Models of World Trade1
Author: Grant B. Taplin

WORLD TRADE MODELS have been developed both because of the inherent interest in the flow of resources from country to country and as a remedy for the oversimplified treatment of the foreign sector in domestic models. In most domestic models, the foreign sector is treated either as autonomous and predetermined or as a function of domestic factors exclusively.2 The international economy, however, is a complex network of interrelated trade flows, capital movements, and payments settlements. It is a system in which domestically induced changes in one country’s income, prices, and other economic forces affect economic activity in other countries, which in turn transmit the changes on to each other and to the country of origin. These influences are especially important in the formulation of domestic policies and in the international coordination of national economic policies.


WORLD TRADE MODELS have been developed both because of the inherent interest in the flow of resources from country to country and as a remedy for the oversimplified treatment of the foreign sector in domestic models. In most domestic models, the foreign sector is treated either as autonomous and predetermined or as a function of domestic factors exclusively.2 The international economy, however, is a complex network of interrelated trade flows, capital movements, and payments settlements. It is a system in which domestically induced changes in one country’s income, prices, and other economic forces affect economic activity in other countries, which in turn transmit the changes on to each other and to the country of origin. These influences are especially important in the formulation of domestic policies and in the international coordination of national economic policies.

WORLD TRADE MODELS have been developed both because of the inherent interest in the flow of resources from country to country and as a remedy for the oversimplified treatment of the foreign sector in domestic models. In most domestic models, the foreign sector is treated either as autonomous and predetermined or as a function of domestic factors exclusively.2 The international economy, however, is a complex network of interrelated trade flows, capital movements, and payments settlements. It is a system in which domestically induced changes in one country’s income, prices, and other economic forces affect economic activity in other countries, which in turn transmit the changes on to each other and to the country of origin. These influences are especially important in the formulation of domestic policies and in the international coordination of national economic policies.

A number of models have been developed since World War II to analyze one aspect or another of the international economic system. This paper surveys models primarily concerned with trade flows, particularly those that seek to analyze the structure of world trade and those that attempt to trace the transmission of short-run fluctuations between countries. Work on these models, as on other empirical studies, has been aided by the emphasis on aggregative variables and the development of a theory of income determination stemming from Keynes’ General Theory; the evolution of econometric technique, which has recast and modified traditional statistical sampling and estimation theory; and the increased availability of high-speed computers, which has enabled researchers to handle larger and larger systems.

The remainder of the paper is divided into four parts. In the first section the concepts of a “model” and of an “import-export matrix” are presented. These are two tools used extensively in this paper. The section will also review the League of Nations’ Network of World Trade and the work of Woolley and Beckerman. This will lead to a discussion of models that study the structure of world trade by Tinbergen, Pöyhönen, Linnemann, and Waelbroeck. A third section focuses attention on the models of Metzler, Neisser-Modigliani, Polak, and Rhomberg. These models investigate the short-run transmission mechanism.3 Some suggestions for future work within the field are presented in the concluding section of the paper.

I. Models and a Trade Matrix

In general, a model, as the term is frequently used in economic analysis, is a set of one or more mathematical equations representing some part of the highly complex world. The equations may be behavioral (e.g., the consumption function), technological (e.g., the production function), or definitional. The equations show relations between a number of economic forces—called variables. The variables are of two kinds: exogenous variables are those determined outside the system or in a time period previous to the one under immediate consideration; and endogenous variables are those determined by the mechanism of the system itself.4 A model is said to be closed if there exists one and only one set of values (a solution) of the endogenous variables for each set of values of the exogenous variables. For a model to be closed, it is necessary to have the same number of equations as jointly dependent variables.5 When a model is not closed, there is not sufficient information to determine all the jointly dependent variables at the same time. Often an equation of a system contains more than one endogenous variable. The “reduced form” of the system is obtained by expressing each equation in terms of the predetermined variables only. The reduced form permits the solving for one dependent variable at a time.

Which variables are exogenous and which are endogenous in any model depends on the particular questions being studied. For example, a model used to study the effects of tariffs might differ from one used to trace the various forces affecting the U. S. balance of payments. In this survey each model will therefore be evaluated in the light of its ability to answer the questions assigned to it. Of course, implications of the model for answering other questions will be indicated.

The data for the past and present are used to quantify the relationship, permitting the measurement of the influence or impact of the various forces. When estimates or guesses of future exogenous variables are combined with quantitative estimates of the relationship, values for the future jointly dependent variables can be forecast. The ultimate goal of our work is to be able to forecast the level and the commodity composition of trade between any two regions.

An import-export matrix will help to point out the differences between the various models. Such a matrix has a row and a column for each of the countries or regions under consideration. Each row shows the exports of a country to other countries, and the sum of the entries in a row equals the country’s total exports. If the data have been reconciled so that both exports and imports are either f.o.b. or c.i.f.—e.g., so that the value of U. S. exports to Japan equals the value of Japanese imports from the United States—the entries in each column represent the imports of the country listed in the column heading, and the sum of the column entries equals its total imports.

In symbolic form, let aij be the flow of merchandise exports from country i to country j. The i and j can be countries or regions, provided the categories are mutually exclusive. The matrix then gives all flows of world trade. When we set the aii = 0, the i-th row represents all of country i’s exports, thus Ei=Σj=1naij. The j-th column represents the j-th country’s total imports, Mi=Σi=1naij. If all countries are included, total world imports equal total world exports, ΣMj=ΣEi=T=ΣiΣjaij. If trade is also disaggregated by commodities, there would be a similar matrix for each commodity group.

