making use of any exogenous information on the values of some of these parameters. In the present study, a priori information and exogenous estimates were used extensively.

The parameter λ0 in the expectation function for the long-run optimal value of the output per man-hour in equation (5) was assumed to be equal to 0.25. This estimate is consistent with the traditional use of a three-year moving average procedure to generate “normal” output per man-hour. The value-added share in manufacturing (v) was estimated from the most recently available input-output tables. The estimates range from a low of 0.58 for Japan to a high of 0.66 for the United States. The substitution elasticity between labor and capital (σ) is difficult to estimate; estimates in the literature are contradictory, although they seem to indicate that it is somewhat less than unity. This parameter was assumed to be equal to 0.8. The last parameters estimated from exogenous information are those referring to direct exchange rate effects on expected average labor compensation and intermediate input prices. The parameters λ2 and λ2 were estimated by postulating that they reflect short-term and medium-term exchange rate effects on average labor compensation and intermediate input prices, respectively. These effects were estimated by employing the Multilateral Exchange Rate Model.13 It was further assumed that entrepreneurs expect exchange rate effects on intermediate input prices to take place instantaneously (τ0 = 1.0) and expect effects on average labor compensation to take place gradually, with 20 per cent of the effects accruing in each semiannual period (τ0 = τ1 = τ2 = τ3 = τ4 = 0.2).

The remaining parameters of the nonlinear equation (10), incorporating the three adaptive expectations schemes (5), (6), and (7), were estimated from semiannual observations in 1958–72 by least-squares multiple regression. The estimation was made with the rate of change in contract prices (ln(PX/PX-1) on the left-hand side. The error term in equation (10) before making the Koyck transformations is composed of moving averages of the error terms of the adaptive expectation schemes u, u’ and u” and the error term v. The Koyck transformations introduce autocorrelation in these error terms. Thus, even if the error terms u, u’ u”, and v are “white noises,” the composite error term in the regression equation is unlikely to be a “white noise.” However, the estimation is based on a small sample and in this case it has been shown that a first-order autocorrelation scheme may provide a sufficiently good approximation for the specification of the composite error term.14

The parameter estimates are presented in Table 2. For each of the five countries considered in this study, the structural equation (10) explains most of the variations in the rate of change of contract prices, with R¯2 being higher than 0.75 in four cases and equal to 0.68 in the fifth one. The coefficient of autocorrelation is relatively large only for Japan (0.39) and the United Kingdom (0.57). The most interesting results are the estimates of the parameters ø and γ which show the relative importance of expected production costs and foreign prices, respectively, on short-run pricing decisions. The estimates of the ø and γ parameters are consistent with a priori expectations. The estimated value of γ is relatively high for France, Germany, and Japan. It is much lower for the United States, where manufactured exports account for a smaller part of total economic activity and are composed mainly of highly differentiated products. The low γ parameter for the United Kingdom may indicate that British entrepreneurs are less oriented toward exports than French, German, and Japanese entrepreneurs or simply that their export products are less subject to foreign competition because they are more differentiated. For each of the five countries, the estimated value of ø is relatively low, indicating a slow adjustment of export prices to expected changes in production costs. This is particularly true for Germany, where the estimated value of ø is only 0.05. The rate of capacity utilization plays an important role only in Germany and in the United States, countries where a higher capacity utilization rate results in higher export prices.

Table 2.Exogenous and Regression Estimates: Export Price Equations1,2(Semiannual observations, 1958–72)
FranceGermanyJapanUnited KingdomUnited States
Point

