The Geographic Pattern of Trade and the Effects of Price Changes1
Author: Paul S. Armington
Publication Date:
01 Jan 1969
eISBN:
9781451947298
Language:
English
Keywords:
SP; investment; substitution elasticity; changes arise; price elasticities of substitution; price effect; price competitiveness; Exports; Trade balance; Imports; Manufacturing; Demand elasticity; Global
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THE DISTRIBUTION of any country’s export and import trade, by destination and by origin, differs substantially from the corresponding distributions for many other countries. Such differences, as well as the differences in size of over-all trade, have an important bearing on the way in which trade flows respond to price changes. For example, if country A expands its exports as a result of a reduction in its price level, the change in value of exports from some other country, B, will naturally depend on the size of B’s total exports, but also on the extent to which B trades with country A and on the extent to which A supplies foreign markets that are important outlets for B’s products. Or, for another example, suppose that A’s trade balance deteriorates as a result of a loss in price competitiveness. The extent to which country B will share in the offsetting improvement in the collective trade balance of other countries will depend on such factors as the importance of A’s products in B’s imports, on the importance of imports in B’s total expenditure, and on the extent to which B’s exports depend on markets that are heavily supplied by A. These structural variables are ratios of recorded trade flows.

Abstract

THE DISTRIBUTION of any country’s export and import trade, by destination and by origin, differs substantially from the corresponding distributions for many other countries. Such differences, as well as the differences in size of over-all trade, have an important bearing on the way in which trade flows respond to price changes. For example, if country A expands its exports as a result of a reduction in its price level, the change in value of exports from some other country, B, will naturally depend on the size of B’s total exports, but also on the extent to which B trades with country A and on the extent to which A supplies foreign markets that are important outlets for B’s products. Or, for another example, suppose that A’s trade balance deteriorates as a result of a loss in price competitiveness. The extent to which country B will share in the offsetting improvement in the collective trade balance of other countries will depend on such factors as the importance of A’s products in B’s imports, on the importance of imports in B’s total expenditure, and on the extent to which B’s exports depend on markets that are heavily supplied by A. These structural variables are ratios of recorded trade flows.

I. Introduction

THE DISTRIBUTION of any country’s export and import trade, by destination and by origin, differs substantially from the corresponding distributions for many other countries. Such differences, as well as the differences in size of over-all trade, have an important bearing on the way in which trade flows respond to price changes. For example, if country A expands its exports as a result of a reduction in its price level, the change in value of exports from some other country, B, will naturally depend on the size of B’s total exports, but also on the extent to which B trades with country A and on the extent to which A supplies foreign markets that are important outlets for B’s products. Or, for another example, suppose that A’s trade balance deteriorates as a result of a loss in price competitiveness. The extent to which country B will share in the offsetting improvement in the collective trade balance of other countries will depend on such factors as the importance of A’s products in B’s imports, on the importance of imports in B’s total expenditure, and on the extent to which B’s exports depend on markets that are heavily supplied by A. These structural variables are ratios of recorded trade flows.

Of course, trade structure by itself does not fully determine the results of price changes. The impact of price changes also depends on how readily buyers in the various countries shift from one source of supply to another in response to changes in relative prices. In other words, price elasticities of substitution in the various markets are important. Substitution elasticities relating to composite trade flows may depend on such factors as the commodity composition of trade, the degree and nature of trade restrictions, the importance of long-term contracts, and traditional loyalties to particular products or particular sellers. The elasticities are parameters that measure the strength of a presumed cause/effect relationship between relative prices and relative quantities demanded. They can be estimated econometrically, albeit with a debatable degree of accuracy. Unlike the structural factors discussed above, the elasticities are not recorded data.

This paper shows how to utilize the data on trade structure to achieve the best possible estimates of the effects of price changes, given any reasonable array of elasticity estimates. The credibility of estimates of price effects depends on thorough and systematic use of these data, as well as on the statistical credentials of the elasticities assumed.

The method illustrated below improves on current practice in two ways. First, whereas procedures currently in use take account of each country’s total trade or the distribution of trade of the country whose price level changes, the calculation outlined below gives due weight to both of these factors as well as to other structural relationships (of the kinds mentioned above) implicit in the distribution of each country’s trade by origin and destination. Second, changes in the internal trade of each country are calculated as an integral part of the process of computing changes in each country’s imports and exports. As a result, substitution between imports and import-competing products is recognized as a factor affecting not only the imports of the country whose price level changes but also the imports of each other country. The calculated changes in exports of each country reflect all of these changes in total imports as well as the changes in import shares. The method involves a single process of computation that economizes on assumptions and ensures the internal consistency of the results.

