The study of a number of important questions arising in international economics, particularly in connection with the design of national policies or international cooperative action with respect to the balance of payments, exchange rates, tariffs, and foreign aid, would be greatly aided by a reasonably complete analytical framework in quantitative terms expressing the interrelationships between national economic magnitudes such as measures of economic activity and prices, on the one hand, and the balance of payments and its components, as well as exchange rates and other determinants of international price relations, on the other hand. Such a model of the world economy would be useful for the following purposes:


The study of a number of important questions arising in international economics, particularly in connection with the design of national policies or international cooperative action with respect to the balance of payments, exchange rates, tariffs, and foreign aid, would be greatly aided by a reasonably complete analytical framework in quantitative terms expressing the interrelationships between national economic magnitudes such as measures of economic activity and prices, on the one hand, and the balance of payments and its components, as well as exchange rates and other determinants of international price relations, on the other hand. Such a model of the world economy would be useful for the following purposes:

I. Introduction

The study of a number of important questions arising in international economics, particularly in connection with the design of national policies or international cooperative action with respect to the balance of payments, exchange rates, tariffs, and foreign aid, would be greatly aided by a reasonably complete analytical framework in quantitative terms expressing the interrelationships between national economic magnitudes such as measures of economic activity and prices, on the one hand, and the balance of payments and its components, as well as exchange rates and other determinants of international price relations, on the other hand. Such a model of the world economy would be useful for the following purposes:

(1) Since national economies are interdependent, it would permit improvements in the forecasting of national economic magnitudes in individual countries;

(2) It would facilitate the forecasting of regional and global developments of trade, payments, and reserves;

(3) It would improve the analysis of a country’s alternative policies with respect to the balance of payments by making it possible to take account of the feedback effects emanating from these policy actions as well as of trends in the rest of the world; and

(4) It would be useful for conducting analyses of the effects of international policies or international cooperative measures such as reserve creation, changes in the mechanism of balance of payments adjustment, or changes in the magnitude and geographic distribution of foreign aid or the terms on which it is extended.

Up to the present, work of this nature had to be conducted by piecing together such quantitative information as is available, typically in the form of partial or complete national economic models for a number of countries, rudimentary trade models, and sporadic research on other balance of payments components such as capital movements. The national models in existence do not typically contain a full articulation of the external relations of the economy in question, while the trade models lack an adequate representation of the national economies whose trade is to be studied. It is the purpose of the present international research project conducted under the auspices of the Social Science Research Council (Project LINK) to link together national economic models that are now available, and some that may be constructed in the future, in such a way as to achieve eventually a world economic model capable of exhibiting in sufficient detail the various relationships and interconnections between domestic economic magnitudes, national economic policies, trade and payments flows, and cooperative international action.

National models could, in principle, be linked either directly or indirectly. Direct linkage would consist of an explanation of trade and financial flows from each of the countries to be linked to any other country in the group. The method of indirect linkage would entail construction of a model of trade and financial flows as a centerpiece of the complete world model and the linkage of each national model to this central trade and financial model. There are a number of considerations, some of economic substance and others relating purely to research strategy, that must be taken into account in the decision of whether to proceed by the method of direct or indirect linkage. Some of the technical considerations bearing on this decision will be reviewed in Section II below. Here it may be sufficient to point out that a world economic model that relies on direct linkage of national models would require such a high degree of detailed attention to external economic relations in each of these models that it would be difficult to preserve a reasonable balance between the domestic and foreign sectors of these models. For this reason, the indirect method of linkage recommends itself from the point of view of research strategy alone. Moreover, the construction of a world economic model must inevitably start with existing national models. Although these will have to be in any case adapted to some extent if any linkage is to be achieved, it is impracticable to require such far-reaching reconstruction of each national model as would be necessary for direct linkage.

This consideration would suggest that work on the project will have to proceed on two fronts: one of these is the construction of a central world trade and payments model to which the national models can be linked; the other is such adaptation of the national models as is necessary in order to provide the required connecting points to the central trade and payments model. The present paper deals mainly with the first of these two tasks, and only incidentally with the second.

Any world economic model resulting from linking national models together will inevitably have some of the characteristics of these national models. In particular, since the national models that are to be connected are, on the whole, constructed so as to explain short-run variations in aggregate economic magnitudes such as economic activity, employment, and over-all price levels, the resulting world economic model will be best suited to explain short-term variations in trade and financial flows and the relationships between these flows and the policies conducted in the various countries with respect to the adjustment of demand and economic activity in the short run. To be sure, the line of demarcation between short-term and long-term models is not hard and fast. But it is clear that there are limits to the use of models, for purposes of forecasting or policy analysis, imposed by the essential characteristics that have been built into them. The existing models do not, on the whole, contain relationships designed to explain longer-term changes in the underlying economic structure. The world economic model resulting from the linkage of these national models cannot, therefore, be expected to be very helpful in connection with any analysis of long-term changes in the world economy such as movements in comparative advantage or trends in the terms of trade. It may, nevertheless, be true that the experience that will be gained from linkage of national models in general may at some future time facilitate a project in which long-run developmental models may be linked together, if and when these become generally available for many countries.

II. Basic Approaches to Model Linkage

Before choosing the structure of a world economic model that could be regarded as practicable and promising in the light of the conceptual and data problems that have to be faced in undertaking this task and in view of the aims of such a model (as stated in Section I), one may wish to consider the basic choices that are open. Each of the basic approaches has, of course, many variants and is capable of refinement. In this section it is intended to present only the essential features of each approach. 2

The “consistency approach

A kind of model linkage, although a rather minimal and somewhat unambitious one, could be achieved by designing a procedure that ensures consistency of national forecasts of imports and exports made in the various countries whose models are to be linked. This could be called the “consistency approach.”

Imports are forecast in each country mainly with the help of domestic variables that are themselves forecast on the basis of policy parameters and other exogenous factors about which information or estimates are available to the national forecasters. By contrast, exports—which are the imports of other countries—would logically have to be forecast mainly on the basis of variables and policy parameters of other countries, with respect to which information is typically not, or not as readily, available to the national forecasters. This has two consequences: First, national export forecasts are often based on the relation of a country’s exports to world exports or to some weighted average of economic activity in the economies of a country’s trading partners, which must themselves be forecast by each national agency on the basis of such more or less ad hoc information as may be available to it at the time of making the forecast. Such forecasts of world exports will not necessarily be consistent with the import forecasts made by agencies in other countries, and any forecasts made in a particular country of economic activity in other countries will not necessarily be consistent with the forecasts made by the national agencies of these other countries. Second, since error is introduced in this manner into the forecasts of a country’s exports, its own forecasts of national income or other economic activity variables will also be impaired. For these reasons, the outcome is typically one where the sum of national import forecasts is at variance with the corresponding sum of national export forecasts. When these forecasts are summed over all countries of the world, this amounts to a simple case of inconsistency. When they are summed for a certain group of countries, as is true of the semiannual collection of trade forecasts by the Organization for Economic Cooperation and Development (OECD), the discrepancy between the sum of forecast imports and the sum of forecast exports implies a corresponding export surplus or import surplus of this group of countries with the world outside the group.