estimate
Standard

error
Point

estimate
Standard

error
Point

estimate
Standard

error
Point

estimate
Standard

error
Point

estimate
Standard

error
Expectation parameters 1
Productivity (λ0)0.250.250.250.250.25
Labor costs (λ0)0.7150.1580.5820.2800.4200.3200.6200.1310.8530.192
Material costs (λ0)1.000.6850.3330.5320.2650.9350.1721.00
(νλ2 + (1 − ν)λ2)40.320.350.260.420.11
Adjustment parameters0.089
Long-run target (ø)0.2170.0900.0500.0640.2240.0820.3140.1230.291
Foreign prices (γ)0.4140.0690.3580.1220.5440.0960.1100.0620.0870.095
Capacity utilization (ξ)0.1010.0680.1720.0400.0140.047–0.0570.0870.1680.034
Production parameters
Value-added share (ν)0.610.630.580.600.66
Substitution elasticity (σ)0.800.800.800.800.8)
Trend coefficient (r)0.00150.00130.01600.0044–0.00140.00170.00800.00210.00370.0015
Constant term (c)–0.4500.307–0.7990.183–0.0510.2130.2050.393–0.7650.154
Effects of price control5–0.0170.006
Seasonal variation 6–0.009400.004110.001170.00273–0.000160.00223–0.000110.00215–0.011080.00251
Rho 70.0700.0850.0340.1320.3930.1490.5690.0980.1030.080
Goodness-of-fit statistics8
R¯20.8010.6830.7800.8250.751
SE0.01150.00760.00760.00740.0075
D-W2.0561.9841.8861.5931.898

The estimates of the expectation parameters λ0 and λ0 are also consistent with a priori expectations. The expectation parameters for average labor compensation (λ0) are high (except in Japan, where it is 0.42 but with a relatively large standard error). The expectation parameters for intermediate input prices (A”λ0) are even larger. For France and the United States, estimates of λ0 are larger than unity. These estimates were rejected on a priori grounds, and the equations for France and the United States were re-estimated under the constraint that λ0 equals unity.

The complete adjustment paths of export unit values for manufactures reflecting changes in competitors’ prices and elements determining production costs are presented in Table 3 for the five countries. These adjustment paths are calculated by combining the results obtained for the equations explaining contract prices with those obtained or assumed for the relation between contract prices and export unit values. The adjustment paths for export contract prices are similar to those for unit values with only a slightly faster response and are not presented here. In all five countries, adjustment of the manufactured export unit value to changes in average hourly labor compensation and intermediate input prices is a slow process. In the United Kingdom and the United States, about half of the changes in these cost elements are reflected in the export unit values by the end of the first year. In the other three countries the adjustment process is slower. Changes in competitors’ prices have marked effects on the export unit values of France, Germany, and Japan for relatively long periods of time. Effects of a 10 per cent increase in competitors’ prices will account for a 2 to 3 per cent increase in the export unit value of these countries two and a half years later.15 Effects of a change in capacity utilization on manufactured export unit values appear gradually. Ultimately these effects become rather large for France, Germany, and the United States. After two and a half years, a 10 per cent cut in capacity utilization results in a decrease in manufactured export unit values of about 3½ per cent for France, 9 per cent for Germany, and 5 per cent for the United States.

Table 3.Magnitude and Timing of Effects of Various Factors on Export Unit Value in Local Currency for Manufactures
Cumulative Elasticity of Export Unit Value for Manufactures with Respect to
Quarterly PeriodY/LWPMPXCy/Y*f
France
0–0.010.050.070.120.10
1–2–0.040.140.200.400.18
3–4–0.100.320.390.320.24
5–6–0.180.450.520.250.29
7–8–0.250.570.620.200.33
9–10–0.320.660.700.160.36
–0.761.001.000.030.47
Germany
0–0.000.010.010.100.17
1–2–0.010.030.030.330.33
3–4–0.030.070.080.340.48
5–6–0.050.120.130.320.63
7–8–0.070.170.180.310.77
9–10–0.100.230.240.290.90
–0.791.001.000.003.44
Japan
0–0.010.020.040.190.01
1–2–0.040.080.100.470.02
3–4–0.100.210.270.420.02
5–6–0.170.340.410.330.03
7–8–0.240.450.520.250.03
9–10–0.310.550.630.200.03
–0.731.001.000.000.05
United Kingdom
0–0.000.000.090.03–0.06
1–2–0.060.170.250.10–0.10
3–4–0.140.400.500.08–0.13
5–6–0.230.570.640.06–0.15
7–8–0.320.700.740.04–0.16
9–10–0.400.790.810.02–0.17
–0.751.001.000.00–0.18
United States
0–0.020.080.090.030.17
1–2–0.060.220.250.080.29
3–4–0.150.450.500.060.37
5–6–0.240.630.650.040.43
7–8–0.340.740.750.030.48
9–10–0.420.810.820.020.51
–0.831.001.000.000.58
Notation: (Y/L) = output per man-hour; W = average hourly labor compensation; PM = price of intermediate inputs; PXC = price of competitors’ products; and (Y/Y*f) = rate of capacity utilization.