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The models to be discussed differ basically in the selection of flows to be studied and in the way the selected flows are approached. For example, on the one hand, Neisser-Modigliani and Polak have separate functions for total imports (Mj) and total exports (E<) of each country, but do not attempt to estimate the individual flows between countries (the aij’s). On the other hand, Rhomberg, Tinbergen, and Pöyhönen look at the individual flows (the aij’s) directly. There are also principal differences regarding the choice of determining variables, the method of closing the system, the nature of the relationship, and the level of disaggregation.

Several studies have shed a great deal of light on the international economic system by providing data to fill in the import-export matrix and by analyzing it without the use of mathematical equations, econometric estimation, and measurement of the influence of determining forces. We shall conclude this section by a review of several of these studies.

Perhaps the first important study to attempt to fill in the import-export matrix was the League’s Network of World Trade. Its purpose was “to describe the pattern of [the] network as it presented itself before the … war and to consider how far that pattern was determined by the natural distribution of resources and how far by other factors of a more ephemeral or less unalterable character.”6 To this end, import and export tables7 based on 17 major geographical units—the Soviet Union was omitted—were constructed using trade data for 1928, 1935, and 1938, expressed in constant exchange rates.

These tables permitted some measurement of the importance of industrial countries in international trade, suggesting that economic activity of these countries determines the trade of the nonindustrial countries. The tables also showed that trade in individual products is highly concentrated because of differences in natural resources. Furthermore, the study maintained that the smooth functioning of the international trade network is intimately tied to the operation of the financial markets. Some of the disruption of trade in the 1930’s, therefore, could be attributable to the financial crisis of 1931. Thus, this reconciliation and compilation of trade data by the League of Nations added important empirical content to theories of trade dating from Ricardo as well as to hypotheses concerning the changes in the multilateral trade system in the 1920’s and 1930’s.

More recently, Woolley has provided transactions matrices on payments for trade, services, and capital flows. He constructed from the accounts of 75 countries a set of matrices of international payments for each year 1950–54. There are matrices for merchandise trade, services, transfers both public and private, capital, gold, and settlements and errors. The construction of the tables required reconciliation of data recorded by payer and recipient. This enormous task, reflecting 10 years’ work, is a reservoir of world transaction information. Its usefulness is limited, however, until the record is extended to cover the more recent past. Then Woolley’s ultimate goal of employing this “record to test hypotheses about the behavior of the world economy”8 can be attempted.

Beckerman has approached the import-export matrix as an input-output system. In such a system the columns represent the origin of various inputs used by particular industries, and the rows represent the destination (or purchases) of the outputs. For each industry the ratios of inputs (expressed in a common unit) to its output give a set of technical coefficients which may be assumed to remain constant or evolve slowly through time. By relating a target output level to the matrix of technical coefficients, the demands for various inputs can be calculated.

For the import-export matrix, Beckerman calculates a set of ratios of country j’s imports from country i to country j’s total exports, in order to analyze how the pattern of world trade shifted from 1938 to 1953. It is clear that once these ratios are obtained they can be applied to calculate theoretical levels of trade, provided that the level of either total world trade or of one of the country flows is given.

This type of analysis is useful under certain circumstances. Its major asset is the ability to handle many countries or sectors. On the other hand, it has two distinct limitations. First, there is no theoretical reason why the ratios should remain constant or, indeed, why for many countries imports are strictly related to exports at all. Imports are related to exports in those countries whose exports consisted largely of transformed raw materials and semiprocessed goods which have been imported. For many of the larger industrial countries, however, this is not the case. Nor is it the case for developing countries that import capital goods in order to be able to export raw materials and semimanufactures in the future. Second, in order to forecast, the system presupposes a knowledge of either total trade or one of the country flows. Thus, it requires to be given what really should be determined by the model.

A somewhat similar approach is based on constant shares. In this case, either the ratio of country j’s imports from country i to country j’s total imports or the ratio of country i’s exports to country j divided by country i’s total exports is calculated. If these shares remain constant, then, given total country trade, individual flows can be calculated. However, such a system fails to account for either “the gradual drift in market shares which sometimes continues for many years” or “the saw tooth fluctuations of those shares produced by devaluations and by domestic inflationary maladjustment.”9

Many studies of a country’s international competitive position are based on constant market shares.10 The level of exports in any year other than the base year is compared to what the level would have been if the country had maintained its geographic or commodity market shares. The changes in shares are then examined in the light of price and income changes and other relevant factors.11 This approach may be useful in enlarging the Rhomberg model, discussed later, especially if some way is found to tie together and calculate simultaneously the shares through time, the level of imports and of exports, prices, and other variables.11a

The network of world trade, the Woolley transaction matrix, and the Beckerman approach give important insight into the structure of the international economy. They are not, however, at present in the form of a model, as defined above. They do not present a way of rigorously testing hypotheses, measuring the impact of various determining trade flows, or forecasting future levels of both total and country trade. Models constructed to handle some of these problems are presented in the next two sections.

II. Structure of Trade Models

Essentially the same model for analyzing the flows between individual countries (the aij’s in the import-export matrix) was separately formulated by Tinbergen and by Pöyhönen.12 According to this model, the value of trade between any two countries is determined by the national income of each country and by the geographical distances. The income of the exporting country reflects the supply potential; the income of the importing country reflects the market size and demand potential. The farther countries are geographically apart, the greater the implicit and explicit transportation costs.13 Other relevant factors incorporated into the Tinbergen model are membership in trade-preference groups, such as the Commonwealth of Nations, and contiguity, i.e., presence or absence of a common border. This model has been modified and extended by both Linnemann and Waelbroeck.