If consistency is aimed at in such an exercise, it would be necessary to revise the first-round forecasts made by national agencies after the extent of the inconsistency has been assessed. For instance, the OECD Secretariat checks the difference between the sum of exports and the sum of imports forecast by the national agencies against a reasonable estimate of the global trade deficit of the non-OECD countries vis-à-vis the OECD countries, derived in part from past trends and in part from an estimate of the availability of financing for such a trade deficit of the group of non-OECD countries through capital flows, foreign aid, and reserve movements. In the event of a discrepancy, the OECD Secretariat suggests revisions to the national export forecasts, taking into account market shares and expected competitive performance of the countries concerned. It is then up to the national forecasters, if they choose to do so, to accept these proposed revisions and to make corrections in their own forecasts of various economic activity variables that may be influenced by exports.

A formalization of this procedure would be a possible contribution that model linkage could make. National forecasts of imports could be summed for all countries and a suitable allowance made for imports of those countries where independent forecasts do not exist. These forecasts would be made on the basis of a first guess as to world exports—a variable affecting national estimates of exports and thus of economic activity. The sum of imports, after an appropriate adjustment to change the valuation from a c.i.f. to an f.o.b. basis, could then be used by national forecasters for revised estimates of national exports, economic activity, and imports. If, in this second round, the sum of imports yields an estimate of world exports that is quite different from the estimate found in the first round, it would be necessary to iterate the calculations in order finally to arrive at a sum of forecast imports that imply approximately the value of world exports that was used in the preceding round for the estimation of each country’s exports, economic activity, and imports. 3

The basic idea behind this procedure is simple. The only reason why it could be considered to deserve the name of a world trade model at all is that it would in any case be necessary to incorporate into the procedure a systematic way of estimating the imports of those countries that are not covered in the joint exercise, e.g., the non-OECD countries. A number of refinements could, however, be incorporated into this simple approach. It would be possible, for instance, to conduct the consistency exercise not only with respect to total merchandise trade but also by commodity groups in such a way that consistency is ensured for each commodity group. If this were done, it would, moreover, be possible to incorporate in the model a procedure for estimating commodity prices on the basis of estimates of demand on the part of the importing countries and of supply on the part of the exporting countries.

But, in spite of these possibilities for elaboration, this approach is essentially a rather limited one. It would neither require the establishment of a large research apparatus nor hold out much promise for policy analysis. It would be basically a marginal improvement in forecasting techniques achieved through international cooperation of forecasters. The principal reason for the limitation of this approach would be that it envisages no improvement in the usually very simple form of export equations used in national models. As soon as these export functions are improved so as to reflect a country’s shares in different markets and changes in these shares over time in response to various causative factors, a world model resulting from a linkage of the individual national models would closely resemble a world trade model based on the market-shares approach (see The structural approach, pp. 9–12) without, however, affording the same advantages of consistency among countries in the treatment of shares adjustment that could be achieved by an explicit global formulation in terms of market shares.

These considerations would appear to lead to the conclusion that the simple consistency approach could be useful at best as a starting point in the project to design a world trade and payments model. It would have the advantage of giving quick results of some usefulness, but it would be too limited in the scope of its application to be considered to be a worthwhile end product of a substantial research effort.

The bilateral approach

The general idea of direct linkage of national models discussed in Section I could best be implemented by what will here be called the “bilateral approach” to the construction of a world economic model. The basic features of this approach are most conveniently discussed in terms of a merchandise trade model.

After deciding on the countries to be included as participants in the exercise and dividing the remaining countries of the world economy into appropriate regional groups, each participant research institution would make provision in its national model for the estimation of imports from each of the countries or regions included in the trade model. These estimates, after being corrected for the c.i.f./f.o.b. difference and summed for each supplying country over all importing markets, would establish estimates of the exports of each country or region of the model. It would also be possible to follow a more truly bilateral procedure by inviting cooperation between the national research organizations to estimate by a joint effort the trade flow from each country to each trading partner as determined by various demand and supply factors agreed between the two respective organizations.

A mere statement of the procedure is already sufficient to convince one of its impracticability.

First, there is the problem of the large number of relationships. If there were 20 countries or regions in the model, the number of import functions to be estimated would be 380 (= 20 x 19) times the number of commodity groups desired, so that the total number of import functions to be estimated and processed in the model might be in the vicinity of 2,000 (assuming five commodity groups). If the number of countries increased to 30, the number of equations would more than double.

Second, with such a large number of relationships, which presumably would be estimated independently by different research groups, it would be difficult to achieve the consistency in the form of the functions, the data being used, etc., that would be required for central processing of the model.

Third—and more important than the two practical obstacles just mentioned, which conceivably could be overcome by diligence—the bilateral approach, if conducted on a grand scale, would inevitably do violence to what might be regarded as the proper economic specification of the desired model. This point deserves further elaboration.

Any model intended to explain the trade flows among a fairly large number of countries and regions must have strong microeconomic features, that is to say, it must be more nearly Walrasian than Keynesian. Neither traditional procedures in the construction of macroeconomic models nor the partial equilibrium models covering individual product markets found in econometric work in the area of agricultural economics are an adequate preparation for the task that one faces in the proper economic specification of a large, disaggregated trade model. One point is clear from the outset: a strictly macroeconomic approach to this essentially microeconomic problem must be inadequate.

Any specification of import functions for various commodity groups by country of origin that follows essentially the macroeconomic procedure of relating these imports to economic activity variables and to one or two relative-price variables would tend to ignore or obscure the competitive relationships between similar imports from alternative countries of origin. These competitive relationships manifest themselves, inter alia, in variations in prices charged by different suppliers, which cannot easily be represented in the bilateral import functions. Again, macro-economic changes in the importing country may impose over-all constraints on imports of all commodity classes and from all sources that cannot conveniently be built into the specifications of import functions explaining the imports from particular partner countries. Moreover, the imports of a particular commodity from a particular supplying country may be significantly affected by changes in supply conditions in that country, but these in turn may have resulted from changes in demand elsewhere for some other product exported by this supplying country. Even if prices fully reflected all these influences—in the manner in which this process is envisaged in the Walrasian system—the short length of time series, the unavailability of certain relevant data, and the essential clumsiness of econometric specification compared with the elegance of a proper theoretical formulation of the problem make econometric progress along these lines almost hopeless.

