A Revised Version of the Multilateral Exchange Rate Model

The multilateral exchange rate model (MERM), like most large models in use, is continuously changing because of ongoing work to improve its logical structure and to increase its empirical content, and also because of the need to modify the model in response to changing economic conditions, thus maintaining its usefulness as a tool for studying policy alternatives. As a result, the description of the MERM presented by Artus and Rhomberg (1973) is now somewhat out of date, and it was felt that an updated description of the model, hereinafter referred to as MERM 2, was needed. At the same time, the basic theoretical approach, which has not changed, is explained further, and the main macroeconomic assumptions are made more explicit.

Abstract

The multilateral exchange rate model (MERM), like most large models in use, is continuously changing because of ongoing work to improve its logical structure and to increase its empirical content, and also because of the need to modify the model in response to changing economic conditions, thus maintaining its usefulness as a tool for studying policy alternatives. As a result, the description of the MERM presented by Artus and Rhomberg (1973) is now somewhat out of date, and it was felt that an updated description of the model, hereinafter referred to as MERM 2, was needed. At the same time, the basic theoretical approach, which has not changed, is explained further, and the main macroeconomic assumptions are made more explicit.

The multilateral exchange rate model (MERM), like most large models in use, is continuously changing because of ongoing work to improve its logical structure and to increase its empirical content, and also because of the need to modify the model in response to changing economic conditions, thus maintaining its usefulness as a tool for studying policy alternatives. As a result, the description of the MERM presented by Artus and Rhomberg (1973) is now somewhat out of date, and it was felt that an updated description of the model, hereinafter referred to as MERM 2, was needed. At the same time, the basic theoretical approach, which has not changed, is explained further, and the main macroeconomic assumptions are made more explicit.

As to the methodological aspects, certain choices made at the time of the model’s conception have not been found to be in need of revision. The model remains a mathematical simulation model with emphasis on the specification of a fully consistent set of demand and supply equations for goods. Its theoretical structure is basically the Walrasian general equilibrium frame-work, simplified to a great extent by the use of input-output relationships. As far as possible, the numerical values for the various behavioral parameters were derived from econometric studies; however, emphasis was placed on maintaining the structural relationships derived from economic theory rather than modifying these relationships according to data availability. A priori judgment was used, when necessary, in the choice of parameter estimates. In part, these methodological choices reflect the specific purpose of the model—the estimation of the medium-term (two to three years) effects of changes in the exchange rates of the various industrial countries on their trade balances. The exchange rate changes of interest here are those that far exceed, or fall far short of, the concurrent inflation rate differentials. Such changes may occur because of discrete exchange rate adjustments among countries maintaining pegged exchange rates, or they may be the result of the effects of disturbances in asset markets on floating exchange rates. As explained below, the model has other applications, including the analysis of the trade balance effects of divergent inflationary tendencies among countries maintaining pegged nominal exchange rates. The MERM differs from most of the existing large-scale econometric models in that forecasts of cyclical variations in the level of economic activity and related issues are not within its purview.

The major economic concepts and assumptions on which the MERM is based are discussed in Section I. The model is presently based on a somewhat finer disaggregation of commodities and components of final domestic demand than it was in 1973. The new disaggregation and the reasons for adopting it are described in Section II. The system of demand equations that reflects this disaggregation and the more explicit specification of input-output relationships are presented in Section III. The supply side is described in Section IV. Various applications of the revised model are described in Section V.

I. Major Economic Concepts and Assumptions

The extremely complex microeconomic structure of the MERM, which includes several thousand demand and supply equations, has tended to obscure the few basic concepts and assumptions that underlie the model and has often led to confusion about what is meant in the MERM terminology by exchange rate effects. In an attempt to facilitate the interpretation of the model results, the crucial concepts and assumptions that underlie the MERM are restated here in the context of macroeconomic theory. The precise ways in which these hypotheses are reflected in the specification of the equations will be discussed in the following sections.

The model focuses on the major factors that determine exchange rate effects after an adjustment period of two to three years. These factors are the degree of adjustment of domestic prices and costs to the exchange rate change, the price elasticities of foreign trade flows, and the aggregate demand management policies followed by the authorities. The model takes these factors into account in a consistent manner for all of the industrial countries simultaneously. Factors that influence exchange rate effects during only the first few months following an exchange rate change are not considered. For example, no account is taken of a possible reversal of the leads and lags, of the currency denomination of foreign trade contracts, or of the existence of delivery delays. In addition, no attempt is made to analyze what effect, if any, a change in the exchange rate may have in the long run.1 The issue considered here is whether the exchange rate can play a role in the adjustment process; this is essentially a medium-term problem.

The MERM rests on three major assumptions—namely, (i) local currency costs and prices are somewhat “inflexible”; (ii) many of the countries, in particular the industrial countries, produce differentiated goods that are faced by finite, in fact sometimes small, price elasticities of demand in world markets; and (iii) the overall level of nominal final domestic demand can be influenced by the central authorities.

