Article

An Indicator of Effective Exchange Rates for Primary Producing Countries1

Author(s):
International Monetary Fund. Research Dept.
Published Date:
January 1976
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The need, for both analytical and policy-making purposes, to represent the evolution of a given currency in terms of its total relationship to other currencies has led, in recent years, to a proliferation of methods aimed at incorporating in a single indicator of “effective” exchange rates the complex of direct and indirect influences on a currency’s value resulting from adjustments in its own as well as in other currencies’ exchange rates. Even though no one methodology is inherently superior to all others and the appropriateness of each must necessarily be judged in relation to the specific purpose for which it is needed,2 it is essential that each such measure be conceptually well defined so as to guard against inappropriate uses. We will comment briefly at a later stage on the imperfect, or even misleading, nature of the information that is occasionally implied by some of the “weighting” schemes that are often used.

The purpose of this paper is to extend to primary producing countries the analysis developed in the Fund’s multilateral exchange rate model (MERM) for industrial countries, that is, to estimate the impact of a given set of changes in exchange rates on a country’s balance of trade after an adjustment period of two or three years. Among its many applications, the model also makes it possible to estimate the effective exchange rate of the currency concerned according to the following definition, the isolated change in the exchange rate of a currency that would be equivalent in its net effect on the trade balance to the whole complex of exchange rate changes that have taken place over a period of time.3 The framework proposed here could, in fact, be viewed as an attempt to identify this effect on the trade position and, hence, on the effective exchange rate of individual primary producers, which MERM currently includes as part of the “rest of the world.”

The paper has two parts. Section I presents the main features of the model, and Section II discusses the application of the model to two primary producing countries—Zaïre and Zambia.

I. Main Features of the Model

EXPORTS

The limited number of products that, in many cases, account for a large portion of a primary producer’s export receipts makes feasible the adoption of a commodity-by-commodity approach in assessing the impact of exchange rate changes on a given country’s export receipts. The general framework adopted here and outlined later is the one suggested by Ridler and Yandle.4 This “partial equilibrium” framework, by defining exchange rate changes as shifts in world demand and supply for a given commodity, allows us to investigate the effect of these changes on the commodity’s price in world markets and, given each supplier’s responsiveness to price changes, to identify the effect on the export receipts of individual producers.

If we let Qmi and Qxi represent, respectively, the volume of world imports and exports of the ith commodity; Pmi, Pxi and Pi the world price of this commodity in importers’, exporters’, and the numeraire currencies, respectively; and Tr and Tk the exchange rate of importers’ and exporters’ currencies, respectively, vis-à-vis the numeraire currency, world trade in the ith commodity could be represented by the following simplified model

In the model, equation (1) is the world demand function and equation (2) is the supply function for trade in the ith commodity, equation (3) is the market clearing condition, and equation (4) is the definitional relationship between prices that must obtain at equilibrium.5 Solving the above for the proportionate change in the world price of the ith commodity (expressed in the numeraire currency) resulting from a given set of changes in the exchange rates of importers and exporters of the commodity, we get

whereK˙=ΣjVixJTj˙is the weighted average percentage change in exporters’ exchange rates in terms of the numeraire currency with weights (Vi,xj) equal to the share of each country in total exports of the commodity
R˙=ΣjVi,mJTj˙is the weighted average percentage change in importers’ exchange rates in terms of the numeraire currency with weights (Vi,mj) equal to the share of each country in world imports of the commodity
andηsi,ηdiare the world price elasticity of supply and demand, respectively, for trade in the ith commodity.

If we then write the percentage change in k’s export earnings (in the numeraire currency) from the ith commodity as the sum of percentage changes in price and volume exported (equal to k’s supply elasticity multiplied by the percentage change in price measured in domestic currency), that is,

and the percentage change in total export earnings as

equal to the weighted average of percentage changes in the value of individual exports, with weights (ωi,xk) equal to the share of each commodity in total export earnings, equations (5) and (7) can then be used to evaluate the impact of all exchange rate changes (including its own) on k’s export earnings.6

IMPORTS

The impact of exchange rate changes on expenditures for imports can be separated conceptually into two distinct components, namely, the induced effect of changes in export receipts on domestic expenditures (and, hence, on imports) and the effect of changes in the price of imports. The framework outlined later specifies these two components as exogenous disturbances in a simple income determination system, resulting in an adjustment of the main economic aggregates, including imports.