The illustrations deal with trade in manufactures only, and the geographic breakdown constitutes ten major industrial countries (individually) plus the Rest of the World (treated as a single country).2 The paper first demonstrates how the structure of trade in manufactures influences the effects on demand for manufactures of a price change in a single country; then the calculation of the effects of simultaneous price changes in several countries is considered. After two digressions on special topics (Sections IV and V), the independent role of the substitution elasticities is examined briefly. This is done by reworking some of the results on the basis of alternative arrays of substitution elasticities. As might be expected, the effects of price changes, in value, are highly sensitive to the assumed level of the substitution elasticities in the various markets. On the other hand, the relative impact of price changes on trade positions of the various countries depends in large measure on trade structure, even if the elasticities vary greatly from market to market.

The scope of this study is limited in several important ways. First, no attempt is made to measure the elasticities. Second, nothing at all is said about the important role of supply. The study deals only with demand relationships, and price changes are treated as exogenous. The study does not purport to analyze the probable effects of changes in policies regarding exchange rates, tariffs, wages, etc., since the connection between such policy changes and price changes is not explored. Third, nothing is said about the time pattern of trade response to price changes. This is solely an exercise in comparative statics.

II. Trade Structure and the Impact of Single Price Changes

From the model of demand that the author has presented in a separate paper, two useful elasticity formulae can be derived.3 These relationships are the basis for calculating how a change in the price level in a single country (other price levels remaining unchanged) will affect trade between any two countries, as well as the internal trade of each country. Regarding demand for any given class of items, such as manufactures, the following relations hold between various elasticities and market shares:

(1)ηji=(1-Sji)σi+Sjiηi,and
(2)ηhi=Sji(σi-ηi),j≠h,where

ηji is the partial elasticity of demand of buyers in the ith country for manufactures produced by the jth country; Sji is the share of the jth country’s manufactures in the ith country’s total expenditure on manufactures; σi is the elasticity of substitution in the ith market between the manufactures of any pair of countries (including the ith country) competing in that market; ηi is the partial elasticity of demand of buyers in the ith country for manufactures-in-general, irrespective of source of supply; and ηhi is the partial cross elasticity of demand of buyers in the ith country, with respect to a change in price of manufactures in j, for manufactures produced in any other country, h. Of course, when i is not equal to j or h, ηji and ηhi are elasticities of import demand. When i = j or h, they are elasticities of domestic or internal demand. Without unduly repeating the material covered in the earlier paper, the three assumptions on which the formulae are based may be restated as follows:

(1) buyers’ marginal rates of substitution between manufactured products are independent of their purchases of nonmanufactures;

(2) substitution elasticities among manufactured products are constants—that is, they themselves do not depend on prices or market shares;

(3) the elasticity of substitution between the manufactures of any pair of countries competing in a given market is the same as that between the manufactures of any other pair of countries competing in that market.

The formulae will now be applied to the analysis of the effects of a given price change. The elasticity of substitution in each market is assumed to be 3, and the elasticity of demand for manufactures-in-general in each market is assumed to be 1. These assumptions are not entirely arbitrary. These values are roughly the orders of magnitude that might be expected on the basis of past research and a priori reasoning; furthermore, if σ1 and ηi are assumed to be the same everywhere, differences in the impact of the given price change on the trade of the different countries will result solely from the initial geographic pattern of trade, so that through this assumption the role of trade structure can be examined in isolation. The shares, Sij, are calculated from a square matrix of trade in manufactures that includes the diagonal elements, internal trade.4 Such a matrix, showing data for 1966,5 appears as Table 1, and the percentage shares themselves are shown in the Appendix, Table 8. The direct elasticities in value terms (i.e., ηij – 1) are shown in the Appendix, Table 9, and the cross elasticities (ηhi) appear in Table 10. These tables indicate how each cell of the trade matrix (Table 1) would be affected, in per cent and disregarding signs, by a 1 per cent change in any price. Hence, a matrix of changes in value can be calculated for any given percentage price change. An example of such a matrix of changes appears as Table 2. It shows what would have happened following an increase, in 1966, of 10 per cent in the price of Italian manufactures, other prices remaining unchanged.6

Table 1.