The practicability of building into a trade model the appropriate microeconomic features of this sort is, of course, a function of the size and degree of disaggregation of the model. In a small model, the difficulties are not insurmountable. For instance, in the Fund’s three-region world trade model, which explains total merchandise trade flows among the United States, Western Europe, and the rest of the world, the bilateral approach was used. 4 There are two separate import equations explaining imports of the United States from Western Europe and from the rest of the world, as well as two separate import equations explaining Western Europe’s imports from the United States and from the rest of the world. The bilateral approach is not fully carried through, since the rest of the world’s global imports are first explained by an over-all foreign exchange constraint and then divided as between goods bought from the United States and goods bought from Western Europe in accordance with an equation containing as an explanatory variable the ratio of export prices of the United States to those of Western Europe.

In this model, the relative-price variable in each of the import functions of the two industrial regions is the ratio of export prices of the supplying region to domestic prices in the importing region. In principle it would have been possible to add in each of these import functions a second relative-price variable, namely, the ratio of export prices of the supplying region to those of the third region. For instance, U.S. imports from Western Europe could be made to depend not only on the ratio of Western Europe’s prices to those of the United States but also on the ratio of Western Europe’s prices to those of the rest of the world. If that had been done, then the full “microeconomic” structure would have been reflected in the model, at least as far as price effects are concerned. In fact, however, it was thought that the substitution in the U.S. market of products that could be bought from the rest of the world for products that were typically bought from Western Europe would not be high, and, similarly, that the substitutability in the European market of U.S. products for exports of the rest of the world would not be strong. Accordingly, price ratios that would reflect this sort of competitive effect as between supplying regions were not used in these import functions.

This simplification would not be legitimate in a model explaining trade flows among several industrial countries that compete in exporting manufactured goods. If the procedure appropriate in this instance were to be applied in a model with, say, 20 countries, one would end up with 19 price ratios in each bilateral import function—1 ratio for the relation between prices in the supplying country in question and domestic prices in the importing country and 18 price ratios to reflect the competitive relation between the supplying country in question and each of the other 18 supplying countries. In order to avoid such an excessive number of variables, one would have to compress the competitive price ratios into an index, perhaps by weighting the individual ratios by the shares of the various supplying countries in the global imports of the importing country. Once such a simplification is being introduced, one would be well on the way to making use of some of the essential features of the method of indirect linkage, which would be based on some sort of trade-shares approach, without, however, making use of all the advantages that such an approach would have to offer. If proper consideration is given to the other microeconomic relationships that affect the imports of a country from a particular partner country, such as the influence of various supply factors that may not in all instances find full reflection in relative prices, the option of the bilateral approach loses further in attractiveness.

What has been said about the disadvantages of the bilateral approach in connection with a trade model holds also for any possible extension of such a model to other balance of payments components, particularly capital movements. Some of the special problems that such an extension would pose are discussed in Section V.

The structural approach

The difficulties associated with the method of direct linkage through the bilateral approach described above can never be eliminated entirely. It is possible, however, to get around them to some extent by designing the model in such a way as to interpose a trade structure, which could initially be assumed to be fixed, between the theoretical Walrasian model and its (essentially macroeconomic) implementation. Methodologically speaking, the idea would be similar to that of using an input/output matrix with fixed coefficients in the analysis of problems that would actually require a full microeconomic supply-and-demand model of many producing and consuming sectors. In contrast to some problems solved with the help of input/output matrices, however, the assumption of fixed coefficients—i.e., fixed trade shares—could only be an initial working hypothesis and would have to be relaxed at an early stage. This approach, which is here named the “structural approach,” may be the most promising type of implementation of the idea of indirect linkage.

The basic features of the structural approach can best be discussed in connection with a model of merchandise trade, although modified versions of such a model might eventually also be applied to service transactions and capital movements.

The first step consists of the estimation of global import functions for each country or region, that is, of equations explaining imports—either in total or by commodity group—from all countries. For the second step, it would be assumed initially that the distribution of a country’s imports by country of origin tends to remain constant. Distribution of each country’s imports in accordance with the estimate of shares of supplying countries would then yield an estimate of each supplying country’s exports to each market. For each exporting country, summation over all markets of its exports to each market provides an estimate of its total exports. It should be noted that this method does not require estimation of an export function for each country. Indeed such export equations would be redundant. By the same token, no use would be made of variables expressing total world exports or world imports, although such totals may be derived from the solution of the model.

There are three major problems with this approach, although the first two are not unique to it.

First, any trade model that can be envisaged at the present time would not incorporate all countries of the world economy as individual sectors. There would be some countries that have to be collected into a category of “rest of the world,” and there may be some other countries grouped into regions for which it might not be practicable to estimate import functions of the traditional type. It is therefore necessary to design an appropriate method for closing such a geographically incomplete model. This problem will be further discussed in Section IV.

Second, there is a problem with respect to the valuation of trade flows. For most countries, imports are recorded on a c.i.f. basis, while exports are valued f.o.b. Unfortunately, the cost of freight and insurance associated with each trade flow from one country to any partner country is not known. What is known in many—although not all—instances is the difference between a country’s recorded imports and the sum of the recorded exports of other countries to the country in question. This difference reflects to a large extent the cost of freight and insurance but to some extent also differences in timing of the recording of imports and exports, errors in the recording of trade flows by origin and destination, and other valuation discrepancies. On the assumption that the systematic part of this discrepancy does arise mainly from the difference in valuation bases (c.i.f. and f.o.b.), and the further assumption that the total cost of freight and insurance associated with a country’s imports are spread over its imports classified by origin in accordance with differences in the distance between the importing country and the country of origin, it is possible to estimate a matrix of freight and insurance cost that can be used to translate the c.i.f. imports estimated for each market into f.o.b. exports associated with each supplying country. Once the required translation from c.i.f. imports to f.o.b. exports has been made, the problem of a possible inconsistency between the world totals of imports and exports is automatically solved in this type of model: apart from this valuation difference, the two totals are necessarily equal.