The behavioral equation describing the demand for imports specifies real imports to be a function of real expenditures only. It thus leaves out the relative price term(s) representing the “pure” substitution between imports and domestically produced substitutes on the assumption that, in most developing countries, technological and/or institutional limitations effectively reduce this competition to an order of magnitude small enough that its exclusion does not hamper the analytical ability of the suggested framework.7 Under this assumption, the adopted specification can be shown to be consistent with the framework developed in MERM8 and based on the earlier work of Armington (1969), who suggests that products are differentiated not only by their kind (MERM, in fact, distinguishes between five kinds of goods, namely, manufactures, food and beverages, crude materials, mineral fuels, and a nontraded good) but also by their origin (French and Canadian agricultural commodities, for example, being of the same kind but two different products competing against each other and other products in every market). As a result, quantification of the second exogenous disturbance, that is, the effect on import prices resulting from all exchange rate changes that have taken place over a given period of time, can be achieved by using intermediate results generated by MERM (viz., the change in export prices, with detail by commodity, of the country’s trade partners resulting from these exchange rate changes) and the country’s trade matrix showing the origin and composition of its imports.

The import-demand equation may then be used in conjunction with a national income identity and an expenditure equation in a simplified model of income determination to be solved for the percentage changes in income (k), domestic expenditure (k) and imports measured in domestic currency (k − Ṫk).9

National income identity

Domestic expenditure equation

Import equation

whereαrepresents the ratio of the variable in subscript to income
ηrepresents the elasticity of the first with respect to the second variable in subscript

and where

VariableMERM Equivalent1Definition
P˙MKΣi=1m1ωki,MΣJKSi,Jk1SikkP˙ij(weighted) Average percentage change in import prices (in the numeraire currency)
P˙kΣi=1mSikΣjSijk(P˙ijT˙k)Percentage change in the deflator of total domestic demand (in local currency)
ηm, dΣi=1m1ωi,MkεikAggregate expenditure elasticity of demand for imports

See the Appendix for definition of terms. The expression for m is the one used to evaluate the change in import prices induced by a given set of changes in exchange rates.

See the Appendix for definition of terms. The expression for m is the one used to evaluate the change in import prices induced by a given set of changes in exchange rates.

Solving the foregoing system of equations for (k − Ṫk) we get

which can be readily solved for the proportionate change in the value of imports measured in the numeraire currency, k.

BALANCE OF TRADE AND SOLUTION FOR EFFECTIVE EXCHANGE RATE

The net effect on the kth country’s trade balance (measured in the numeraire currency) resulting from given percentage changes in the value of its imports and exports can be written as

whereX0kand M0k represent, respectively, levels of exports and imports in the reference period. Substituting for k from equation (7) and for k from equation (11), the balance of trade equation can be rewritten more explicitly as

from which the change in the trade balance resulting from all exchange rate changes that have taken place over a given period of time can be computed, provided that the relevant elasticities (ηM, D,ηD, Y) and price changes of exports (calculated for each major commodity from equation (5)), imports (calculated from changes in export prices of trade partners as outlined previously), and domestically produced and consumed goods 10 are known.

The resulting change in the kth country’s trade balance (which is now a known magnitude, say Δβ¯k)may then be used to estimate the isolated change in the kth country’s exchange rate ((T˙k*)) that would have had the same effect on its trade balance, that is, the change in the effective exchange rate. This is done by setting all the js other than k equal to zero and solving the resulting equation for the k that will produce the same Δβ¯k.11

where

The resulting T˙k*, the “notional uniform” change in the country’s effective exchange rate, could also be interpreted as the converse of the change in the kth country’s exchange rate that would have offset the effect on its trade balance of all rate changes (including its own) introduced during the period. It should be noted that this effect could be asymmetric in that the objective of offsetting the effect on the trade balance may not, and in general will not, lead to an identical reversal of individual import and export flows. This would be true especially for smaller countries, which are unable to alter world prices for their exports and would have to offset this effect mostly from the import side.

Application of the model to Zaïre and Zambia proceeds step by step, as outlined earlier, to illustrate the effect of exchange rate changes on the relevant economic magnitudes (prices, revenues, payments). Alternatively, and to simplify repetitive application of the preceding formula, a set of weights could have been derived to directly combine changes in the exchange rate of all foreign currencies into the desired effective exchange rate index for the country under study. The weights, obtained from simulation of the foregoing model, would be equal to the relative effect of a change in the exchange rate of each foreign currency on the trade balance of the country under study.