The first assumption underlies the whole structure of the MERM. If all costs and prices adjusted rapidly and without any difficulty to variations in the money supply, then, as the global monetarists 2 have pointed out, exchange rate changes would never be needed, since nothing would prevent the domestic economy and the external balance from reaching an equilibrium position, whatever the prevailing exchange rate. The authorities would only be required to maintain the money supply at a level consistent with the prevailing exchange rate—a requirement that would be costless if prices and costs were perfectly flexible. The fixed exchange rate system would be the optimal system. Further, any change in the exchange rate parity would, under such conditions, be a meaningless policy decision; its only effect would be to place the economy in a position of disequilibrium that could be corrected only by adjusting the money supply in proportion to the change in the exchange rate.

The assertion that the authorities cannot, in fact, adjust costs and prices up or down at will by changing the money supply is not the subject of any serious controversy. In this sense, prices are sticky or inflexible. This is not to say that costs and prices cannot be influenced by monetary policy but only that reducing costs and prices once they have gotten out of line with other countries’ costs and prices is often not a feasible solution. It is not feasible because, given the inflexibility of costs and prices, the restrictive monetary policy that would be needed to achieve the required cost and price adjustments would lead to a prolonged and severe recession and a socially unacceptable rate of unemployment. Under the most favorable conditions, a country with a fixed exchange rate that has experienced a much higher rate of inflation than its major trading partners for a substantial period of time and that, as a result, faces balance of payments difficulties may be able to reduce its inflation rate to the level prevailing in its trading partners. To expect that it would be able to lower its inflation rate substantially below the level prevailing in other countries, especially if this level is low, may simply be asking too much. In that case, a change in the exchange rate may be the only way to re-establish a sustainable external position.

The assumption that costs and prices are somewhat inflexible has a strong Keynesian flavor, although it need not rest on the rather restrictive assumptions adopted by Keynes. In Keynes’s analysis, the inflexibility of the money wage rate causes the equilibrium overall level of output to be determined by the price level. The full employment level of output is only one of the possible equilibrium states, the one that corresponds to the “right” price level given the existing money wage rate. Post-Keynesian analysis has focused on “money illusion” as a reason for the inflexibility of the money wage rate. In fact, this is only one of the reasons, and probably not the most important one. Labor legislation (e.g., minimum wage laws) and the negotiation of labor contracts at the industry or country level rather than between individual employers and employees restrict even more the flexibility of the money wage rate.3

While costs and prices in local currency are somewhat inflexible, there is nevertheless a tendency for costs and prices to be adjusted so as to offset sudden exchange rate changes that may be the result of a policy decision, under a pegged exchange rate system, or of a shock in the financial asset markets, under a floating exchange rate system. The effect of a change in the exchange rate on a country’s external position will depend on how strong this feedback effect is. If, for example, a depreciation tends to be automatically offset by an increase in the money wage rate, profit margins, and prices, the authorities of a country faced with an unsustainable trade deficit would be left with an unhappy choice—either let the money supply rise to accommodate the wage-price increase resulting from the depreciation, in which case they would be back to square one after experiencing a temporary increase in inflation, or refuse to accommodate the wage-price increase, in which case they would arrive at the same unemployment rate that they would have had if they had chosen to reduce nominal domestic demand rather than let the exchange rate depreciate. Clearly, if the real prices of the factors of production are inflexible, no adjustment at the full employment level is possible, with or without an exchange rate change.

There is no doubt that the recent period of high inflation has greatly increased the tendency for changes in domestic costs and prices to offset automatically a change in the exchange rate. Money illusion may still prevail, but it has certainly been greatly reduced. Cost-of-living indexation clauses in labor contracts have also become widespread. At the same time, there is no doubt that, even under present conditions, it remains true for most industrial countries that changes in exchange rates are not immediately and fully offset. The evidence presented in Chart 1 on the changes in exchange rates and relative overall levels of factor prices (that is, the gross domestic product (GDP) deflators) among industrial countries during 1967-79 shows clearly that changes in exchange rates lead to sustained changes in relative factor prices among countries.

Chart 1.
Chart 1.

Five Industrial Countries: Nominal and Real Effective Exchange Rates, 1967-79

(1967=100)

Citation: IMF Staff Papers 1981, 002; 10.5089/9781451946871.024.A002

Source: International Monetary Fund, International Financial Statistics, various issues.1 Indices of effective exchange rates refer to relative GDP deflators adjusted for variations in exchange rates.

In practice, the degree of automatic offset depends on conditions specific to each country. The MERM does take into account these conditions in calculating offsetting changes in prices and costs. The model estimates the effects of exchange rate changes on the costs of production and prices of domestically produced goods resulting from changes in the local currency prices of imported raw materials, fuels, and other intermediate goods. The model also takes into account the fact that the money wage rate, profit margins, and even indirect taxes are adjusted to offset changes in the cost of living and, more generally, changes in prices in the goods markets. Such adjustments lead to a series of cost and price increases. The money wage rate, profit margins, and indirect taxes are not, however, assumed to offset fully variations in prices in the goods markets, so that the chain of cost-price adjustments converges to a solution that does not imply that exchange rate changes are fully offset within the two-to three-year period considered. The size of the offset varies from country to country, depending on the degree of wage indexation, the openness of the economy, and so forth.