Third, there is the problem of estimating the trade-shares matrix, which is the centerpiece of the model. As had already been mentioned, it would not be appropriate to proceed on the assumption that the shares matrix remains constant. To do so would not only result in inaccurate forecasts but also severely limit a number of important types of policy analysis that one would hope to be able to conduct with the help of such a model. Changes in trade shares presumably reflect to some extent changes in competitive relations influenced by relative prices or other factors of international competitiveness. A constant-shares matrix would be appropriate only in a model that did not include price influences at all. Such a model could not be used, for instance, for the analysis of effects on trade flows of changes in exchange rates, border taxes, tariffs, domestic prices, or the degree of demand pressure.

Methods must, therefore, be found for modifying the trade-shares matrix from some initial set of values (e.g., average shares during a recent period) in correspondence to relative-price changes and other factors that may be thought to influence these shares. Ideally, this process of share modification should reflect the main features of the Walrasian process which gives rise to changes in trade shares. This means that the process of estimating the shares matrix, which would involve the taking into account of all the influences on the supply side that may induce changes in shares, would proceed jointly with the estimation of export prices of each supplying country. This topic will be further discussed in Section IV; a method suggesting a solution to the problem is contained in the Appendix to this paper.

Several possible trade models designed in accordance with the structural approach are outlined in Section IV. Extensions of such models to cover payments and receipts for services and capital flows are discussed in Section V.

A mixed approach?

There can be no doubt that it will not be possible in the course of constructing a complete world economic model to follow in all instances what might be considered the optimal approach, or even a uniform approach, to the solution of particular problems of model construction. It may be necessary, for instance, to combine an explanation of real imports for some countries with an explanation of nominal imports for others, or to mix approaches that are possible where a complete record of transactions by origin and destination exists, as in merchandise trade, with approaches that must be chosen where such complete records do not exist, as in service transactions or capital flows. In some instances it may be advisable to adopt a mixture of approaches, not because this is imposed by the character of the available data but because a mixture of principles is appropriate to the nature of the relationships that are to be approximated.

In particular, the question has been raised whether it might be beneficial to combine the bilateral approach with the structural approach. Such a combination could take the form of estimating imports into a particular country from certain important major trading partners—thus following to that extent the bilateral method—and estimating the remainder of imports as a separate function, which would then yield the input to a shares calculation in which the exports of the members of this residual group would be calculated.

It is no doubt possible to obtain satisfactory estimates of imports from certain partner countries whose shares in a country’s foreign purchases are large. For instance, it would be possible to estimate separately U.S. imports from Canada, or Canadian imports from the United States, and obtain a satisfactory statistical explanation, perhaps a better one than can be achieved by estimating these trade flows in the course of calculations following the market-shares approach. Such a combination of approaches would, nevertheless, entail considerable difficulties. First, for different importing countries the bilateral flows that it might be appropriate to estimate separately would cover different partner countries. For the United States, imports from Canada and Japan might be bilaterally estimated, but for the Netherlands, those from Germany and the United Kingdom might be so treated. The random removal of trade flows from the global shares approach would make a systematic coverage of the remainder of trade by this approach almost impossible, especially if the aim is to modify the shares matrices in the manner that has been discussed above. Moreover, the proper specification of the separately estimated bilateral flows would still remain problematical, even though a good statistical fit may be obtained. There is no escape from the fact that the variables traditionally found in import functions influence global imports but do not typically affect the distribution of imports by country of origin.

For these reasons, it would on the whole seem inadvisable to plan from the outset for a mixing of approaches. However, when allowance must be made for special circumstances affecting particular cells in the matrix of trade flows—for instance, the U.S.-Canadian automotive agreement—it may be necessary to correct such cells in accordance with information derived from a study of the bilateral trade flows in question. This could be done within the framework of the shares approach by changing the affected shares and making such offsetting changes elsewhere in the shares matrix as are necessary to preserve its consistency.

III. Data Framework

The purpose of this section is not to give a complete survey of the data needed for the world economic model, but rather to discuss certain limitations that the availability of such data will inevitably impose. This question must be raised before it is possible to propose the structure of the model in any detail, because absence of certain data will force the adoption of compromises in the construction of the model.

It may be taken for granted that for the industrial countries, which are to be included separately in the model, all the national economic vairables that it may be desirable to use in estimating import functions are available. The same is true for import data in any desired commodity detail according to the Standard International Trade Classification, at any rate in value terms.

At some cost, which may not be inconsiderable, it would also be possible to construct certain volume and unit value series of imports from the published trade statistics, where such series do not yet exist.

However, a complete coverage of global imports by commodity group in volume terms could not be achieved from internationally published series, although there may be national compilations giving volume series by major commodity groups in some instances. As regards internationally published data, volume series are available only for those subclasses for which unambiguous volume units, such as tons, can be used to measure the volume of trade.

With respect to imports of developing countries, there would be no difficulty in obtaining total imports for all these countries together or certain groups of countries in value terms and, to a limited extent, data series for the value of imports of certain broad commodity groups. Some of the published data for nonreporting countries are derived from reports by partner countries, and this technique could be used in other instances as well. Data on trade among developing countries may be available only for totals of all commodities and in value terms.

Again, the trade flows data necessary to construct shares matrices would generally be available for matrices whose rows and columns corresponded to the industrial countries, or all developed countries (a group of 25 countries consisting of 14 industrial countries and 11 “other developed countries”) and a residual sector of the rest of the world derived from global totals after subtracting the trade with the individual developed countries. For the value of total trade a further division of the rest-of-the-world sector into individual countries or groups of countries can be achieved for approximately the last 10 years from the Fund and World Bank’s publication, Direction of Trade. For shares matrices by commodity group and any such matrices, whether for total trade or for trade by commodity group, that are to be cast in volume terms, no geographic classification of the world outside the developed countries is likely to be obtainable. To be sure, detailed commodity trade statistics by country are maintained in the Statistical Office of the United Nations. But, unfortunately, these data are arranged on some 1,500 magnetic tapes in such a way that processing would involve a major effort as well as a major expenditure. For this reason some data, although they are recorded, must be judged to be effectively unavailable for purposes of model construction at this time.

This means, in practice, that data problems impose few limitations as regards the implementation of the structural approach to model construction for a model in terms of trade values covering essentially the major industrial countries and a residual sector for the rest of the world. Even for this geographic configuration, there would be difficulty in the attempt to cast the model in volume terms and in the derivation of the requisite unit value data. Severe limitations have to be faced as regards the availability of volume and price series or commodity disaggregation whenever a general geographical disaggregation of the sector of developing countries is attempted. A structural model distinguishing major geographic areas of the developing world might at present be feasible only if constructed in terms of the value of total trade.