Direction of External and Internal Trade in Manufactures of the Selected Countries, 19661

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For sources and footnotes, see page 185.Footnotes to Table 1Sources: Organization for Economic Cooperation and Development (OECD), Foreign Trade, Series B: Commodity Trade—Analysis by Main Regions; OECD, National Accounts Statistics; national statistics.

External trade data refer to Standard International Trade Classification (SITC) sections 5 through 8. Regarding internal trade, see footnote 3.

Foreign sales of the ten individual countries are their f.o.b. export data. Foreign sales of the Rest of the World, treated here as a single country, are based on c.i.f. import data of the ten and a standard conversion factor from c.i.f. to f.o.b. Owing to asymmetries in the collection of data and other statistical problems, the figures labeled “Total, imports,” as well as “Total, exports,” of the Rest of the World may differ substantially from reported import and export data, respectively.

The figures are rough estimates of the ratio of exports of manufactures (SITC 5-8) to gross value of sales in manufacturing. In addition to very limited data on sales in manufacturing available in national sources, OECD national accounts data for gross domestic product originating in manufacturing, plus a standard allowance for the relation between gross value and value added in manufacturing, have been taken into account in making the estimates. The diagonal elements of the matrix, as well as totals for purchases and sales, are derived from these estimated exports/sales ratios, and only these ratios have been rounded to suggest the degree of probable accuracy. An attempt is made later in this paper to determine the sensitivity of the main results to alternative assumptions concerning these ratios.

The estimate of the exports/sales ratio for the Rest of the World is more arbitrary than the others, since for this residual group little data are readily available on value added in manufacturing. Given the external trade data for the Rest of the World, any guess about the exports/sales ratio implies a corresponding guess about the imports/purchases ratio. The possible pairs of exports/sales and imports/purchases ratios are indicated in Chart 1 by the curve marked “Rest of World Possibility Locus,” and this locus can be seen in relation to the estimated positions of the ten individual countries. The position of the Rest of the World is selected at a more or less arbitrary point on this locus—the selection reflecting a judgment about the general degree of “openness” of the Rest of the World in comparison with the ten individual countries.

An examination of the changes in total trade shown in Table 2 provides a good picture of the ways in which trade structure exerts its influence. Italy’s exports decline in value by almost 20 per cent, and each other country increases its exports. For each of these other countries, the percentage gain depends, first, on Italy’s global market share and, second, on the extent to which the markets in which Italy’s share is relatively high (including the Italian market) happen to be important markets for the other country’s exports. Since Italy is the principal supplier of the Italian market, the impact on any other country’s exports depends heavily on how important the Italian market is for that country. But third-market effects are also important. The table shows that French and German exports expand by far the most, in per cent, while Japanese and Canadian exports are least affected. On the import side, Italy’s price increase causes an 18 per cent increase in the value of its imports; imports into other countries decrease as the increases in their average import prices cause net substitution of domestic for foreign items. The extent of these decreases, in per cent, depends mainly on how important Italy is as a supplier of imports to these countries. Again, France and Germany are by far the most affected.

Table 2.

Effects on All Flows of a 10 Per Cent Increase in the Price of Manufactures of Italy1

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Sources: Tables 1, 9, and 10.

Less than $0.05 million.

In each market σi is assumed to be 3 and ηi is assumed to be 1. Prices of manufactures of other countries are assumed to remain unchanged.

Since ηi is assumed to be 1, the change in each country’s total purchases in value should be zero. The small changes shown result from rounding in the computation of market shares (Table 8) on which the elasticities in Tables 9 and 10 are based. Calculated percentage changes in each country’s total purchases are each approximately zero.

The change in trade balance of each country (except Italy) expressed as a per cent of the total offset ($1,879.7 million) to the deterioration in Italy’s balance. The sum of these numbers equals 100, apart from rounding.