The second major assumption used in the MERM is that the price elasticities of demand for the goods produced by the various countries are finite, so that purchasing power parity (PPP) does not hold. The view behind this assumption is that one of the major effects of an exchange rate change is to cause a limited shift in demand among the similar, but differentiated, goods produced by various countries. For example, an appreciation of the deutsche mark will tend to increase prices of German automobiles relative to prices of automobiles produced by other countries, and this will lead to a shift in demand in the Federal Republic of Germany and in the rest of the world, from German automobiles to automobiles produced by other countries. Even for a substantial relative price increase, however, the demand for German automobiles will not vanish completely; in fact, experience shows that the fall in demand may not be all that large. A number of other kinds of relative price effects are also taken into account in the MERM, but they play a secondary role. For example, demand can be shifted from one broad group of commodities to another as a result of a change in the relative prices of these commodity groups. In particular, a change in the exchange rate may lead to a change in the price of traded goods relative to nontraded goods and a change in the pattern of demand between these two groups of goods in a given country.4 On the supply side, changes in relative prices may also lead to a change in the structure of the economy, with a shift of resources between the traded goods and the nontraded goods sectors. Shifts in demand and supply among broad groups of goods and economic sectors are, however, seen as being relatively small during the medium-term period considered here.

While the MERM focuses on the role played by relative prices in the goods markets, it does not rest on a partial equilibrium approach, as does the simple price elasticity approach to the analysis of exchange rate effects. On the contrary, the main characteristic of the MERM is its general equilibrium aspect—all goods markets for traded and nontraded goods are taken into account. A well-defined government policy is also specified. Thus, the analysis of relative price changes made in the MERM is consistent with the absorption approach or the monetary approach to the balance of payments.5

The third assumption, that the level of nominal final domestic demand can be influenced by the central authorities, is the basis for the proposition that the central authorities use monetary and fiscal policies to offset whatever effect an exchange rate change may have on the overall level of economic activity in real terms. Thus, domestic absorption in money terms is “controlled,” so that the expenditure-switching effects that result from the changes in relative prices induced by the exchange rate change are not accompanied by an increase or decrease in the total (domestic and foreign) aggregate demand for domestically produced goods in real terms.

This last assumption regarding the control of the central authorities over the level of domestic final expenditure contrasts sharply with much of modern balance of payments theory, which focuses on the effect of a change in the exchange rate on the level of nominal final domestic demand. This effect is not analyzed in the MERM. The idea is that central authorities have more efficient policy tools than the exchange rate to influence the level of nominal final domestic demand; consequently, what is important about a change in the exchange rate is not its impact on nominal final domestic demand but its effect on the allocation of demand. In the MERM, a devaluation, for example, is not seen as a means of cutting the level of real absorption per se; it is viewed as a means whereby a cut in the level of real domestic absorption, resulting from restrictive monetary or fiscal policy, can be achieved without an accompanying fall in the level of economic activity and a rise in unemployment induced by price inflexibility in the factor markets. The devaluation substitutes foreign demand for domestic demand at the “right time,” despite the inflexibility of domestic prices and costs. This allows the restrictive demand management policy to lead to a smooth transfer of resources from the domestic to the foreign sector without the adjustment costs and dislocation that might result from the restrictive policy alone. Rather than focusing upon hypothetical exchange rate effects on nominal final domestic demand, the MERM is used to estimate the extent to which domestic demand should be changed in order to maintain real output under different assumptions about the exchange rate and, in each case, to explain the implications for the trade balance.

II. Disaggregation of Goods and the Components of Final Demand

In the original version of the MERM, five goods, or commodity classes, were considered (shown with the Standard International Trade Classification (SITC) number): agricultural commodities (SITCs 0-1); raw materials (SITCs 2 and 4); mineral fuels (SITC 3); manufactures (SITCs 5-9); and nontraded commodities (commodities and services that are not internationally traded). These commodity classes were further divided into those satisfying final demand—agricultural commodities, manufactures, and nontraded commodities—and those satisfying intermediate demand—raw materials and mineral fuels.

The demand in a particular country for a good going to domestic final demand was then related to the level of domestic final demand in that country and the prices of the three goods satisfying final demand. Similarly, the demand in a particular country for each good satisfying intermediate demand was related to total real output in that country and the prices of the two intermediate goods.