Data for balance of payments components other than merchandise trade are generally available only in terms of global totals. There are only a few countries (e.g., the United States) that publish or compile some limited geographical distribution of such balance of payments components. Some years ago a pioneering study on the geographical distribution of balance of payments components other than merchandise trade was undertaken by Herbert Woolley in a volume published by the National Bureau of Economic Research. 5 The basic study covers the years 1950–54, but there was some extension of the work up to 1958. Here one would be faced with a situation like that in which researchers desiring to study the structure of the economy with the help of input/output methods found themselves when, until fairly recently, the only input/output matrix in existence for the United States was that for the year 1947. In the area of foreign transactions, and particularly capital flows, it is of course much less reasonable to rely on any constancy over time in geographical distribution of transactions. It is likely, therefore, that in any extension of the model to items other than merchandise trade quite novel methods and procedures will have to be devised in order to make progress.

There is one other question that may be disposed of in this context, namely, that of annual versus quarterly data. Most of the trade data described above as being more or less readily available are published in quarterly as well as annual form. Indeed in many instances monthly data are available. However, the magnitude of the data collection problem would increase considerably if quarterly data were desired. The increase is not merely by a factor of 4, since in many instances the quarterly or monthly data must be painfully pieced together from material that is often published in rather inconvenient form. For this reason alone—although there are others—it may be advisable to proceed initially with an annual model and to postpone work based on a shorter unit period until a later stage in the project.

There would in any case remain the question as to whether it might not be sufficient, if a period shorter than one year is to be chosen as the unit period, to select half-yearly data rather than quarterly data. A half-yearly unit period would conform well to the forecasting efforts now made in most industrial countries and collected by the OECD. It would also be sufficient for the study of cyclical and other short-term variations of trade, while at the same time minimizing the problem of seasonal variations.

IV. Design of Various Trade Structure Models

In this section a number of possible trade structure models are outlined, beginning with a simple model set up in terms of the value of total trade, proceeding to one that is disaggregated by commodities, and finally coming to problems associated with a statement of the model in terms of trade volumes and prices.

A value-of-total-trade model

Data availability does not impose any limitations on the geographical disaggregation in a trade model cast in terms of the value of total merchandise trade. In particular, it would be possible to form any desired grouping of developing countries on the basis of geographical or other considerations.

As a matter of simplification, it may be assumed initially that trade prices, although they could depend on domestic variables in the exporting countries, are exogenous from the point of view of the trade model. For each country or region, i, there would be an import function, explaning the value of imports, of the following form:



  • m = c.i.f. value of total merchandise imports,

  • x = f.o.b. value of total merchandise exports,

  • β = proportion of exports spent on imports (directly, or indirectly through the multiplier process), and

  • μ = imports not induced by exports.

What is essential in this formulation is the separation of imports into a part x) that depends on current exports and a remainder (μ) that does not. Apart from this requirement, the functional form of μ could differ from country to country. For developed countries, it would typically contain, in addition to economic activity variables, a ratio of import prices to domestic prices. The domestic price variable in such a price ratio would be determined in the national model in question, while the price of imports could be represented by an index of export prices of partner countries weighted by their shares in the country’s imports. The form of the function does not impose any constraints on the manner in which the value of imports could be estimated: it may be derived as the product of separate estimates, or forecasts, of the volume and the average price of imports, or, again, it may be the sum of separately estimated import values for various commodity groups. For a developing region, imports may be estimated as depending, partly or entirely, on current and past gross foreign exchange earnings from exports and net capital inflows. 6 In this case, the part of imports that is induced by current export receipts would be contained in the term βx, and only the remainder in μ.

An estimate of the f.o.b. value of exports, x, of each country (or region) is obtained by summing over all markets the products of (ci.f.) imports into each market and the market share, aij, of exporting country i in market j, the latter adjusted by the multiplicative factor δij (which is, on average, in the vicinity of 0.9) indicating the scaling down of the trade flow from country i to market j necessary to change the valuation basis from c.i.f. to f.o.b. The export function of country i is thus


Indicating the adjustment of market shares for the f.o.b./c.i.f. ratio by an asterisk (a*ij=δijaij) and using matrix notation, the vectors of imports and exports of each country (m and x, written without subscripts) are related as follows:


where μ is the vector of imports not related to exports, B is a diagonal matrix containing the coefficients βi and A* is the matrix of adjusted market shares. The solution for imports and exports is found by calculating


where I stands for the identity matrix and the superscript — 1 signifies the operation of matrix inversion.

The sources of error in this model are discrepancies between actual and estimated values of (1) “autonomous” imports, μ, (2) export multipliers on imports, β, and (3) adjusted market shares, a*. Problems relating to the estimation of the shares matrix are discussed on pages 19–20. The question of estimation of μ and β are not discussed in this paper, since they relate to the adaptation of national models preparatory to linking them to the trade model to be constructed. It is worth emphasizing, however, that the procedure calls not for an estimate of total imports from the national models but rather for separate estimates of the coefficients (β) indicating the dependence of imports on exports (in the simplest case this could, for instance, be the traditional export multiplier times the marginal propensity to import) and of the value (μ) of imports that do not depend on exports.

It is clear that the assumption that trade prices are exogenous to the model and do not depend on trade is of doubtful validity. If it were to be relaxed, the simple method sketched here would not be adequate, since national forecasters could no longer take the export prices of partner countries, as forecast in the national models of these countries, as given inputs for the purpose of estimating their own imports. (See pp. 20–21.)

A value-of-trade-by-commodity model

The extension of the model to cover trade by commodity class requires a change in the import function, since imports of any commodity will depend on exports of all commodities. This is so whether imports are affected by exports through the multiplier process or through the constraint of gross foreign exchange earnings. If there are s commodities, the import function for commodity k would be written


There is no change in the basic form of the export function


where a*ij,k is the share of country i in the imports of commodity k by market j, adjusted for the f.o.b./c.i.f. factor, δij,k, applicable to this trade flow.

The solution for imports and exports of each commodity depends on the solution for every other commodity, and a simultaneous solution for imports and exports of all commodity classes would have to be applied.

There remains the question of how many commodity classes to distinguish. It is safe to say that, provided the essential relations and constraints in terms of total trade are preserved, any separation of trade by commodity class would be better than none, but it is difficult to foresee what the optimum separation would be. In earlier discussion it was proposed to use four commodity classes in accordance with the Standard International Trade Classification (SITC):

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This degree of separation may have to be accepted for the near future, since any finer classification would impose an undue burden of data collection and processing on the project.