Chart 1 presents the adjustment paths of export contract prices for manufactures for a 10 per cent devaluation. The adjustment paths corresponding to a revaluation would be symmetrical in the present model. These adjustment paths were not calculated for more than three years, because the exchange rate effects on production costs, estimated exogenously, correspond only to short-term and medium-term effects. These adjustment paths rest on the assumption that there are no exchange rate effects on the total output of the manufacturing sector, that is, no effects on the optimal output per man-hour. If domestic demand was not adjusted to make room for additional exports, the total output would rise, causing further increases in export prices in the short run because of decreasing marginal return and higher capacity utilization. The adjustment paths show clearly that contract prices for manufactures in local currency react rapidly to a change in the exchange rate. For France and Japan, the immediate impact on contract prices amounts to about one half of the change in exchange rate. The immediate impact amounts to about one third of the change in exchange rate in Germany, one quarter in the United Kingdom, and only one tenth in the United States. This immediate effect corresponds to the attempt by exporters of the devaluing country to minimize sudden changes in their prices relative to competitors’ prices, and its magnitude is affected hardly at all by the magnitude of the exchange rate effects on production costs, which have been estimated exogenously. Gradually these short-run dynamic effects vanish and are overtaken by the exchange rate effects taking place through production costs.

Chart 1.Cumulative Effects of a 10 Per Cent Devaluation on Export Contract Prices in Local Currency for Manufactures

Adjustment paths of manufactured export unit values for a 10 per cent devaluation are presented in Chart 2. They correspond to the adjustment paths of export contract prices, with a certain lag caused by delivery delays and some temporary differences resulting from a valuation effect. This valuation effect is particularly important for Japan, where 80 per cent of export contracts for manufactures were estimated to be denominated in U. S. dollars. For the three European countries, the valuation effect is small. It is negligible for the United States.

Chart 2.Cumulative Effects of a 10 Per Cent Devaluation on Export Unit Value in Local Currency for Manufactures

III. Conclusion

The model presented in Section I, which is derived from formal economic theory, provides a satisfactory explanation of the short-run evolution of the export price index for manufactures in France, Germany, Japan, the United Kingdom, and the United States. It is important to bear in mind, however, that (1) this model is based on some fairly restrictive assumptions, particularly concerning the formation of expectations; (2) data on export prices are not quite reliable; (3) little is known about the small-sample properties of nonlinear models with a compound error term of the kind present in the equations explaining export contract prices; and (4) the estimates obtained in most cases from observations corresponding to the period 1958–72 may not necessarily be valid for later periods.

After allowance is made for the limits of the model and data, several results seem to be well established by the present study. In the short run, competitors’ prices play a crucial role in the pricing decisions of French, German, and Japanese exporters of manufactures, whereas the export pricing decisions of British and U. S. exporters of manufactures are much less influenced by competitors’ prices. In all five countries, the adjustment of export contract prices for manufactures to changes in production costs is slow, with only half of the change (or less) reflected in contract prices after a year. This adjustment is particularly slow for Germany and Japan. Differences in the behavior of entrepreneurs or in the commodity composition of exports may account for differences in pricing behavior observed at the aggregate level. Empirical studies at the firm or industry level would be needed for a better understanding of entrepreneurs’ pricing behavior.