Linnemann modifies the model by including the populations of the importing and exporting countries as separate variables. He reasons thus: a country trades because of the difference between domestic production and domestic demand. “Potential foreign trade should … be defined as that part of a country’s production which will not be oriented towards domestic needs if we assume that all countries are subject to exactly the same trade resistance in their dealings with the world market” (italics in the original).14 Thus, potential trade is determined by a country’s “national product, and [by] the ratio between production for the home market and production for foreign demand (as these magnitudes would be established under conditions of equal trade resistance throughout the world).”15 The ratio of domestic market orientation to foreign market orientation, DM/FM, is related primarily to the population size of a country rather than income levels. Linnemann argues that in order to avoid costs such as transportation, “every country will try to produce as much of its requirements as possible at home.”16 The size of the market and the endowment with natural resources determine the extent to which each country attains this goal. The larger the domestic market the greater, ceteris paribus, the efficiencies of scale; the cheaper it is to produce at home, the less need to rely on foreign sources. Linnemann cites studies of Balassa and Chenery17 as supplying empirical evidence to support his contention.18

Linnemann examines, in more detail than Tinbergen, the distance variable as a proxy for trade resistances. There are two types of trade resistance—natural and artificial. The natural ones consist of implicit and explicit transportation costs, including freight and insurance fees, time necessary for shipments, and the need to maintain larger inventories because of the distance between supplier and purchaser. Of course, these costs vary for reasons other than geographical distance between trade partners; nevertheless, distance reflects most of the variation in these costs. Artificial impediments, such as tariffs and quotas, can be “created, maintained, or removed by government action.”19 At any moment of time the artificial barriers are assumed to apply to all trade flows more or less equally. Departures from this regularity are assumed to be randomly distributed and are accounted for by the error term in the regression. Tinbergen used this residual to identify the impact of artificial barriers. When the actual level of trade exceeds the level calculated by the equation, artificial trade barriers are taken to be less than average; when the reverse holds, artificial barriers are assumed to exceed the average.

In the Linnemann model the individual trade flows are expressed as follows:


where aij represents the value of exports from i to j, Ep and Mp stand for potential exports and imports, Y denotes some measure of income, N population size, and Dij distance between countries i and j; the a’s are the parameters to be estimated.

The model warrants several comments. First, if Y is total income, and α1 = α2, and α3 = α4, the equation is then in terms of per capita incomes in the two countries. Linnemann assumes (and substantiates), however, that ɑ1 ≠ α2, and α3 ≠ α4. He states that even if per capita income were a relevant variable, its influence would be much less than total income and population.20 Second, trade between two countries may be influenced by whether or not the trading countries have a common border, as well as by the distance between the trading centers. Furthermore, trade might be greater among members of a customs union of trade preference area such as the Commonwealth of Nations. Both Linnemann and Tinbergen have dummy variables to account for these factors.21 Third, as Tinbergen points out, the variables, while accounting for potential supply and demand, are not “separate demand and supply functions for exports [but] the equation is a turnover relation in which prices are not specified.”22

Prices are omitted from this model for two reasons. In the first place, it is a cross-section model, using data for each country at the same point in time. Prices are not relevant variables in cross-section models since each purchaser (or country) is confronted with the same set of prices. For example, the prices of French or German exports (exclusive of freight and insurance) are the same, in principle, for the United States as for Japan. Furthermore, since prices in international trade are in index form, all that is known is the relationship of current prices relative to prices in a base year, not the actual prices themselves. Unlike cross-section data, price indices in time series move through time. Thus, we can, to some extent, trace and measure the effect of these price changes on quantities demanded (imports) or supplied (exports). Difference in price levels between various country suppliers would be relevant in cross-section models, but such information is usually difficult—if not impossible—to obtain. In the second place, prices are omitted because in equilibrium there is “equality of supply and demand on the world market,” which “implies that no country can have, in the long run, ‘too low’ a price level, or ‘too high’ a price level,” for “in both cases there would be a permanent disequilibrium of the balance of payments.” Therefore, “except in the short run … the general price level will not influence a country’s potential foreign supply and demand.”23 Linnemann uses data averaged over a three-year period24 to reflect this equilibrium characteristic. Junz and Rhomberg25 have shown, however, that the influence of price changes on trade flows takes more than three years to make itself fully felt. This time lag indicates that data over a longer period of time should be used to eliminate the influence of short-run price changes.

The other thing to note about this Tinbergen-Pöyhönen-Linnemann approach is that it has the same limitation as the constant-share method discussed above. That is, it is static and pays no attention to the development of trade over time.26 Thus, this model does not capture shifts or changes of trade which might develop in the long run because of more complicated interrelationships between prices, income, and imports. Nevertheless, the model has great value. Its value lies in its ability to identify extreme cases of artificial barriers to trade, the role of distance, and the effects of membership in various customs union and trade preference groups.