The next step in the direction of refining the commodity classification, in order to be meaningful, would substantially increase the number of classes. For instance, a proper treatment of manufactures alone might have to distinguish about a dozen types of manufactured goods, not merely for the purpose of achieving sufficient product homogeneity within each class but also in order to remove from the subclasses certain categories to which special considerations apply or that are subject to quantitative controls, such as textiles, automobiles, aircraft, ships, and certain agricultural commodities.

Forecasting the shares matrix

The most severe limitation on the applications of a market-shares model results from the assumption of constant shares. This assumption can be relaxed, short of specifying a complete demand-and-supply model, by allowing market shares to be modified by changes in relative prices that are considered to be exogenous to the trade model.

Two procedures are possible: Elasticities of substitution, for each commodity class included in the model, may be computed from regression analysis with pooled time-series and cross-section data for all exporting countries and all markets, 7 and these substitution elasticities together with the exogenous changes in export prices can then be used to compute the price-induced changes in market shares in the forecast period compared with the shares in a historical period. Alternately, elasticities of substitution may be calculated separately for each market, or for subgroups of markets with presumed common characteristics, and these elasticities may then be used to modify the shares in each market.

Export prices are not the only factors affecting market shares. They may also be influenced by (1) shifts in the commodity composition of demand in the various importing countries and (2) by supply influences in exporting countries that do not find expression in relative prices. As regards the factor mentioned in (1), the only remedy lies in refinement of the commodity classification used in the model. With respect to supply shifts under (2), the matter may be more difficult. First, there may be long-run changes in the relative supplying power of various producing countries at unchanged relative prices (constant returns to scale), which, in an essentially short-run analysis, may have to be expressed in the form of time trends in shares that are not otherwise explainable in the model (e.g., the rise in Japan’s market shares in manufactures). Second, there may be influences on export supplies of short-term variations in the degree of demand pressure that for various reasons are not reflected in relative supply prices. It may be possible to estimate share equations including both relative prices and relative demand pressure as explanatory variables; one could also follow the interesting suggestion by Mr. Siebrand of the Central Planning Bureau of the Netherlands 8 for a somewhat more systematic integration of both prices and demand pressure into the model. If this were done, the model would closely resemble the “ideal” model discussed next.

A complete demand-and-supply model

The ideal solution of the problem of the construction of a world trade model would call for an elaboration of the supply side of the model with the same care with which the demand side is ordinarily treated. Unfortunately, supply functions are more difficult to study than are demand functions, partly since their study requires in many instances a detailed knowledge of production processes and techniques for each commodity, as well as of patterns of interdependence in the production of various commodities. Because of these complications, econometric information about price elasticities of supply is almost completely absent.

Imagining for a moment that these difficulties could be overcome to some degree, one could envisage a model specifying for each country and each commodity a demand function and a supply function, both related inter alia to the price of the commodity (as well as to other prices). The solution of such a model would yield the quantities traded and the prices at which trade takes place. Such a solution could take the form suggested in the Appendix, which presents a demand-and-supply model developed for a particular purpose initially unrelated to the present project, but which could be adapted to the requirements of a complete world trade model.

If it were possible to make progress in research on supply functions, on long term as well as on short term, this would go far in making the model useful for longer-run analysis and projection.

V. Service Transactions and Capital Movements

In this brief section, included in this paper essentially for the sake of completeness, a short description is given of the difficulties that loom ahead when the model is to be extended to balance of payments categories other than merchandise trade.

One problem that both of the principal remaining categories, service transactions and capital movements, have in common is the almost complete absence of published information about transactions by origin and destination. In general, it would therefore not be possible, for these balance of payments components, to rely fully on the type of structural approach that was suggested for merchandise trade.

There may be some exceptions to this statement. For instance, receipts and payments for transportation services could be related to the trade flows with which they are associated. The geographic distribution of the entries on transportation account could be derived from the published (generally global) figures on payments and receipts and the c.i.f./f.o.b. differences found for the various trade flows. Again, some regional disaggregation of service accounts of some major countries are available and could, with the help of auxiliary data, be expanded into the full geographic detail desired. In some instances it may also be possible to obtain from national sources data that are compiled although not ordinarily published.

In the Fund’s three-region model mentioned on page 8, equations for four categories of service payments (demand for services) are estimated: (1) travel, (2) transportation, (3) income from investment, and (4) other private services; (“other government services” are taken to be exogenous). Estimation of these functions presented no particular difficulties, and reasonably good forecasting results have been achieved over the years. Logic, as well as experience with these functions, suggests, however, that these categories of transactions respond to quite different variables9 and should be kept apart.

For the purpose of integrating into the model private capital movements and those service categories for which a quasi-structural approach is impracticable, the only method open in the near future might be what was called in Section II the “consistency approach.” This means that national forecasts of global transactions, or of transactions by such geographic distribution as can be achieved from the national sources, would be collected and checked for consistency in the world totals. Any inconsistency discovered in this way would be eliminated by more or less ad hoc methods in the manner in which trade forecasts are now treated in the semiannual exercise of the OECD Secretariat.

As regards capital flows, the primary difficulty is not so much a lack of data as an absence of theoretical foundation that could be translated into testable hypotheses with respect to capital movements in a multiregional setting. Except for a small number of studies, chiefly on U.S. capital movements, econometric work in this area is not yet very far advanced, and the pioneering will have to be done to a large extent by individual research directed toward a better understanding of the determinants of the magnitude and direction of capital flows, rather than in connection with the present efforts to link existing models together.

Econometric study of the capital accounts of various countries’ balances of payments presents a number of special problems, which are not equally prominent in commodity trade, including that of the consistency of classification of transactions in the accounts of different transactors, the short unit period necessary for the proper study of the effects of interest rates on capital flows, the dominant role of expectations in the determination of some of the flows, and the presence of public controls. It may, therefore, never be possible in short-term forecasting of capital movements to come close to the quality, such as it is, that can now be achieved in forecasting trade flows. It could be, however, that longer-run analysis of capital flows, which may be less subject to the difficulties just mentioned, may eventually prove more amenable to quantitative work than short-run analysis seems to be.


A Many-Country Model of Equilibrating Adjustments in Prices and Spending

Paul S. Armington *,

The trade model outlined below is part of a study on the methodology of forecasting the effects of changes in exchange rates. This fact helps to explain the present form of the model. Certain features of the model, mainly the use made of data on the structure of trade, may prove to have more general application in a model designed to study the international interaction between prices, trade, incomes, and expenditures.