Putting the export and import sides together, Italy’s trade surplus in manufactures declines, and the offset is distributed among the other countries according to the percentages shown at the bottom of Table 2. This distribution is also shown at the top of Table 3. The relative impact of Italy’s price change on trade balances, in value, will depend not only on market shares and the patterns of export dependence but also on the relative sizes of total exports and total imports. To isolate the former effects, the relative size of each country’s total trade (exports plus imports) is also indicated at the top of Table 3, and the difference between the two distributions follows underneath. These differences indicate, for example, that Germany’s share of the offset to the change in Italy’s balance is about 11 per cent higher than would have been expected solely on the basis of the relative size of Germany’s total trade. Conversely, the positions of countries such as Japan, the United States, and Canada, whose channels of trade are not so closely interlocked with Italy’s, are affected less than in proportion to their total trade. Table 3 permits a similar analysis of the offsets to changes in the trade balances of the Netherlands, the United Kingdom, and Canada. The figures in italics—the differences—are indicative of the inaccuracy of the more traditional approach that distributes the offsets according to the relative size of each country’s total trade.

Table 3.

Analysis of the Offsets to Changes in Trade Balances of Italy, the Netherlands, the United Kingdom, and Canada

(In per cent)

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Sources: Tables 1, 9, and 10.

See lowest row of figures in Table 2 and footnote 3 of that table.

Total exports plus total imports of each of the nine countries and the Rest of the World, expressed as a per cent of the sum of these numbers.

The percentage change in each country’s total sales (including domestic sales) resulting from the price change in Italy is shown in Table 2, 7 and these data appear again as the third row of Table 4. Table 4 provides a different and more comprehensive view of the role of trade structure. It shows how world demand for manufactures of each country would be affected by a price change in any one of the countries. Again, the basic elasticities are assumed to be the same (σi = 3, ηi = 1) in each market. The very substantial differences in the numbers, from row to row and from column to column, serve to emphasize the importance of structural factors alone in determining the impact throughout the system of given price changes.

Table 4.

Effects of Single Price Changes on World Demand, in Value, for Manufactures of the Selected Countries

(In per cent)

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Sources: Tables 1, 9, and 10.

Less than 0.05 per cent.

In each market σi is assumed to be 3 and ηi is assumed to be 1.

Chart 1.
Chart 1.

Ratios of Imports to Total Purchases and of Exports to Total Sales

(In per cent)

Citation: IMF Staff Papers 1969, 002; 10.5089/9781451947298.024.A001

Source: Table 1.1 See Table 1, footnote 3.

III. Computing the Combined Effects of Multiple Price Changes

In most applications it is necessary to evaluate the combined effects of several price changes that occur simultaneously. In this event the procedure is to calculate a matrix of changes, such as Table 2, for each price change taken separately, using in each case the same base matrix (such as Table 1). The sum of the resulting matrices shows the combined effects of the set of simultaneous price changes.

A way to check that this method works is based on the fact that, if ηi = 1, a given percentage change in one country’s price must have the same effects as an equal and opposite change in prices in all other countries.8 For example, a 10 per cent increase in Italy’s price must have the same effect on Italy’s trade balance as a 10 per cent reduction in all other prices (or, in other words, a 10 per cent increase in every country’s price must leave the Italian balance unchanged). According to Table 2, a 10 per cent increase in Italy’s price causes a deterioration in Italy’s trade balance of $1,879.7 million. The effects on the Italian balance of a 10 per cent change in all other countries’ prices—each effect calculated in the same manner as Table 2—are shown in Table 5, column A, and their sum is also $1,879.7 million.

Table 5.

Effects of Multiple Price Changes and the Effective Change in a Single Price

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Sources: Tables 1, 9, and 10.

That is, if Italy’s price had increased by 2.073 per cent—the calculated effective change—and if no other price changes had occurred, the change in Italy’s balance would have been — $390 million, which equals the combined effect of the 11 price changes given in column E. As can be shown by a general proof, this equality rests on the fact that, in column A, the figure for Italy is the same (disregarding signs) as the total excluding Italy.

Thus, the effects of multiple price changes on any given flow or aggregate of flows can be calculated by a routine extension of the method described in the previous section.9

IV. Computing the Effective Change in a Country’s Price

For certain purposes it is useful to aggregate price changes directly, rather than to aggregate their effects, as described above. For example, the problem of aggregating price changes arises when a summary measure of change in A’s price competitiveness is desired. In econometric work many price variables cannot in practice be included in an equation explaining, say, A’s trade balance, and a single statistic may be needed to serve as a proxy for the entire array of price changes in the various countries (including A). A statistic that serves this proxy function rigorously may conveniently be called the effective change in A’s price. In the paragraphs that follow, the concept of effective change is defined; the method of computing it is stated; and proof is given that the method yields results that satisfy the definition.