Waelbroeck adapted the Tinbergen-Pöyhönen model to study short-run balance of payments problems. As the Tinbergen-Pöyhönen model stands, income is the only variable available to policymakers to determine trade flows. This “implies that countries are unable to control their balance of payments surplus or deficit otherwise than by modifying their rate of economic growth.”27

To adapt the model to the short run, Waelbroeck first transforms the trade flows of the Tinbergen-Pöyhönen model to shares and then introduces prices. He points out, however, that “it is difficult to estimate the price effects for individual elements of the trade matrix.”28 The problem is further complicated by the importance of prices in countries other than the two involved in trade. For example, Germany’s exports to the United Kingdom might fall off sharply if the price of U.S. exports declined. The other prices must be entered in some sort of index form, leading to index number problems. Waelbroeck approaches this problem by first considering groups of countries which are geographically close together and calculating the share of each country’s income in the total income of the group. These shares provide the weights necessary to calculate the aggregate price index based on the assumption that the share of country i in the total imports of any country not a member of the group is equal to the share of country i in the total exports of the group. However, there may in fact have been substantial discrepancies between the two ratios, especially if the countries grouped together on geographical criteria are not economically homogenous. Furthermore, he does not indicate how the individual country prices are to be obtained, although he presents results of statistical estimates using his weighted prices for “1958 exports of some 400 commodities by France, Germany, Belgium, Luxembourg, Italy, and Holland.”29

Waelbroeck uses his model primarily for analytical purposes. He shows that the balance of payments is far less sensitive to large changes in the growth rate than is commonly supposed. Waelbroeck shows further that the system has very strong stability characteristics. The introduction of prices is important in reshaping the Tinbergen-Pöyhönen system and makes this model potentially useful for trade forecasting.

III. Transmission Models

The four models surveyed in this section sought primarily to establish “the main relationships between the level of domestic economic activities in the various countries and their international transactions”30 so as to see how fluctuations in the former affect the latter. Metzler focuses attention on changes in investment, Neisser and Modigliani on income and capital flows, and Polak on autonomous investment and price changes. In the Rhomberg model, income, prices, and capacity in the industrial countries are the exogenous variables.

Metzler model31

The Metzler model rests on the definition of national income or product, Y = C + I + (XM). That is, national income or product (Y) is the sum of consumption (C), investment (I), exports (X) less imports (M). In his system, C, I, and M “are dependent upon the level of income and employment at home.”32 The key to the model is the treatment of exports; all exports are considered as imports of the recipient countries and are, therefore, a function of income in these countries. Thus the whole pattern of world trade can be described by import functions, i.e., any aij is a function of income in country j,

aij = fi(Yj), for all i.



The model assumes that determinants of imports other than income, such as prices, costs, and exchange rates, are fixed. It also assumes that “the level of output in each of the n countries is [initially in] a state of balance in the sense that the country’s rate of output of goods and services is equal to the demand for such goods and services.”33 A disturbance of the economic forces governing income is then assumed to take place in one of the countries; the rate of current investment in each country is either given or is a function of income.

Changes in economic activity are transmitted through the system as follows. An autonomous rise in investment in one of the countries increases output and income. The increased income leads, through the marginal propensity to spend, to larger expenditures on goods and services, both domestic and foreign. These expenditures stimulate exports from all the country’s trading partners. The rise in exports increases the demand for domestic output and, therefore, income in those countries. Increased demand and income, of course, lead to larger imports. Metzler concludes that if the marginal propensities to spend are less than one, the system is stable; that is, an autonomous shock will work its way throughout the system to a new equilibrium point.

There are as many unknowns as independent equations—one for each aij. The diagonal terms represent domestic consumption and investment and are determined by domestic income. This is, therefore, a closed system with a unique solution. In contrast to the three studies discussed below, Metzler did not apply data to his model.

Neisser-Modigliani model

Neisser and Modigliani constructed a model in which a country’s total imports and total exports were considered separately but tied together by assuming constant participation of exports in world markets. That is, each country’s income (Y) determines its total imports (M). Its exports are determined by its shares in the total imports of the other countries. The shares may be modified by the effects of the exogenous variables in the system. The exogenous forces detemining both imports and exports are income and industrial output, prices, net change of stocks (inventories), and net capital flows. The inclusion of these other variables, as well as the separate consideration of imports and exports, makes this model more complicated than Metzler’s.

In the model, trade flows were divided into three commodity groups and six geographical regions, determining 36 trade flows. The model was estimated with data for the interwar period. For three of the years, 1928, 1932, and 1935, the equation system was solved by expressing the endogenous variables in terms of the predetermined variables only. In this manner, the impact of changes in the predetermined variables, such as income, prices, and capital flows, can be easily traced. Neisser and Modigliani used such an approach to analyze the decline in international trade in the 1930’s.

The usefulness of the model is limited, however, by several factors. First, income and industrial output are treated as given, predetermined variables. Thus, it is not possible to use the system directly to “reveal how the different countries’ incomes would be affected”34 by changes in international conditions, a goal which Neisser and Modigliani set for themselves. They attempted to add to the system equations relating income to the net trade balance, but found that their reliability was in serious doubt owing to large statistical errors. Accordingly, they were not able to answer directly their question: what conditions must be fulfilled by a country’s international economic activity in order to assure a certain level of the domestic economy? This limitation might be overcome by using recently developed estimating techniques. But, it is more likely that this question can be answered only by linking together large, multisector models of each country. The Neisser-Modigliani model is also limited in the sense that it explains only total imports and total exports for each country (of each commodity class) and that it does not explain flows between individual countries and regions.