Main features of the model

Goods are assumed to be differentiated in use according to the country of production. Hence, if there were m goods and n countries, there would be mn different items of consumption, or “products,” each supplied by only one country. 10 As presently used, the model identifies n countries but only one good (i.e., n products); this one good may refer to merchandise-in-general, or (with appropriate alterations in elasticity parameters) it may refer to a particular class of merchandise, such as manufactures. 11

World demand for a product—that is, for the output of a single country—is related to each country’s total money expenditure on the good and to each country’s price. World demand here includes domestic demand, and the explanatory variables include domestic money expenditure and the domestic price, along with foreign prices and expenditures.

The variables are expressed as proportionate (or percentage) changes, and the coefficients of the price terms represent the partial direct and cross elasticities of world demand for a given country’s product with respect to the price level in each country. 12 These partial elasticities depend in a complicated way on the substitution elasticities in the various markets and on market shares. 13 Given n estimates of the substitution elasticities in the respective n markets, and given a full n-by-n matrix of trade in the good, the price coefficients are calculated by computer.

Apart from the effects of price changes, each country of origin is assumed to maintain its share, by value, in each market—that is, its share in the total spending, on the good, of each country of destination. 14 Hence, the coefficients of the expenditure terms in the demand equations are simply the market shares implicit in the initial n-by-n matrix.

For each world demand equation there is a corresponding supply equation, relating the ex ante supply of a product to its price level in the producing country. The n market-equilibrium equations, following the conventional procedure in comparative statics analysis, state that the initial excess demand for (or excess supply of) a country’s product is exactly offset by the effects of the equilibrating adjustments in prices and expenditures. 15

The 3n demand, supply, and market-equilibrium equations are matched by the 3n unknown changes in demands, supplies, and prices, leaving the n expenditure changes yet to be determined. It is assumed, broadly speaking, that changes in national expenditures (on the specified good) depend on national policies affecting the rate of saving. The model represents this assumption in two alternative ways. One way expresses the change in a country’s expenditure as the sum of an exogenous component and an endogenous component—the former relating implicitly to policy change, and the latter depending on the change in money income. Alternatively, the change in expenditure (on the good) can be expressed as the difference between the change in money income (derived from producing the product) and the change in the trade balance (in the good). In this instance the trade balance is taken to be a given target of national policy. In a particular solution of the model, trade targets may be adopted for some countries and not for others, depending on the information available and on the questions to be answered.

Given a set of imbalances arising from policy changes (such as changes in exchange rates), or given a set of exogenous expenditure changes or trade targets, the model is solved for the changes in prices and expenditures that will remove those imbalances. These equilibrating changes, in turn, can be fed into the same computer program that was used to calculate the elasticity coefficients in the demand equations (see above), and the output of this step is the final n-by-n matrix of trade or trade shares.

The equations

The demand equations can be written

  • Xj = initial world demand for the product of country j, in dollars; 16

  • X*j = proportionate change in Xj, i.e., ΔXj/Xj (the asterisk over a symbol will in general indicate proportionate change);

  • Di = initial expenditure of country i on the good, in dollars, and D*i its proportionate change;

  • Xji = initial demand of country i for the product of country j, in dollars;

  • P*i proportionate change in the price level of country i’s product; and

  • ηé = partial elasticity of world demand for j’s product with respect to a change in i’s price level. The direct elasticities are thus indicated by ηij 17, and the cross elasticities are indicated by ηij, i ≠ j.

The first term on the right-hand side of (1) is the average growth in markets (including the home market) for country j’s product. The second term measures the deviation of j’s sales from constant-shares sales in all markets combined, caused by the n price changes.

The supply relations are written simply

  • xj = initial supply of j’s product, in dollars, and x*j its proportionate change;

  • p*j = proportionate change in the price of j’s product owing to, or causally linked with, the change in output, x*j;

  • αj = elasticity of supply of f’s product in value terms, (αj- l) being the corresponding elasticity in volume terms;

  • p¯*j = proportionate change in the price of j’s product owing to factors other than output variation. This variable is given exogenously and can be viewed as a vertical shift factor in the supply function. 18


That is, the actual proportionate change in the price of j’s product is the sum of the endogenous and exogenous components.

The market equilibrium equations can then be written


On the left side of (4) is the initial excess demand for j’s product. On the right side are the changes in supply and demand, brought about by the equilibrating adjustments in prices and expenditures in each country, whose algebraic sum is an excess supply precisely equal to the initial excess demand. To these equations can be added


where DjD*¯j represents an exogenous change in spending on the good attributable to change in policy, and where mj is the proportion of the change in money income that is spent on the good; alternatively,


where ΔBj is a stipulated change in j’s balance of trade in the good.

In summary, there are 5n equations to determine the following 5n variables:


Méthodes possibles de construction d’un modèle du commerce et des paiements mondiaux


Cette étude a été préparée à l’occasion d’un projet international de recherche en vue de la construction d’un modèle du commerce mondial au moyen de la liaison des modèles économétriques existants et d’une représentation adéquate des économies des pays et régions pour lesquels de tels modèles n’existent pas encore. Dans l’examen des méthodes possibles, on a donné la préférence à la méthode qui consiste à lier indirectement les modèles nationaux en construisant un modèle central du commerce mondial auquel sont reliés les modèles nationaux et régionaux. Cette méthode permet d’éviter de nombreuses difficultés théoriques et pratiques, auxquelles on se heurterait si les modèles particuliers devaient être liés directement entre eux au moyen d’une détermination complète des relations bilatérales de commerce entre chaque modèle et chacun des autres. Selon la méthode de liaison indirecte, chaque modèle régional ou national contiendrait des fonctions d’importation pour un ensemble convenu de catégories de produits. Les importations calculées à partir de ces fonctions seraient intégrées au modèle central du commerce, qui consisterait principalement en une série de relations destinées à établir, pour chaque catégorie de produits, une matrice des parts de marché des pays exportateurs sur la base de parts antérieures, des variations des prix relatifs et de l’emploi de la capacité de production, peut-être aussi d’autres facteurs influant sur les parts de marché. Les importations de chaque région et ces matrices des parts de marché serviraient à calculer les exportations de chaque pays ou région du modèle. Après avoir passé en revue les données disponibles pour la construction de modèles de ce type, cette étude présente plusieurs exemples de modèles construits selon les grandes lignes de cette méthode générale. Les exemples vont d’une structure simple dans laquelle les importations sont censées n’être affectées que par l’activité économique et les parts de marché supposées constantes, à un modèle complet de l’offre et de la demande, dans lequel les prix et volumes des échanges seraient déterminés simultanément. En outre, il est fait brièvement allusion à certains des problèmes qui se poseraient si le modèle international devait être élargi pour couvrir, non seulement le commerce de marchandises, mais également les flux de services et de capitaux.