Suppose that the given array of price changes in the various countries (including A) has the same effect on A’s trade balance as would a hypothetical x per cent change in A’s price alone. Then, clearly, x is the effective change in A’s price; it serves as a rigorous proxy for the entire array (assuming that the trade balance is the variable to be explained). Hence, the effective change in A’s price may be defined as that hypothetical change which, alone, would affect A’s trade balance in the same way as the given set of price changes.10

The effective percentage change in A’s price is computed as the difference between the given (or actual) change in A’s price and a weighted average of the other given price changes; the weight attaching to any one of these other price changes is proportional to the change in A’s trade balance that would be caused by a unit percentage change in that price, ceteris paribus.10 For example, the weights pertinent to the effective change in Italy’s price in 1966 are proportional to the values shown in Table 5, column A, and the weights themselves are given in Table 5, column B.

Table 5 shows that this manner of weighting does indeed yield the effective change in Italy’s price, as defined. Column E shows an arbitrarily chosen set of price changes, which, for purposes of this illustration, are supposed to have occurred in 1966. The change in Italy’s balance resulting from this set of price changes is computed from columns A and E and equals —$390 million (see bottom of table). The effective change in Italy’s price, computed from columns B and E, is 2.073 per cent, and if Italy’s price had changed by that amount (and if no other price changes had taken place), then Italy’s balance would have changed by —$390 million, as above. The table also shows that alternative weights, columns C and D, yield only rough approximations, i.e., 2.443 and 2.281, respectively, to the effective price change. Had Italy’s price changed by either of these amounts (and if no other price changes had taken place), the effect on Italy’s balance, i.e., —$459 million or —$429 million, would have been quite different from the — $390 million actually resulting from the given set of price changes.

Obtaining the proper weights does not require any computations additional to those involved in calculating change matrices like Table 2. The distribution in Table 5, column B, is identical to the distribution of the offset to a change in Italy’s balance, shown in Tables 2 and 3. More generally, the set of weights to be used in computing the effective change in A’s price is equivalent to the relative impact of a price change in A on other countries’ balances. This follows from a symmetry that is inherent in the simplifying assumptions: if A’s balance is, say, twice as sensitive to B’s price as to C’s, then a change in A’s price will have twice as much effect on B’s balance as on C’s balance.

V. The Role of Internal Trade

The figures for internal trade—the diagonal elements of Table 1—are subject to wide margins of error.11 Not only is there a lack of solid data (that is, data on gross dollar value of sales of manufactures, classified on a basis consistent with exports) but it is unclear what the coverage of the data should be in principle. Regarding the latter problem, it might be argued that a substantial portion of internal sales does not compete, or competes very little, with foreign supplies, and that therefore the diagonal elements of Table 1 are overstated. In this section the importance of these difficulties is evaluated by testing the sensitivity of some of the results to alternative assumptions about internal sales.

Table 6 shows the implications, for the distribution of the offset to a change in Italy’s balance, of four different assumptions. Assumption I, for purposes of comparison, is that internal sales are as shown in Table 1. Assumption II is that internal sales are such that the ratio of exports to total sales in manufacturing is the same as the ratio of total exports of goods and services to gross national product (GNP). The relevance of this assumption lies in the question whether some rough indicator of the general degree of openness of the economies would be adequate for present purposes. Assumption III is that internal sales are only half as large as shown in Table 1. This is roughly equivalent to assuming that, on average, manufactures sold at home are only half as substitutable for imports as imports from different sources are for each other. Assumption IV, finally, is that internal sales are zero. The relevance of this assumption lies in its frequent implicit use, as a simplifying device, in studies of how price changes affect exports. The assumption implies that

Table 6.

Sensitivity of Estimates to Alternative Assumptions About Internal Trade1

(In per cent)

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Sources: Tables 1, 9, and 10.

In each market σi is assumed to be 3 and ηi is assumed to be 1.

Assumption I: internal sales are as shown in Table 1.