Polak model

Although Polak would have preferred to describe the transmission mechanism by linking together the models for individual countries, such models were not—and still are not—available for a sufficient number of countries. To achieve the same end, he built the following model: exports determine income through a modified multiplier mechanism. Imports are a function of income. Imports of all countries equal total world trade, which in turn determines the volume of exports of each country. In symbolic form:


where X refers to exports, Y to income, and M to imports, and subscript i refers to the i-th country and w to world total. The share of country i in world exports is αi, and γi is the marginal propensity to import. The “export multiplier” is βi. Exogenous variables such as autonomous investment and price ratios are added to determine the system.

Polak used this system to trace out and measure the effects of autonomous changes in the world economy. He calculated the marginal propensity to import, the export multiplier, and the share of world trade for 25 countries using data for 1924–38. Polak also used this model to calculate how the international system as a whole responded to autonomous changes in any one country. He found “that an initial autonomous increase in imports would lead to a further increase in world trade of approximately equal magnitude.”35

In addition to the insights that the model provided of the economic world between the wars, the model could be used for forecasting total imports and exports of any country, for which estimates were calculated, provided the total volume of world trade was known. If the model were extended to include all the countries of the world and if either the total exports or the total imports of any one of the countries was known, then the level of world trade could also be determined.

The major importance of the Polak model was to relate income to exports through the export multiplier. Income is thus determined by the system and fills in a step missing in the Neisser-Modigliani formulations. Nevertheless, this step opens the model to another criticism. The assumption that income is a function of exports is quite reasonable for nonindustrial countries whose exports are usually concentrated in a few products and which account for a large portion of total output. It even may be reasonable for industrial countries like Luxembourg, the Netherlands, and Belgium, where the foreign sector is large. It is clearly less reasonable for industrial countries like the United States and Germany where the foreign sector is relatively smaller. On a conceptual level, the dependency of income on exports also makes investment a simple function of income.36 Furthermore, by combining equations (2) and (3) above, the Polak model relates imports to exports, and “unless a very great weight is attached to the price mechanism, [this] approach lacks an effective income determinant that can be controlled to a sufficient extent by the country’s monetary authorities.”37 Neisser and Modigliani concluded that the equation can only be valid by chance.

Polak recognized these points in principle. In the estimations, however, only for the United States is income not related to exports. The United States was assumed, therefore, to play a dominant role as the origin of autonomous changes in investment in the international system.38 Moreover, in subsequent work directed at some of the same questions, when presumably the chance to merely update this model presented itself, Polak (and Rhomberg, who joined him in this work) chose to completely revamp it and cast it in terms of import functions alone. The latest version of this model is described next.

Rhomberg model

Work on world trade models has continued at the Fund. Polak and Rhomberg presented in 1962 a model which represented Polak’s continuing interest in the transmission mechanism.39 More recently, studies carried on by Rhomberg have examined the transmission mechanism with special reference to U.S. balance of payments. The work has been reported from time to time in Staff Papers and unpublished papers.40 The latest version of the model is substantially the same as that reported in 1964, although the time span of estimation is different (it is now 1953–65), and some new exogenous variables have been incorporated.

The model determines the flow of goods and services among three regions—the United States, Western Europe (i.e., European OECD member countries), and the rest of the world (including Canada and Japan). All trade flows are viewed as imports. For Western Europe and the United States, trade flows are a function of such factors as income, inventory investment, demand pressure, and relative prices. Total imports of the rest of the world are determined by a definitional rather than a behavioral relationship. This region’s imports equal its net foreign exchange inflow from exports, capital, and transfers, less net additions to monetary reserves. Its balance of goods and services, therefore, is equal to the sum (with sign reversed) of the net trade balances of the United States and Western Europe corrected for additions to the monetary gold stock. The U.S. and West European shares in these imports are related to relative prices. Service flows are determined by trade flows, income, investment position, and other relevant variables. An alternative version of the model has equations to explain each of the three export price indices.

Changes in income and prices affect the model as follows. If U.S. income rises, the United States purchases more goods and services from Western Europe and the other areas. Since these purchases increase the foreign exchange receipts of the rest of the world, the rest of the world steps up its imports from the United States and Western Europe. In like manner, a rise in domestic prices in Western Europe leads to increased purchases from the United States and the rest of the world; these increased purchases in turn stimulate U.S. exports to the rest of the world.

To calculate directly the effect of a change in any predetermined variable on the dependent variables, the system is expressed in its reduced form. The coefficients obtained this way show, for example, that the U.S. current account expands by $51 million for every billion dollars’ growth in European income, but contracts by $38 million for every billion dollars’ growth in U.S. income.

Another way of looking at short-run changes is by calculating income and price elasticities. The elasticities, according to the model, are shown below:

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Final income; excludes inventories.


Notice that U.S. imports from the rest of the world are less price-sensitive than those from Europe. This is reasonable in light of the different types of commodities imported, since imports from the rest of the world consist of raw materials and agricultural commodities, many of which have no domestic substitutes. Imports from Europe, on the other hand, are primarily manufactures, goods which are typically responsive to price. The same considerations hold for the price sensitivity of West European imports.

The model can also be used for forecasting. By specifying the values of the predetermined variables in the forecast period, the values of the trade and service flows for that period can be obtained. The current model will be tested as soon as all the 1966 data are available. Previous versions of the model have given fairly good results for one-year forecasts.