Export contract prices in local currency for manufactures are affected rapidly by exchange rate changes. Within the first six months following a hypothetical 10 per cent devaluation, the estimated increase in contract prices in local currency amounts to 4.8 per cent for France, 3.8 per cent for Germany, 6.0 per cent for Japan, 2.4 per cent for the United Kingdom, and 1.2 per cent for the United States. For the most part this short-run effect reflects an attempt by exporters of the devaluing country to minimize sudden changes in their prices as relative to competitors’ prices. It is only gradually that contract prices are readjusted to reflect the post-devaluation production costs. Except for the United Kingdom, the short-run exchange rate effects on contract prices are larger than the price adjustment corresponding to medium-term exchange rate effects on production costs; that is, there is a tendency in the short run to overshoot the new medium-term optimal price. Effects of revaluation would be symmetrical in the present model. Export unit values for manufactures reflect contract price changes with a relatively short lag averaging about three months. In Japan, export unit values are also influenced by a large valuation effect during the first few months after a change in the exchange rate between the yen and the U. S. dollar because of the high proportion of export contracts denominated in U. S. dollars. The valuation effect is much smaller for the other four countries.

APPENDIX Sources of Statistical Data

The coverage and the particular statistical properties of the main data series employed in this study are presented below.

Manufactured exports unit value indices (PXD), 1955–73 (April)

Monthly data on each country’s unit value index for manufacturing exports were obtained from national sources. Indices for Japan and the United States are based on the Fisher ideal formula. Moving-weight Paasche indices are used by France and Germany. A fixed-weight Laspeyres index is employed by the United Kingdom. The indices for Japan and the United Kingdom do not include aircrafts or ships.

Manufactured exports contract price indices (PX), 1958–73 (April)

Monthly data for Germany were taken from Wirtschaft und Statistik. The German index is based on the fixed-weight Laspeyres formula with a 1958 base for the period 1958–61 and a 1962 base thereafter. Monthly data for Japan were taken from the Price Indices Annual of the Bank of Japan. The Japanese index excludes ships, and it is based on the fixed-weight Laspeyres formula with a 1958 base for the period 1958–64, a 1965 base for the period 1965–69, and a 1970 base for 1970–73 (April).

Capacity utilization in manufacturing industry (Y/Y*f), 1958–72

The Wharton School quarterly indices of capacity utilization were used for France, Germany, the United Kingdom, and the United States. For Japan, an index of capacity utilization was derived by the author from production data by employing a variant of the Wharton School method. These indices have the serious disadvantage of being based on the potential manufacturing output corresponding to the full utilization of factors of production available in the economy rather than on those actually employed by the manufacturing firms as called for by the present model.

Competitors’ price indices for manufactures (PXC), 1958–72

Quarterly indices of competitors’ prices in SDRs were derived from unit value indices for exports from nine industrial countries: Belgium, Canada, France, Italy, Netherlands, Sweden, Switzerland, the United Kingdom, and the United States; and from contract price indices for exports from Germany and Japan. In the calculation of competitors’ price indices, observations on unit values were given a lead of one quarter to make them more comparable with contract prices. The aggregation over products indicated by formula (14) resulted from a series concerning 7 industries shown with the Standard International Trade Classification (SITC) number: chemicals (SITC 5), paper products (SITC 64), textile products (SITC 65), steel products (SITC 67), nonferrous metals (SITC 68), machinery and road motor vehicles (SITC 71, 72, 732), and other manufactures, excluding ships and aircraft (SITC 61/63, 66, 69, 8). The aggregation over markets resulted from a series on 17 markets: the 11 countries indicated above, plus Developing Countries in Africa, Developing Countries in the Far East, Developing Countries in Latin America, Developing Countries in the Middle East, Council for Mutual Economic Assistance (CMEA) Countries and Mainland China, and Rest of the World. The trade weights were the 1962 trade flows for the period 1958–66 and the 1970 trade flows for the period 1967–72. The statistical quality of the price series used ranges from good to extremely poor. For the United States some of the series are based on domestic wholesale prices rather than export unit values.

Production, man-hours, and average hourly labor compensation in manufacturing industries (Y, L, and W), 1958–72

Semiannual series of production, man-hours, and average hourly earnings in manufacturing industries were obtained from national sources. Comprehensive annual data on man-hours and average hourly labor compensation in manufacturing for the five countries considered here were provided by the U.S. Department of Labor, Bureau of Labor Statistics. These annual data were employed to adjust the often less comprehensive semiannual data available from national sources.