Posibles enfoques de un modelo de comercio y pagos mundiales


El presente trabajo se preparó en relación con un proyecto de estudio de alcance internacional al objeto de construir un modelo de comercio mundial mediante la vinculación de modelos econométricos existentes, teniendo adecuadamente en cuenta las economías de los países y regiones para los cuales todavía no existen modelos. En el estudio de los diversos enfoques posibles se da preferencia al método de vincular indirectamente los modelos nacionales mediante la construcción de un modelo central del comercio mundial al cual se conectan los modelos nacionales y regionales. Este método evitaría muchas de las dificultades de índole teórica y práctica que se presentarían en el caso de que cada uno de los modelos se vinculara directamente por medio de una especificación completa de las relaciones comerciales bilaterales entre cada modelo y cada uno de los demás modelos. De conformidad con el método indirecto de vinculación, cada modelo nacional o regional contendría funciones de importación relativas a una serie convenida de clases de productos. Las importaciones calculadas a partir de estas funciones se introducirían en el modelo central del comercio, el cual consistiría principalmente en un conjunto de relaciones concebidas con el fin de pronosticar, para cada clase de productos, una matriz de la participación correspondiente a cada país exportador en cada mercado, basándose en sus participaciones tradicionales, en las variaciones en los precios relativos, en las variaciones en la utilización de la capacidad productiva y, quizás, en otros factores que ejercen influencia en las participaciones en los mercados. Las importaciones de todas las regiones y estas matrices de las participaciones en los mercados servirían para calcular las exportaciones de cada país o región que figure en el modelo. En este estudio, después de analizarse los datos disponibles para la construcción de modelos de este tipo, se presentan varios ejemplos de modelos construidos conforme a los lineamientos de este método general. Los ejemplos varían desde una estructura sencilla, en la que se supone que las importaciones se ven afectadas únicamente por la actividad económica y que las participaciones en el mercado son constantes, hasta un modelo completo de demanda y oferta, en el que el volumen del comercio y los precios se determinarían simultáneamente. En el estudio también se hace alusión a algunos de los problemas que podrían presentarse en caso de que se ampliara el modelo internacional con el fin de que comprendiera no solamente el intercambio de mercancías sino también servicios y movimientos de capital.


Mr. Rhomberg, Assistant Director in the Research Department, is a graduate of the University of Vienna and of Yale University and has been a member of the faculty of the University of Connecticut and of Yale University. He has contributed chapters to several books on economic subjects and articles to economic journals.


A paper presented at the first annual working session of Project LINK, held September 16–20, 1969, in Hakone, Japan. Project LINK is an international research project with the purpose of constructing a world trade model through linking together existing econometric models and giving suitable representation to the economies of countries and regions for which models do not yet exist. At present, public and academic research organizations from eight countries and two international organizations are participating in the project, which is directed by Professor Lawrence R. Klein of the University of Pennsylvania.


For a survey of existing trade models, see Grant B. Taplin, “Models of World Trade,” Staff Papers, Vol. XIV (1967), pp. 433–55, especially the bibliography on pp. 452–53.


See also the approach to this problem chosen by F. G. Adams, H. Eguchi, and F. Meyer-zu-Schlochtern in Chapter VI of An Econometric Analysis of International Trade (OECD, January 1969), pp. 43–59.


Rudolf R. Rhomberg and Lorette Boissonneault, “Effects of Income and Price Changes on the US. Balance of Payments,” Staff Papers, Vol. XI (1964), pp. 59–124.


Herbert B. Woolley, Measuring Transactions Between World Areas, (Columbia University Press, 1966).


See Rudolf R. Rhomberg, “Transmission of Business Fluctuations from Developed to Developing Countries,” Staff Papers, Vol. XV (1968), pp. 1–29.


See, e.g., Helen B. Junz and Rudolf R. Rhomberg, “Prices and Export Performance of Industrial Countries, 1953–63,” Staff Papers, Vol. XII (1965), pp. 224–71, and Mordechai E. Kreinin, “Price Elasticities in International Trade,” The Review of Economics and Statistics, Vol. XLIX (1967), pp. 510–16.


J. C. Siebrand, “The Short-Term Impact of Pressure of Demand Fluctuations on International Trade” (a paper submitted to the meeting of the European Group of Project LINK in Paris on May 22, 1969).


For instance, in the Fund’s three-region world trade model, travel is related to consumption or gross national product (GNP), transportation to trade, investment income to the stock of foreign investments and rates of earnings, and other services to GNP.


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.


See Paul S. Armington, “A Theory of Demand for Products Distinguished by Place of Production,” Staff Papers, Vol. XVI (1969), pp. 159–78.


Extension of the model to cover any number of goods is under study.


The trade variables and the elasticities are expressed in value terms.


See Paul S. Armington, “The Geographic Pattern of Trade and the Effects of Price Changes,” Staff Papers, Vol. XVI (1969), pp. 179–201. Data similar to the elasticity coefficients used in the model are shown in Table 4 (p. 189) of that paper. Note that if the good identified in the model refers to merchandise-in-general, the parameter η, discussed in that article, is probably about unity. On the other hand, if the good refers to some subclass of merchandise, the model’s price coefficients may depend importantly on estimates of the price elasticities of demand for this subclass, as well as on the elasticities of substitution.


This assumption derives from the assumed linear homogeneity of the underlying behavior functions. See Armington, “A Theory of Demand for Products Distinguished by Place of Production” (cited in footnote 10), pp. 161 and 165–66.


Of course, the initial excess demand might be zero, in which case the corresponding market-equilibrium equation would ensure that this balance would not be disturbed by price-expenditure changes necessitated by initial imbalances elsewhere.


The word “initial” here and below refers to the situation of imbalance. The initial demands, supplies, and expenditures may not refer to observed values, therefore, but rather to ex ante values computed on ceteris paribus assumptions.


These direct elasticities, of course, are measured in value terms: that is, they are equal to the corresponding volume elasticities plus unity.


In the analysis of exchange rate changes, the exogenous price variable serves to incorporate factors such as monopolistic cost-price adjustments which are occasioned by the exchange rate changes but not related directly to the output-capacity-unemployment situation.