As noted in Artus and Rhomberg (1973), the classification of goods as going to final demand or going to intermediate demand was rather arbitrary, since each good usually satisfies both intermediate and final demand. Furthermore, the lack of disaggregation of domestic final demand into private consumption, private gross investment, and government expenditures made it impossible to analyze the effects on imports of the changes in the composition of domestic final demand that might result from, or accompany, a change in exchange rates. These effects are important because the different components of domestic final demand tend to have different direct and indirect import contents.6

In MERM 2, the simplifications described previously have been modified to make the model more realistic and to increase its usefulness for policy simulations. A distinction is now made between semifinished manufactures and finished manufactures so that the model includes six goods: agricultural commodities (SITCs 0-1), raw materials (SITCs 2 and 4), mineral fuels (SITC 3), semifinished manufactures (SITCs 5-6), finished manufactures (SITCs 7-9), and nontraded commodities.7 Each good satisfies both intermediate demand and final demand, and detailed data on the input-output structure of each country are taken into account in the specification of the system of demand equations. Further, domestic final demand is divided into its components—private consumption, private gross investment, and government expenditures. As a result, restrictions can be placed on any or all components of domestic final demand, and the effects of exchange rate changes can be simulated under these restrictions. This enables the model to be used for a wide range of policy alternatives—for example, a cut in private consumption rather than investment as part of a devaluation package.

One might argue that an even more disaggregated classification of the various commodities might be needed for the proper specification of the demand and supply side of the model. A disaggregation at the industry level, in particular, would allow for a better specification of the effects of changes in relative prices on market shares. After all, it is difficult to speak of the price elasticity of demand for “French semifinished manufactures” because this group of commodities includes such diverse items as steel, chemicals, and textiles. Similarly, a classification at the industry level would allow for a more precise specification of the input-output relationships on the supply side. The difficulty with this kind of disaggregation, however, is that it requires an amount of knowledge about microeconomic relationships that we do not have. In particular, there is a large amount of information about import and export price elasticities for the various countries for broad categories of commodities such as foodstuffs, raw materials, and semifinished manufactures, but the amount of information on foreign trade price elasticities at the industry level is small or nonexistent for most of the industrial countries. For this reason, the present model remains at a fairly aggregate level.

III. Demand Equations

The demand equations in MERM 2 remain based on the theoretical framework developed by Armington (1969) for products distinguished by place of production. In this framework, commodities are distinguished by kind and by country of production. MERM 2 presently distinguishes 20 countries or groups of countries,8 each of which produces 6 goods. In Armington’s (1969) terminology, a kind of commodity, such as finished manufactures, is a good. Furthermore, a good produced by a particular country is a product—that is, German finished manufactures and Japanese finished manufactures are the same good but different products. Products are assumed to be imperfect substitutes for each other. The demand for a product in a particular market is determined by a two-step procedure. First, the demand for the good in general is derived by maximizing utility subject to a budget constraint. Second, the demand for the product is determined by minimizing the cost of purchasing the amount of the good derived in the first step, subject to a linear homogeneous utility index.9

In MERM 2, the determination of the demand for a good in general is modified to take into account the input-output structure of each country. The amounts of a good used for intermediate demand, government expenditures, and gross private investment are determined by fixed coefficients that represent the proportions of these three types of expenditures spent on the good considered in the base period. The fixed coefficients are derived from detailed input-output tables for each country. The amount of a good used for private consumption depends upon the level of total expenditures on private consumption and the relative prices of all goods. The form of the demand equation for good i in country k is

Dik=Σn=16ainkQnk+bik antilog[ɛikln(Ck)+Σn=16η¯i/nkln(Pnk)]+cikGk+dikIk(1)

where i, n = 1, 2, …,6 (goods)

k = 1, 2, …,20 (countries)

and where for a given country k,

Dik = total domestic demand (in real terms) for good i

Qnk = total real output of good n

Ck = total real private consumption

Gk = total real government expenditure

Ik = total real gross private investment

Pnk = price of good n

aink = proportion of the cost of producing good n accounted for by the intermediate demand for good i in the base period

bik = proportion of private consumption spent on good i in the base period multiplied by C¯/C¯ɛik, where C denotes the level of real private consumption in the base period

cik = proportion of government expenditure spent on good i in the base period

dik = proportion of gross private fixed investment spent on good i in the base period

ɛik = expenditure elasticity (in volume terms) for good i

η¯i/nk = price elasticity of demand (in volume terms) for good n with respect to the price of good n

In the second step, the demand for a specific product ij (namely, good i produced by country j) in country k is related to the total demand for good i in country k, Dik, and to the prices of the various products of the same kind in country k Pilk,. The form of the equation is

Dijk=fijk antilog[ln(Dik)+Σlη¯ij/ilkln(Pilk)](2)

where i = 1, 2, . . . , 6 (goods)

j,k,l = 1, 2, . . . ,20 (countries)

and where, for a given country k,

Dijk = demand (in real terms) for product ij

fijk = share of good i supplied by country j in the total supply of good i in the base year

Pilk = price of good i produced by country l

η¯ij/ilk = price elasticity of demand (in volume terms) in country k for good i produced by country j with respect to the price of good i produced by country l

All variables in equations (1) and (2) are expressed in the same numeraire currency (the U. S. dollar in the present model). The variables Dik,Dijk,Qnk,Ck, Gk and Ik are all expressed in constant 1977 dollars. The price variables are in index form (1977 = 1.00).

The price index for good n in market k,(Pnk), is defined as a geometrical average of the price indices of the various products of the same kind, (Pnlk), where the weights are based on the expenditure shares in market k,

Pnk= antilog[Σtsdnlkln(Pnlk)]

where sdnlk = share of good n supplied by country l in country k’s total expenditure on good n.