What then are the favorable and unfavorable aspects of this model? Its primary strength probably lies in that it is a simply formulated, closed model in which all trade flows are uniquely determined and that it can be used for forecasting. This model estimates the aij’s directly and not merely a country’s total imports and exports, as did the other transmission models. It does not make all income of industrial countries other than the United States dependent on exports, as the Polak model does, nor is income of the rest of the world predetermined as in the Neisser-Modigliani model. Rather, income is predetermined for the industrial countries, but for the rest of the world, income depends implicitly on exports.

The fact that the model is closed is important. If errors are made in the assumptions underlying the projections and, e.g., imports of the United States from the rest of the world are underestimated, exports to the rest of the world will also be underestimated. The resulting error in the trade balance, in all likelihood, will be smaller than the original error.

The Rhomberg model has export-supply equations, in which export prices are determined by domestic prices and the volume of trade. In this manner both the supply and the demand sides of trade flows are expressed. These equations are necessary in a logically consistent model. In practice, however, the estimates of these equations are not as good as others in the model. Furthermore, better predictive results are obtained by assuming that the export prices are predetermined variables.

The model also takes into account the role of demand pressure in imports. As a country approaches full utilization of domestic capacity, its imports often rise faster than income, reflecting the higher prices of domestic relative to foreign goods. The need for such a variable is due to the nature of the unit-value indices, the usual measure of import prices. In fact, the unit values measure the average value of goods shipped. The index is not completely responsive to actual price movements, particularly when increased prices have caused particular commodities to be removed from the basket of goods traded. Furthermore, implicit price factors such as discounts or delays in filling orders are not accounted for at all. The unemployment rate in the United States captures some of this in the U.S. import function. For Western Europe, inventory investment performs this role.

The model has several drawbacks. In the first place, it is too highly aggregative. It does permit the calculation of the U.S. trade balance, but not the trade balances of other individual countries. There are occasions when it would be extremely helpful to be able to forecast the trade balance of the United Kingdom, Germany, or some other country. Furthermore, the high degree of aggregation hides some of the shifts in the commodity composition of trade and in the importance of various geographical markets. This might be solved by increasing the number of regions. Davis, for example, has achieved some success with a four-region model where Canada is a separate region.41 Perhaps one or two other countries or regions could be incorporated into the model. However, as the number of regions increases the model would become progressively unwieldy. Because the data are lacking, the service equations would have to be dropped. Future efforts to separate trade into commodity groups may avoid some of the weaknesses of aggregation, but it will be at the cost of directly estimating the individual trade flows.

The assumption used to close the model suggests another of its limitations. It will be remembered that the model does not have a behavioral equation determining either reserve accumulation or imports of the rest of the world. Rather, reserve changes were autonomous and imports defined by an identity. This situation is unsatisfactory. Either reserves or imports must be explained behaviorally for the model to more closely approximate reality.

Perhaps another weakness in the model is its failure to incorporate financial flows other than the net flow of capital to the rest of the world, used to close the model. Although there has been some investigation of the relationship between trade, capital flows, and interest rates in recent years,42 this work is not yet far enough advanced to be incorporated in a world trade and payments model. It is known that direct investments and long-term loans stimulate exports and that short-term flows finance trade. Neisser and Modigliani, it will be remembered, had some success in relating imports and exports of each country group to net capital inflows. This variable could be tried in the Rhomberg model. More extensive use of capital-flows information is prevented by the lack of data.

The present model is static in nature, with all trade flows determined by forces acting in the same time period. The model does not take into account the time lag necessary for adjustment. More realism might be attained by introducing time lags.

IV. Some Suggestions for the Future

A variety of approaches to the study of world trade have been surveyed. Each approach has added to our knowledge of the structure of trade and the forces determining it. Nevertheless, each approach has fallen short of the mark of explaining the level and the commodity composition of trade between any two regions. The constant-share approach, in particular, has permitted the disaggregation desired, but either total trade or one of the country flows has had to be predetermined. Furthermore, they have been too rigid to capture shifts of the share coefficients. The Tinbergen-Pöyhönen-Linnemann model also had the same degree of disaggregation as the constant-share approach, but the disaggregation had to be sacrificed when Waelbroeck adapted the model for short-run uses by introducing prices as explanatory variables. Rhomberg is able to capture shifts and changes, and has had some success in forecasting. But his model only gives total trade between three regions.

It appears that we need a model which incorporates (1) the disaggregation possible with a constant-share approach and (2) the flexibility and economic content inherent in the transmission models. It is not completely clear how this can be accomplished, but a few ideas can be sketched out here.

At the first stage we could consider the import demand by each of 10 or 12 regions and countries for six categories of goods. The categories probably would be food and animals, raw materials, chemicals, transportation equipment and machinery, finished manufactures, and miscellaneous goods. Each country’s demand schedule for each category of imports would be determined by income or industrial output, relative prices, demand pressures, consumption, domestic agricultural output, and other relevant variables. Price would be a purer variable here than in the Rhomberg model, since the import baskets would be of greater homogeneity.

The second step would involve determining what share the other countries have in supplying the given country’s imports. This would probably be related to historical market shares, modified by short-run factors such as limitations of resources, differential rates of growth, tariffs, and price changes. For any commodity, a country’s share in supplying the imports of a given country might be inversely related to the ratio of the supplier country’s price to the index of price of all countries supplying the commodity.

The third part would tie in the export-supply schedule. Export supply would be determined by factor availabilities, prices, and costs. It probably could be approximated by exports of the previous period, modified by rates of growth, developments such as droughts and floods, price changes, change in labor supply, and so forth.