Assumption II: internal sales are such that the ratio of exports to total sales in manufacturing is the same as the ratio of total exports of goods and services to GNP.

Assumption III: internal sales are half as large as shown in Table 1.

Assumption IV: internal sales are null.

(1) substitution takes place only between foreign supplies (and not between foreign and domestic supplies) in given markets;

(2) elasticities of demand for imports from particular sources depend on import shares, rather than on shares in total expenditure;

(3) elasticities of demand for total imports of manufactures are equal to elasticities of demand for manufactures-in-general, and, in particular, if ηi = 1, imports in value from all sources are unaffected by price changes.

Assumptions II and III yield results that are very similar to those previously obtained (Table 6). A comparison of I and II suggests that even a very crude indicator, such as the ratio of total exports to GNP, will suffice for most purposes as a basis for calculating internal sales of manufactures. Halving these sales makes a little difference here and there, but the differences seem hardly large enough to matter for practical purposes. Assumption IV, however—that internal sales are zero—yields widely differing results from the other three assumptions, as could be expected merely from the fact that, in this case, each country’s import total is fixed, and changes in balances stem solely from the export side. Unrealistic results are obtained when, by omitting the diagonal elements, the role of internal trade is ignored. On the other hand, if the diagonal elements are estimated in any reasonable fashion, a high degree of confidence can be placed in the results, at least as regards the effects of price changes on external trade.

VI. Sensitivity of Estimates to Alternative Assumptions About Substitution Elasticities

Up to this point all numerical examples have been based on the assumptions that substitution elasticities (σi) equal 3 in every market and that elasticities of demand for manufactures-in-general (ηi) equal 1 in every market. The latter assumption, at least, is probably not far from the facts; ηi is almost certainly small, and this alone restricts to the point of insignificance the range of probable error arising from inaccurate specification of this parameter. The substitution elasticities, on the other hand, are relatively large numbers and constitute an important source of possible error in the results.12

It may be important in some contexts that the relative effects of price changes—e.g., the distributions shown in Table 6—are largely independent of σi as long as this parameter is similar in all markets.13 Whereas one’s view about the “typical” value of σi will have an important influence on expected changes in the value of trade flows arising from a given price change, any distributional characteristics of these changes can be pinned down independently. Or, if the price change itself is determined by a trade target—e.g., the target of improving the trade balance by a given amount—all other absolute changes can be calculated without knowledge of σi (again, assuming it is similar in all markets).

Of course, if σi varies greatly from market to market in some unknown way, even the relative impact of price changes becomes difficult to guess. Table 7 shows some results of two alternative sets of arbitrary assumptions about σi labeled Set A and Set B. The assumptions are as follows:

Table 7.

Sensitivity of Estimates to Alternative Assumptions About Substitution Elasticities1

(In per cent)

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Sources: Tables 1, 9, and 10.

Internal trade is assumed to take the values shown in Table 1, and ηi is assumed to be 1 in each market.

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Naturally, the substitution elasticity assumed in any particular market tends to dominate the effect of a given price change on imports into that market. On the export side, however, the role of structural factors shows through relatively strongly, no matter what the elasticities are. The impact of a given price change on a country’s exports will be greater, the more that country’s exports are concentrated in markets in which substitution elasticities are high, and vice versa,14 but for most countries strong correlations of this kind are not probable.

The general conclusion to be drawn from Table 7 would seem to be that the information implicit in the base-period matrix is not sufficient to yield results—even about the relative impact of price changes—in which a high degree of confidence can be placed. It remains essential to employ substitution elasticities that are supported by the historical record. Nevertheless, the role of trade structure is vitally important. Proper recognition of this role may provide the basis for more successful estimation and forecasting of price effects than has been possible in the past.

STATISTICAL APPENDIX

Table 8.

Market Shares in Manufactures of the Selected Countries, 1966

(In per cent)

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Source: Table 1.
Table 9.

Direct Price Elasticities of Demand, in Value, for Manufactures of the Selected Countries

(With σi = 3 and ηi = 1 in each market)

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Sources: Elasticity formula (1) and Table 8.
Table 10.

Cross Price Elasticities of Demand, in Value, for Manufactures of the Selected Countries

(With σi = 3 and ηi = 1 in each market)

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Sources: Elasticity formula (2) and Table 8.