There are 2,400 (20 markets with 6 × 20 = 120 products in each market) product demand functions in MERM 2, each of which has 6 direct-price and cross-price elasticities for goods and 20 direct-price and cross-price elasticities for products. Estimation of so many parameters is impractical, given the length and quality of available price series.

An alternative approach is to impose restrictions on the relevant utility functions that will enable one to derive the price elasticities from a small number of basic parameters, which can then be estimated econometrically or chosen a priori. In order to derive price elasticities of demand for goods entering private consumption, restrictions must be placed on the utility function that governs choices among goods. By assuming good i is want-independent of all other goods, Frisch (1959)10 derived a method of computing the compensated direct-price and cross-price elasticities of demand for goods that relies on the Frisch Coefficient, a measure of the “flexibility of the marginal utility of money,” expenditure elasticities, and the shares of the various goods in demand. The assumption of want-independence becomes increasingly unrealistic at lower levels of aggregation; however, since the level of aggregation used in MERM 2 is high, this assumption is a reasonable one.

Parametrization of the compensated price elasticities of demand for product ij with respect to product il in market k has been described in detail by Armington in the appendix to the article by Artus and Rhomberg (1973). The parametrization is based on specifying a CRESH (constant ratio of elasticities of substitution production functions that are homothetic or homogeneous) index function 11 as the utility index governing choices among products of the same kind. Parameters of the CRESH index measure the substitutability of product il for all other products in a particular market. If these parameters are assumed to be the same in each foreign market (they may be different in the home market), then they can be derived from import and export price elasticities of demand and trade shares. Given the CRESH parameters, the direct-price and cross-price elasticities of demand for products can be computed.

Empirical estimates of the import and export price elasticities of demand for each good in each country are obtained from econometric studies, and the CRESH parameters are derived. These parameters are then used to compute the price elasticities, η¯ij/ilk andη¯ij/ijk. Where reliable empirical estimates of the direct-price and cross-price elasticities of demand for products exist, these estimates override the calculated elasticities, and the remaining calculated elasticities are then adjusted for consistency. A priori information about the institutional structure of the market for some goods and/or products and the substitutability of goods or products is also taken into account.

IV. Supply Equations and Price Identities

The specification of the supply equations has remained unchanged from the 1973 version of MERM, except for use of a log-linear relationship between variables expressed in level form rather than the specification of a linear relationship between variables expressed as proportionate changes. In a given country j, the supply of product ij in volume terms, namely Qij is expressed as

Qij=hij antilog[Σnαij/njln(pnj/Snj)]Tj(4)

where αij/nj = price elasticity of supply (in volume terms) of product ij with respect to the price of product nj

pnj = price of product nj expressed in local currency

Snj = average cost indicator for product nj based on the local currency price of the factors of production

Tj = value of country j’s currency in terms of the numeraire currency

A further parametrization of the supply side assumes that 12

αij/ij=VijΦj+γij(γjVijγij)(5)

and

αij/nj=Vnj(Φjγijγnj),ni(6)

where Vij = share of value added in sector ij in the total gross domestic product in country j

Φj = aggregate supply elasticity

γij = factor mobility of sector i relative to all other sectors in country j

γj = aggregate coefficient of factor mobility such that

γj=ΣiVijγij

One can easily verify that Φj is equal to the aggregate supply elasticity in country j, that is,

ΣiVij(Σnαij/nj)=Φj(7)

As long as prices are somewhat inflexible,Φj is always strictly positive. Its magnitude reflects the extent of the trade-off between higher prices and higher activity levels in country j. Whenever the model is used to simulate effects of various policies under the constraint that the overall activity level does not change, the absolute magnitude of Φj is not important. However, for stability purposes, the slope of the aggregate supply curve must be sufficiently elastic to enable the model to converge.

The parameter γj measures the degree of factor mobility in country j. The parameter γj is usually assumed to be rather small because of the relatively short period of time considered here (only two to three years). For all practical purposes, exchange rate effects are considered to lead to a reallocation of the output of the various sectors between the home market and foreign markets rather than to a reallocation of the factors of production among sectors. In this sense, it can be said that the model is still focused on the macroeconomic, rather than microeconomic, aspects of a change in the exchange rate.

The parameter γij reflects the relative factor mobility of a particular sector. There is no doubt that, in the medium term, it is easier to move factors into and out of some sectors than others. In the applications presented below, it has been assumed that the greatest resource transfers will occur among the non-traded goods sector and the two manufacturing sectors. Specifically, factor mobility in these three sectors has been assumed to be twice as high as it is in the three other sectors—agriculture, raw materials, and fuels.

On the supply side, even more than on the demand side, the values of the parameters are not seen as being invariant in the face of policy changes. For example, the degree of factor mobility will depend on the particular policy package that is implemented. Factor mobility may be increased by use of fiscal incentives or by policies to engineer a short recession. This, of course, complicates the lives of model builders, since econometric estimates based on certain historical samples provide little guidance in this context. In recent applications, the parameters have been chosen on what remains an ad hoc basis. However, as mentioned above, if the time horizon considered is relatively short, the magnitudes of the cross-price elasticities are expected to be small. This expectation, along with consideration of the stability properties of the system, has guided the choice of supply parameters.