The determination of each trade flow would be the intersection of the supply and demand schedules. Once a reasonable method of determining these flows is achieved, the number of countries or regions in the model can probably be extended. It must be kept in mind that this is a big model, much larger than the time series studies of Neisser-Modigliani, Polak, or Rhomberg. The first step alone requires 60 equations. It appears, however, that the model would take us a step closer to a satisfactory explanation of world trade flows and to successful forecasting of trade balances and international price movements.


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Modèles de commerce mondial


Ce document passe en revue plusieurs méthodes qui ont été utilisées pendant la période d’après-guerre pour étudier le commerce mondial. Pour plus de commodité, on peut les appeler: 1) la méthode de la part constante du marché, 2) les modèles de la structure du commerce international, et 3) les modèles de transmission.

Dans la méthode de la part constante du marché, on suppose que la part de chaque pays dans les importations des autres pays demeure constante. C’est cette méthode qui est utilisée le plus souvent pour les études relatives à la position concurrentielle internationale d’un pays. Les modèles de la structure économique internationale décrits sont ceux élaborés par Tinbergen, Pöyhönen et Linnemann. Il s’agit de modèles “cross-section” dans lesquels les échanges entre deux pays quelconques sont déterminés par la puissance économique, l’importance du marché et les frais de transport. En ce qui concerne les modèles de transmission, Neisser et Modigliani, Polak et Rhomberg ont construit des modèles destinés à retracer l’impact des variations des revenus, des fluctuations des prix et d’autres facteurs internes sur les échanges internationaux.

L’auteur évalue ces études à la lumière de l’objectif recherché, à savoir l’élaboration d’un modèle qui permette de déterminer simultanément le total des importations et des exportations des principales nations et régions commerçantes, et leurs flux commerciaux d’un pays vers un autre. Ceci peut nécessiter jusqu’à 15 ou 20 classifications géographiques, et il sera peut-être nécessaire de répartir le total des échanges commerciaux en groupes de produits. La présente étude montre que la méthode de la part constante permet de réaliser la désagrégation souhaitée, mais il faut pour cela que l’on détermine à l’avance soit le total des échanges commerciaux, soit l’un des flux du pays. Cette méthode est également trop rigide pour enregistrer les variations des coefficients des parts. Bien que le modèle de la structure commerciale présente également le même degré de désagrégation que la méthode de la part constante, il s’agit d’un modèle d’équilibre, et l’on sacrifie la désagrégation lorsque le modèle est adapté à une courte période. Le modèle de Rhomberg, dernier en date des modèles de transmission, peut déceler les déplacements et variations et a été utilisé avec succès pour établir des prévisions, mais dans ce modèle, le monde n’est divisé qu’en trois secteurs géographiques. Il semble que les travaux futurs devront être orientés vers la construction d’un modèle combinant la désagrégation potentielle d’une méthode basée sur la part constante, ainsi que la souplesse et le contenu économique inhérents aux modèles de transmission.

Modelos sobre comercio mundial


Este trabajo pasa revista a diversos métodos que han sido utilizados después de la guerra para estudiar el comercio mundial. Por conveniencia puede denominárselos: (1) método de la participación constante en el mercado, (2) modelos sobre la estructura del comercio, y (3) modelos sobre transmisión.

El primero de dichos métodos, es decir, el de la participación constante en el mercado, parte del supuesto de que la participación de cada país en las importaciones de los demás permanece constante. Este método se ha empleado profusamente al estudiar la situación competitiva internacional de un país. Entre los modelos relativos a la estructura del comercio figuran los de Tinbergen, Pöyhönen, y Linnemann. Son modelos transversales en los cuales los factores que determinan el comercio entre dos países cualesquiera son el poderío económico, las dimensiones del mercado, y los costos de transporte. En cuanto a los modelos sobre transmisión, Neisser y Modigliani, Polak y Rhomberg han estructurado modelos para determinar qué impacto producen sobre el comercio internacional los cambios en el ingreso, las variaciones de precios, y otros factores internos.

El trabajo evalúa estos estudios a la luz de la aspiración de disponer de un modelo que sirva para determinar, simultáneamente, el total de las importaciones y exportaciones de los principales países y zonas comerciales, y el flujo comercial entre los mismos. Este objetivo puede requerir que se hagan hasta 15 ó 20 clasificaciones geográficas, y es posible que haya que subdividir el comercio total según grupos de mercancías. El estudio pone de manifiesto que el método de la participación constante permite ese desdoblamiento, pero requiere que se determinen de antemano el comercio total o las corrientes comerciales de uno de los países. Además, por ser demasiado rígido no capta las alteraciones que ocurren en los coeficientes de participación. Aunque el modelo sobre la estructura del comercio permite usar de subdivisiones en el mismo grado que el método de la participación constante, es un modelo de equilibrio, y la adaptación del mismo a estudios sobre un plazo abreviado obliga a sacrificar ese desdoblamiento. El modelo de Rhomberg, que es el más reciente de los de transmisión, permite captar variaciones y cambios y se lo ha usado con buenos resultados al hacer pronósticos, pero divide al mundo tan sólo en tres grupos geográficos. Según parece, los trabajos futuros deberán orientarse hacia la confección de un modelo que reúna las posibilidades de desdoblamiento que ofrece el método de la participación constante a la vez que la flexibilidad y el contenido económico de que están dotados los modelos sobre transmisión.