Indices of prices of intermediate inputs for manufacturing industries (PM), 1958–72

Semiannual series of prices of intermediate inputs for manufacturing industries were calculated from available series on prices of services and products other than domestic manufactures used as inputs by manufacturing industries. Series on prices of services were derived from the implicit deflators of the amounts of gross domestic product originating in transportation and communication, banking, insurance, and other business services. Reliable series on prices of intermediate products other than domestic manufactures are available for Japan, the United Kingdom, and the United States. For France and Germany, the available series covers only industrial raw materials and fuels.

Mr. Artus, economist in the Special Studies Division of the Research Department, holds degrees from the Faculty of Law and Economics in Paris and from the University of California at Berkeley.

In addition to thanking staff colleagues for their assistance, the author wishes to express his appreciation to Mr. Patrick Minford for his comments on an earlier draft of this paper, but the opinions expressed and any errors are those of the author.

See Edmund S. Phelps and others, Microeconomic Foundations of Employment and Inflation Theory (New York, 1970); and William D. Nordhaus, Recent Developments in Price Dynamics. Discussion Paper No. 296, Cowles Foundation for Research in Economics (Yale University Press, August 1970). This latter paper also contains an extensive survey of econometric studies on pricing.

The derivation assumes that

PX* = νCVAe + (1 − ν)PMe(CVAe)ν(PMe)1 − ν

where CVA is the cost of the value added (that is, the total unit cost of production less the value of intermediate inputs contained in one unit of output).

In equations (6) (7), the exchange rate relative should be defined in reference to the value of a suitably weighted “basket of world currencies” in terms of local currency. For equation (6) the composition of the basket should reflect the relative importance of the various foreign currencies as to their exchange rate effects on the average labor compensation of the country considered. For equation (7) the composition should reflect exchange rate effects on intermediate input prices; the SDRs are taken as a substitute for those baskets of world currencies.

The long-run desired level would also be influenced by the actual export price if prices of factors of production were dependent on this actual price.

See William C. Brainard, “Uncertainty and the Effectiveness of Policy,” American Economic Association, Papers and Proceedings of the Seventy-Ninth Annual Meeting (American Economic Review, Vol. 57, May 1967), pp. 411–25.

A survey of this literature is presented in Nordhaus, “Recent Developments in Price Dynamics” (cited in footnote 1).

This problem of aggregation over products has been thoroughly discussed in the economic literature and does not need to be reviewed here. See, for example, Edward E. Learner and Robert M. Stern, Quantitative International Economics (Boston, 1970), pp. 41–48.

The nonlinear estimation was made by the gradient method, using the Econometric Programming Language (EPL) computer program supplied by Data Resources, Inc.

This effect is small for Japan because the weights in the contract-price index have been revised in 1965 and 1970. However, the weights in the German contract- price index have not been revised since 1962. For Japan, the contract and unit-value indices exclude ships.

Since the regression model is nonlinear, the ordinary technique to calculate standard errors does not apply. The standard errors appearing in Table 1 are large-sample standard errors. Strictly speaking, the statistical significance of the estimated parameters cannot be tested by the use of the t test.

Actual factor prices are taken as exogenous in this model. To the extent where this assumption is not quite valid, for example, because of the reversed causality referred to in footnote 4, some minor statistical biases may have been introduced in the analysis.

The computation steps involved are described in Marc Nerlove, Distributed Lags and Demand Analysis for Agricultural and Other Commodities, U. S. Department of Agriculture, Agriculture Handbook No. 141 (Washington, June 1958).

Jacques R. Artus and Rudolf R. Rhomberg, “A Multilateral Exchange Rate Model,” Staff Papers, Vol. 20 (November 1973), pp. 591–611.

See Dennis J. Aigner, “A Compendium on Estimation of the Autoregressive-Moving Average Model from Time Series Data,” International Economic Review, Vol. 12 (October 1971), pp. 348–71.

This effect may help to explain the spread of inflation from the United States to Japan and Europe in the late 1960s. See William D. Nordhaus, “The Worldwide Wage Explosion,” Brookings Papers on Economic Activity, No. 2, (1972), pp. 431–65.

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