The cost indicators are specified by taking into account the whole input-output structure of each country, specifically, 13

ln(Sij)=Σnspnijln(Pnj/Tj)+spwijln(Wj)+sprijln(Rj)+spixijln(TXj)(8)

where spnij = share of good n (as an input) in the total cost of production in the yth sector; analogously, spwij,sprij,andsptxij represent the shares of wages, capital, and taxes, respectively, in the cost of the ijth sector

Tj = value of country j’s currency measured in the numeraire currency

Pij = price of good i in country j measured in the numeraire currency

Wj = money wage rate in the jth country (in index form)

Rj = rental price of capital in the jth country (in index form)

TXj = (net) tax payments in the jth country (in index form)

The prices of the factors of production—labor, capital, and government services—are decomposed into two analytical components. The first one expresses their sensitivity to other relevant prices, while the second one accounts for exogenous factors. These relationships are specified as follows:

ln(Wj)=wjln(COLj)+ln(WFj)(9)
ln(Rj)=rjln(DINVj)+ln(RFj)(10)
ln(TXj)=rjln(DDDj)+ln(TFj)(11)

where, for each country j,

COLj = consumer price index

DINVj = investment deflator index

DDDj = domestic demand deflator index

wj, rj, and tj = feedback parameters

and where WFj RFj, and TFj are exogenous factors that affect the prices of the factors of production.

The consumer price index and the deflators of investment and domestic demand are endogenous variables calculated as weighted averages of the prices of the relevant products.

Some work has been done to estimate the sensitivity of the prices of the factors of production to price variations in the goods markets. However, here again, there is no particular reason to assume that such coefficients would not be affected by policy changes; therefore, ad hoc judgments have been just as important as econometric estimates based on historical data in influencing the choice of the particular values retained for the simulation of a given policy package.

As in the 1973 model, the price identities

Pij=pijTj(12)

relate prices in local currencies, pij, and prices in the numeraire currency, Pij, and the market equilibrium equations

Dij=Qij(13)

stipulate that, ex post, demand and supply for the various products must be equal.

To conclude the presentation of the model, it must be noted that no distinction is made between the foreign and domestic price of a product. Specifically, the possibilities of trade contracts being denominated in foreign currencies, of price discrimination among various markets, or of other mechanisms that may cause the domestic price to differ from the foreign price are not taken into account, and this may be unrealistic in some cases.14

Furthermore, two modifications to the general structure of the model have been introduced on an ad hoc basis to enhance its policy relevance. First, the price of oil for all countries is assumed to be equal to the price of oil for the oil exporting countries; in turn, the price of oil for the oil exporting countries is assumed to be proportionate to the average price of the products imported by these countries. Second, for the countries grouped in the rest of the world, prices of their agricultural goods and raw materials are assumed to be proportionate to the average price of their total imports.

V. Applications of the Model

The model, consisting of the preceding equations, needs one more equation in order to be closed. The choice of the equation depends on the intended application of the model. The applications considered in this section relate to the use of the model as a tool of analysis to study the effects of exchange rate changes, and for this purpose the model is closed by constraining the overall level of output in each country to remain unchanged. This constraint permits isolation of the effects of a change in exchange rates. Alternatively, a constraint can be imposed on the components of final domestic demand in the various countries and the model used to calculate implications of these constraints on aggregate output and trade balances under different hypotheses as to exchange rates. However, not much work has been done on this second line of potential applications.

The main behavioral parameters used in the model are the foreign trade price elasticities and the proportions of the relevant domestic demand deflators that are automatically reflected in a change in wages, capital costs, and taxes. The trade price elasticities used in recent applications of the model are presented in Table 1. Such elasticities refer to trade effects after a period of adjustment of two to three years. They are based on various empirical studies made by the Fund staff as well as on the results presented by Stern and others (1976) in their overall review of existing empirical estimates of price elasticities. These elasticities, along with the other parameters of the model presented here, are illustrative rather than definitive; the final choice of parameters reflects the judgment of the user and is strongly influenced by the specific policy package under consideration.

Table 1.

Foreign Trade Price Elasticities1

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Price elasticities referring to a three-year period.

In the applications shown later on, two sets of feedback parameters have been assumed for illustrative purposes. The first set of parameters corresponds to low-feedback effects and the second to high-feedback effects. Specifically, in the low-feedback simulations, the feedbacks of the consumer price index on wages and the domestic demand deflator on taxes are both assumed to be 0.50, and the feedback of the investment deflator on the return to capital is assumed to be 0.30. In the high-feedback simulations, these parameters are assumed to be 0.85 and 0.70, respectively. Again, the choice of parameters is meant to be illustrative. The feedback effects are, in fact, thought to be higher for some countries than for others because of general indexation or other considerations. In actual practice, the choice of parameters would take into account various a priori considerations, such as the current policy stance, in addition to available empirical evidence.