Structure géographique des échanges et incidences des variations de prix

Résumé

La répartition par destination et par origine des exportations et des importations d’un pays diffère considérablement des répartitions correspondantes de nombreux autres pays. Ces différences, ainsi que celles ayant trait à l’importance du commerce total exercent une influence considérable sur la manière dont les courants commerciaux réagissent aux variations de prix. Supposons que la balance commerciale de A se dégrade par suite d’une augmentation du niveau des prix de A; la mesure dans laquelle B profitera de l’amélioration compensatrice de la balance commerciale collective des autres pays dépendra naturellement, en partie, de l’importance relative du commerce total de B; mais elle sera également fonction de variables telles que: l’importance des produits de A dans les importations de B, l’importance que représentent les importations de B par rapport au total de ses dépenses, et enfin la mesure dans laquelle les exportations de B sont à la merci de marchés où l’offre est largement assurée par A (marché A y compris). Ces variables structurales représentent des rapports entre les courants commerciaux. Cet article montre comment utiliser toutes les données relatives à la structure du commerce afin d’effectuer les meilleures prévisions possibles des incidences des variations de prix, en prenant comme point de départ une série rangée de prévisions plausibles concernant l’élasticité de substitution en fonction des prix sur les différents marchés. Cette méthode est supérieure à la pratique actuelle à deux égards: tout d’abord, parce qu’elle dorme toute l’importance voulue aux rapports structuraux que l’on néglige dans les méthodes qui ne tiennent compte que du commerce total de chaque pays ou de la répartition du commerce de A (qui enregistre des variations de prix), et ensuite parce que l’on considère que la substitution des importations par des produits de remplacement influe non seulement sur les importations de A mais aussi sur la totalité des importations de tous les autres pays, et le calcul des modifications des exportations de chaque pays traduit toutes les variations du total des importations aussi bien que celles de la part de chaque pays.

Estructura geográfica del comercio y efectos de la variación de los precios

Resumen

La estructura que presenta el comercio de exportación e importación de cualquier país, según su destino y origen, difiere considerablemente de la de muchos otros países. Estas diferencias, así como las que muestra la magnitud del comercio global, ejercen una influencia importante en la forma en que las corrientes comerciales reaccionan ante las variaciones de los precios. Por ejemplo, si la situación de la balanza comercial del país A empeora debido a que el nivel de los precios en ese país experimenta un alza, la participación que le corresponda al país B en la mejora resultante en la balanza comercial colectiva de otros países dependerá en parte, naturalmente, de la magnitud relativa del comercio total de B; pero también dependerá de variables tales como la importancia que los productos de A tengan para las importaciones de B, del monto que corresponda a las importaciones de B en el total de sus gastos, y del grado en que las exportaciones de B dependan de mercados que se abastecen de modo considerable de productos provenientes de A (incluido el propio mercado de A). Estas variables estructurales constituyen coeficientes de las corrientes comerciales. En el presente trabajo se expone un método mediante el cual se pueden utilizar todos estos datos relativos a la estructura del comercio, a fin de calcular con la mayor exactitud posible los efectos que producen las variaciones de los precios, en caso de que se cuente con una serie más o menos adecuada de estimaciones de las elasticidades de sustitución en función de los precios en los diversos mercados. Este método es mejor que el que se usa actualmente, en dos aspectos: en primer lugar, atribuye la importancia apropiada a aquellas relaciones estructurales que no se tienen en consideración en los procedimientos que solamente se circunscriben al comercio total de cada país o a la estructura del comercio del país cuyo nivel de precios varía (en este caso, el país A). Segundo, se reconoce que la substitución que se lleva a cabo entre los productos de importación y los que compiten con ellos es un factor que influye no solamente en las importaciones de A sino también en las importaciones totales de cada uno de los demás países, y las variaciones que muestran los cálculos de las exportaciones de cada país son reflejo de todas estas variaciones que muestran las importaciones totales así como de los cambios referentes a la participación en las importaciones.

*

Mr. Armington, economist in the Current Studies Division of the Research Department, is a graduate of Swarthmore College and the University of California at Berkeley. Before joining the Fund in 1965, he was a Research Fellow in Economics at the Brookings Institution.

1

This paper represents an application of the material presented in the author’s “A Theory of Demand for Products Distinguished by Place of Production,” in Staff Papers, Vol. XVI (1969), pp. 159–78. At various points in the present paper, the reader is referred to the earlier one as a source of certain derivations and proofs, but these are not necessary to a general understanding of what follows.