Mr. Taplin, economist in the Special Studies Division of the Research and Statistics Department, is a graduate of the New School for Social Research. He was previously on the staff of the Federal Reserve Bank of New York and has taught at Fairleigh Dickinson University and the Graduate School of Business Administration, New York University.


A preliminary version of this paper was presented to a seminar on the application of quantitative techniques to the solution of economic and social problems at the University of Pittsburgh, February 3, 1967.


E.g., see Maurice Liebenberg, Albert A. Hirsch, and Joel Popkin, “A Quarterly Econometric Model of the United States: A Progress Report,” Survey of Current Business, U.S. Department of Commerce, Vol. 46, May 1966, p. 13.


See Bibliographical Appendix (p. 452), Nos. 1, 11, 12, 14–16, 18, 21, 26, 30, and 31, for complete citations to the studies mentioned.


Although there are technical distinctions between the terms, “exogenous” will be used here interchangeably with “predetermined” and “independent”; similarly, “endogenous” will be used here interchangeably with “jointly dependent” and “dependent.”


Other conditions are necessary, but we will assume that they are met.


P. 7.


Since exports are measured f.o.b. and imports c.i.f., the tables are not, strictly speaking, a trade matrix as described above.


Woolley, p. 77.


Waelbroeck (No. 30), p. 4.


See, e.g., the studies of Fleming and Tsiang, Kuznets, Tims and Meyer zu Schloctern, Tyszynski, and Waelbroeck (Bibliographical Appendix, p. 452, Nos. 6, 10, 25, 27, and 29).


This approach has also been used in the Fund’s Annual Report, e.g., Annual Report, 1966, pp. 46–47.


For an example of such an approach, see F. Gerard Adams, H. Eguchi, and F.M. Meyer zu Schloctern, “An Econometric Analysis of the International Trade of OECD Member Countries,” a paper presented at the ad hoc meeting of experts on import and export projections, Economic Commission for Europe, Geneva, May 1967.


According to a footnote in the Pöyhönen article, “the one and the same theory seems to have been elaborated simultaneously but independently at two different research centres” (by Pöyhönen in Finland and by Tinbergen in the Netherlands), p. 93.


Tinbergen, p. 263.


Linnemann, p. 11.


Ibid., p. 12.


Ibid., p. 13. This statement appears to argue against the theory of comparative advantage. Indeed, Linnemann states (p. 22), “comparative advantages are predominately man-made, and their existence is a consequence as much as a cause of foreign trade … comparative advantages are not an autonomous or exogenous variable but rather an endogenous factor. They hardly contribute therefore to an understanding of the size of trade flows or the magnitude of potential foreign supply.”


Bela Balassa, The Theory of Economic Integration (London, 1962), p. 131; and Hollis B. Chenery, “Patterns of Industrial Growth,” The American Economic Review, Vol. L (1960), pp. 624 ff. (cited by Linnemann, pp. 15–19).


Kuznets gives arguments that the ratio is not a function of population. An alternative approach might be to remove, as a first step, the influence of size of the countries involved and then to look for flows which depart “significantly” from what would be expected on the basis of size. A method for removing the size factor, suggested by Savage and Deutsch, involves solving a set of quadratic equations which are based on the characteristics of the data and not by any outside factors. The method is analogous, in some sense, to seasonal adjustment. See Savage and Deutsch (Bibliographical Appendix, p. 453, No. 23) and Goodman (No. 7) for refinements of the Savage and Deutsch approach.


Linnemann, p. 31.


On the basis of his statistical estimate, Linnemann concludes “that no effect of per capita income on trade could be established” (p. 211).


A dummy variable attempts to reflect factors that are difficult to quantify. It usually has a value of 1 if a certain characteristic is present (e.g., membership of the Commonwealth) and zero if it is not.


Tinbergen, p. 263.


Linnemann, p. 24.


Linnemann used data for 80 countries for 1958–60. Tinbergen estimated the parameters with 1959 data for 18 and 42 countries, while Pöyhönen tested his model for 10 countries with 1958 data.


Junz and Rhomberg (Bibliographical Appendix, p. 452, No. 8).


Tinbergen, p. 263.


Waelbroeck (No. 30), p. 7.




Ibid., p. 11.


Neisser and Modigliani, p. v.


Metzler’s contribution lies in the extension of the traditional two-country analysis to n countries. Machlup considered more than two countries but only with severe restrictions on the propensities; he also talks about “foreign induced” exports (i.e., exports determined by incomes abroad) and “autonomous” exports (see Bibliographical Appendix, p. 452, No. 13, and Chipman, No. 3, p. 355).


Metzler, p. 333. Government expenditure can be assumed to be part of consumption and investment.


ibid., p. 330.


Neisser and Modigliani, p. 30.


Polak, p. 164.


Neisser and Modigliani (p. 57) called this an “unacceptable oversimplification.” Although the Neisser-Modigliani study was published before Polak’s, they addressed themselves to several points of the Polak model, which had been presented in preliminary form in 1949 and 1950 (see Econometrica, Vol. 18 (1950), pp. 70–72).


Neisser and Modigliani (p. 57)


Polak, pp. 55–58.


See Polak and Rhomberg (Bibliographical Appendix, p. 453, No. 17).


By Rhomberg, Rhomberg and Boissonneault, and Rhomberg and Fortucci (ibid., Nos. 20–22).


Davis (Bibliographical Appendix, p. 452, No. 5).


By Bell, Cohen, Kenen, and Stein (Bibliographical Appendix, Nos. 2, 4, 9, and 24).