Other parameters included in the model are the expenditure elasticities for the various categories of goods and the supply parameters. The expenditure elasticities for all countries have been taken to be 1.0 for crude materials, fuels, and nontraded goods; 0.75 for food; and 1.25 for semifinished and finished manufactures. The supply parameters ϕ and γ have been taken to be 1.25 and 1.50, respectively, for all countries. The input-output coefficients used in the cost indicator equations were obtained from input-output tables available for various years, namely, Australia for 1974-75; Austria, Belgium, France, the Federal Republic of Germany, Italy, Japan, the Netherlands, and the United Kingdom for 1970; Ireland and Sweden for 1968; the United States for 1967; Canada and Denmark for 1966; Finland for 1965; Norway for 1964; and Spain for 1962. The Austrian table was used for Switzerland, a country for which no input-output table could be found.

A few applications of the model are presented here for illustration. Tables 2 and 3 show the medium-term effects of an isolated change in the exchange rate of a country on the value and volume of its trade flows, its import and export prices, its trade balance, and its GDP deflator. The last column shows the reduction in final domestic expenditure in real terms required to keep the level of output constant in each country. For all countries, the 10 per cent devaluation leads to an improvement in the trade balance—that is, any perverse short-run effects disappear after the assumed adjustment period of about three years. The cost in terms of domestic price increases is between 1.4 and 3.0 per cent in the low-feedback simulations shown in Table 2 and between 3.9 and 6.8 in the high-feedback simulations shown in Table 3. In general, the variations in domestic prices correspond to the degree of openness of the countries. Also, the terms of trade deteriorate as export prices fall more than import prices in terms of foreign exchange.

Table 2.

Effects of 10 Per Cent Exchange Rate Depreciationon Trade Flowsand Pricesof Depreciating Country:1 Simulationswith Low-Feedback Parameters2

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The authorities of each country are assumed to manage domestic aggregate demand so that the exchange rate change does not lead to a change in the overall level of economic activity.

Effects on the trade flows are evaluated at the scale of world trade in 1977.

For the United States, the figures relate to the effects of an 11.1 per cent revaluation of all other currencies with respect to the U.S. dollar (this is equivalent to a 10 per cent devaluation by the United States).

For these simulations, the feedback of the cost of living on wages is 50 per cent, the feedback of the investment deflator on the return to capital is 30 per cent, and the feedback of the domestic demand deflator on taxes is 50 per cent.

Table 3.

Effects of 10 Per Cent Exchange Rate Depreciationon Trade Flowsand Pricesof Depreciating Country:1 Simulationswith High-Feedback Parameters2

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The authorities of each country are assumed to manage domestic aggregate demand so that the exchange rate change does not lead to a change in the overall level of economic activity.

Effects on the trade flows are evaluated at the scale of world trade in 1977.

For the United States, the figures relate to the effects of an 11.1 per cent revaluation of all other currencies with respect to the U.S. dollar (this is equivalent to a 10 per cent devaluation by the United States).

For these simulations, the feedback of the cost of living on wages is 85 per cent, the feedback of the investment deflator on the return to capital is 70 per cent, and the feedback of the domestic demand deflator on taxes is 85 per cent.

Results presented in the previous paper, Artus and Rhomberg (1973), were based on a 75 per cent feedback of changes in the consumer price index on wages and taxes only, and, therefore, it is difficult to make a direct comparison with the results shown here. However, if differences in the size of trade flows between 1971 and 1977 are taken into account, the effects of exchange rate changes using the model described here are, for most countries, smaller than those derived from the original model, even in the low-feedback simulations. There are several reasons for this. The import and export price elasticities of demand have been revised downward in line with more recent empirical evidence. In addition, to these parameter changes, the new distinction between semifinished and finished manufactures and the respecification of the demand equations to include both intermediate and final demand for each good have further reduced the estimated effects of exchange rate changes. In particular, the recognition that the demand for imported semifinished manufactures is related to the level of output in the various sectors rather than only to the level of final domestic demand, as previously assumed, has caused a reduction in the estimated effects of exchange rate changes on imports, since in the simulations, the overall level of output does not change while the level of domestic demand is reduced. Finally, the share of oil in the value of total imports has increased tremendously. Since the import elasticity of demand for oil is low, the overall import price elasticity has fallen.

In Table 4, the trade balance effects of the simulations shown in Tables 2 and 3 have been adjusted for valuation effects 15 and have been expressed as percentages of the size of trade flows and GDP. The trade balance changes as percentages of GDP measure the impact of exchange depreciation in relation to the size of the economy, and as expected the impact is greater for the more open economies, the United Kingdom and Switzerland being exceptions, owing to their relatively low import and export price elasticities. In relation to the size of trade flows, the trade balance effects reflect mainly the price elasticities and the degree of openness of the economy, the countries with low price elasticities and highly open economies (and therefore larger feedbacks on domestic prices) showing the smallest trade balance effects.