2

The selected industrial countries are Belgium-Luxembourg, Canada, France, Germany, Italy, Japan, Netherlands, Sweden, United Kingdom, and United States. The geographic breakdown used in this paper, while adequate and convenient for illustrative purposes, may prove to be less than satisfactory for purposes of practical application, since a large share of the impact of price changes is found to fall on the residual, “Rest of the World.” An expansion of the calculation, involving data for more individual countries, is under study.

3

See Armington, op. cit., pp. 169–70 and 174–75. Formulae analogous to these have a long history in the literature on price theory and have been derived and applied in the context of trade models by Professor P. J. Verdoorn. See Armington, op. cit., p. 170, fn. 21.

4

The role of internal trade, including statistical and conceptual difficulties in measuring it, is discussed on pages 193–94 and in Table 1, footnote 3, page 185.

5

Since the trade matrix relates to 1966, the hypothetical price changes to be considered take place at that time. Similarly, estimating the effects of prospective price changes would involve forecasting the matrix for the future period.

6

Of course, a change in the Italian price level might well have caused other price levels to change, in amounts determined both by all the demand elasticities and all the supply elasticities. Thus, Table 2 may not describe the ultimate reaction of the trade pattern to the initial change assumed. The method of calculating the effects of simultaneous changes in price levels is described in the following section.

7

These results depend substantially on the degree of openness of each economy. Both for Italy and for the other countries, internal sales change less in per cent than external sales, so that, other things being equal, a high ratio of exports to total sales is associated with a large percentage change in total sales.

8

As long as a country’s total expenditure on manufactures is unaffected by price changes (which is implied by ηi = 1), percentage changes in any trade flow depend solely on percentage changes in ratios of prices of manufactures. (This is a property of the demand functions on which the elasticity formulae are based.) A given percentage change in one country’s price affects all price ratios in the same proportion as an equal and opposite change in prices in all other countries. Therefore, the effects must be the same.

9

A general proof of this proposition can be obtained by total differentiation of the basic demand model, from which it is seen that the percentage change in any flow can be written as an additive function of percentage changes in prices (the coefficients depending on market shares). See “A Theory of Demand for Products Distinguished by Place of Production” (cited in footnote 1), pp. 168–70.

10

If the variable to be explained is exports (or imports) only, read exports (or imports) in place of trade balance in this sentence.

11

See Table 1, footnote 3, page 185.

12

The specification of ηi, unlike that of σi may in practice be guided as much by the need for simplicity as by a concern for accuracy within narrow limits. The assumption that ηi = 1 may be viewed simply as the logical basis for treating trade in manufactures, in value, as if it were a closed system, unaffected by changes in the price level of manufactures-in-general.

13

Suppose that the substitution elasticity is assumed to be the same in all markets and that this assumed value, σ, is altered in such a way that the new value is K times the original value. Then if ηi is assumed to be 1 in every market, all cells of the original change matrix (such as Table 2) are multiplied by the constant Kσ-1σ-1 (as can be shown with reference to the elasticity formulae on page 181). For example, if the assumed value of σ is changed from 3 to 2, then K = 2/3, and the original change matrix is simply multiplied by the scalar 1/2. Thus, all possible relative magnitudes in the original change matrix are preserved as σ is varied. The assumed level of σ might be made to depend on a variety of considerations, including the time allowed for price effects to work themselves out and the size of the assumed price change itself.

14

See, for example, the relatively large change in Japan’s exports if σi = Set A; this reflects the high substitution elasticity assumed for the United States and the Rest of the World, which are relatively important markets for Japan.

Same Series

Other IMF Content

Other Publishers

Cover IMF Staff Papers
IMF Staff papers: Volume 16 No. 2
Author: International Monetary Fund. Research Dept.
Volume/Issue:
Volume 1969: Issue 002
Publisher:
International Monetary Fund
ISBN:
9781451947298
ISSN:
1020-7635
Pages:
218
DOI:
https://doi.org/10.5089/9781451947298.024
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    Ratios of Imports to Total Purchases and of Exports to Total Sales

    (In per cent)

Ratios of Imports to Total Purchases and of Exports to Total Sales

(In per cent)