The medium-term effects of an isolated change in the exchange rate of a country on its trade balance and the trade balances of its major trading partners are shown in Tables 5 and 6 for the low- and high-feedback simulations, respectively. Such tables have various applications. They can be used, for example, to calculate the currency realignment, versus a given numeraire currency, that is necessary to reach any particular, but consistent, set of trade balance targets. The results presented in Tables 5 and 6 can also be used to derive weights that can be employed as an alternative to simple trade weights for the calculation of effective exchange rate indicators.16

Table 4.

Effects of 10 Per Cent Exchange Rate Depreciationon Trade Balances Normalizedby Sizeof Trade Flowsand GDP1

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The effects on trade flows are evaluated f.o.b. at the scale of world trade in 1977. The size of trade flows is measured as the average of imports and exports in 1977.

The valuation effects are adjusted for by deflating the final trade balances (the trade balances resulting from a particular set of exchange rate changes) by the average changes in import and export prices for the corresponding countries (resulting from the same simulation) and subtracting the initial trade balances.

Table 5.

Trade Balance Effects of 10 Per Cent Devaluation: 1 Simulationswith Low-Feedback Parameters2

(In millions of U.S. dollars)

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Effects on trade balances are evaluated f.o.b. at the scale of world trade in 1977. For the United States, the figures relate to the effects of an 11.1 per cent revaluation of all other currencies with respect to the U.S. dollar (this is equivalent to a 10 per cent devaluation by the United States).

For these simulations, the feedback of the cost of living on wages is 50 per cent, the feedback of the investment deflator on the return to capital is 30 per cent, and the feedback of the domestic demand deflator on taxes is 50 per cent.

Table 6.

Trade Balance Effects of a 10 Per Cent Devaluation: 1 Simulationswith High-Feedback Parameters2

(In millions of U.S. dollars)

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Effects on trade balances are evaluated f.o.b. at the scale of world trade in 1977.

For the United States, the figures relate to the effects of an 11.1 per cent revaluation of all other currencies with respect to the U.S. dollar (this is equivalent to a 10 per cent devaluation by the United States).

Positive and negative zero entries indicate trade balance effects that amount to less than $500,000.

For these simulations, the feedback of the cost of living on wages is 70 per cent, the feedback of the investment deflator on the return to capital is 70 per cent, and the feedback of the domestic demand deflator on taxes is 85 per cent.

To do this, however, one must take into account the “valuation” effect that arises when countries’ trade balances are not initially in balance. For example, for a 10 per cent devaluation by the United States, Table 5 shows a change in the trade balances of France and the Federal Republic of Germany of -$1,231 million and +$400 million, respectively. At first sight, such estimates are surprising. The reason for the large differences between the two estimates is, however, quite simple—namely, France has a large initial trade deficit (about -$2.7 billion) while Germany has a large initial trade surplus (about $19.8 billion). The depreciation of the U.S. dollar leads to a general rise of goods prices expressed in dollars, and this valuation effect tends to increase both the French deficit and the German surplus expressed in dollars. The estimates to be used in calculating effective exchange rates should reflect only the real effects of exchange rate changes on trade balances—that is, the volume effects and the terms of trade effects. The valuation effects need to be eliminated by deducting from the estimates presented in Table 5 the valuation effect corresponding to the product of the initial trade balance expressed in dollars and the average increase of export and import prices in dollars. After adjusting for valuation effects in the previous examples, the changes in the trade balances of France and the Federal Republic of Germany are -$892 million and -$1,348 million, respectively. The weights derived from Table 5 to calculate effective exchange rate indicators are presented in Table 7.

Table 7.

Weights Derivedfrom Multilateral Exchange Rate Modelfor Calculationof Effective Exchange Rates1

(Based on simulations in Table 5)

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The effective exchange rate index of any country in the stub is calculated by applying the weights shown in the row for this country to the exchange rate relatives of the corresponding countries in the heading.

In order to evaluate the sensitivity of the model solutions to the choice of import and export price elasticities, a third set of simulations was carried out. In these simulations, the import and export price elasticities for semifinished manufactures and finished manufactures were decreased by 25 per cent. The results of these simulations are shown in Table 8, along with the low-and high-feedback simulations. Clearly, the results are quite sensitive to the choice of both price elasticities and feedback parameters.

Table 8.

Table 8. Sensitivity Analysis: Trade Balance Effects of a 10 Per Cent Exchange Rate Depreciation Under Alternative Assumptions1

(In millions of U.S. dollars)

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Effects on trade balances are evaluated f.o.b. at the scale of world trade in 1977. For the United States, the figures relate to the effects of an 11.1 per cent revaluation of all other currencies with respect to the U.S. dollar (this is equivalent to a 10 per cent devaluation by the United States).

For this solution, the export and import price elasticities for semifinished manufactures and finished manufactures shown in Table 1 were reduced by 25 per cent, and the feedback parameters are the same as in the low price feedback solution.

For this solution, the feedback of the cost of living on wages was assumed to be 0.85, the feedback of the investment deflator on the return to capital was assumed to be 0.70, and the feedback of the domestic demand deflator on taxes was assumed to be 0.85.