II. Application of the Model

ZAÏRE

The parameter values required for application of the model to Zaïre were obtained as follows. All three equations—(15), (16), and (17)—were estimated by 2SLS (as part of an overall income determination model) modified for the nonlinearity of the system.12

Import function:

whereFEA=foreign exchange available equal to the sum of aid and export receipts less payments for factor income
D62-66=1 for the period 1962-66
=0 otherwise

Imports are seen to be a positive function of domestic demand and a negative function of restrictive licensing (over the period when controls were applied). The bracketed term represents the reaction function of the authorities as regards the refusal of import licenses, which is, itself, negatively related to the purchasing value of exchange receipts. Consumption function:

The consumption function was estimated over a shorter period than the import function because of data problems. For the same reason, income rather than disposable income had to be treated as the right-hand side endogenous variable in the first stage of the estimation procedure, thus making tax receipts exogenous.

Domestic price equation:

where Y/PY¯, the “normal” real gross domestic product, is assumed to increase at a constant rate over time.

The price of domestically produced and consumed goods 13 is thus seen to be a positive function of import prices and the ratio of actual to “normal” output, increasing faster or slower than normally as output increases faster or slower than usual. The inverse of the coefficient on the latter variable, in fact, can be shown to provide an estimate of the elasticity of supply for the economy as a whole.14

The supply and demand elasticity parameters required for the evaluation of changes in export prices and/or receipts were given the following values:

World
SupplyDemandZaïre’s Domestic Supply
123123123
yearyearsyearsyearyearsyearsyearyearsyears
Copper0.160.240.37−0.11−0.27−0.350.1730.2970.387
Cobalt***−0.32−0.55−0.79***
Coffee0.210.31−0.60−0.60−0.600.2390.325
Manufactures******0.3800.6100.750
Other******0.1600.250
* Not required.
* Not required.

Price elasticity values for copper, cobalt, and coffee were obtained mostly from recent econometric studies.15 The domestic supply elasticity for coffee is the elasticity value for Africa rather than for Zaïre itself, for which no satisfactory results were obtained. No supply elasticities were required for cobalt, which, as mentioned in footnote 5, was analyzed in the context of a dominant supplier (Zaïre) maximizing its profits subject to world demand and the supply response of other producers.16 Domestic supply elasticities for “manufactures” and “other” exports were derived from the overall supply elasticity implicit in the above-mentioned domestic price equation and the relative elasticities of supply for manufactures, agricultural products, and primary products used in MERM; speeds of adjustment were set arbitrarily. Changes in the prices of these products induced by exchange rate adjustments were assumed to be equal to the changes in export prices of “food,” “other primary materials,” and “manufactures” generated by MERM for the category, “the rest of the world.”

The weighted average percentage changes in exporters’ (K˙) and importers’ (Ṙ) exchange rates relative to the numeraire currency (the U.S. dollar) as well as the induced changes in world prices and Zaïre’s export receipts are shown in Tables 1, 2, and 3, respectively. Percentage changes in prices and export receipts are shown after one, two, and three years, since the nonstatic nature of the model postulated earlier requires that it be solved dynamically to yield a solution after three years.

Table 1.Zaire: Weighted Average Percentage Changes in Importers’ and Exporters’ Exchange Rates Relative to the U. S. Dollar, Second Half 1971-First Quarter 1975(In per cent over the preceding period)
SecondFirstSecondFirstSecondFirstSecondFirst
HalfHalfHalfHalfHalfHalfHalfQuarter
Product19711972197219731973197419741975
Importers’ Currencies
Copper2.905.12−0.566.303.91−4.48−0.363.37
Coffee2.023.354.734.44−3.300.943.71
Cobalt2.163.92−0.844.982.77−3.04−0.332.63
Exporters’’ Currencies
Copper10.850.560.572.232.88−2.32−5.89−0.94
Coffee−2.39−1.281.711.48−4.64−2.84−0.78

The approach suggested by Ridler and Yandle (1972) postulates that changes in exchange rates are fully reflected in relative prices. Even though this may be a reasonable simplification if the changes are small enough, it clearly becomes unrealistic for large changes—in. particular, for exporters, if mechanisms exist that link production costs to such changes in exchange rates either directly or indirectly (for example, through their effect on domestic inflation). The “supply shift” effect of Chile’s devaluations was modified accordingly to take into account the increases in production costs (from imported and domestically produced materials and supplies, and wages in the copper mining industry) related to the devaluations as well as the application by the Chilean authorities of a special exchange rate for copper. If we let Ṫc represent the percentage change in the dollar/escudo rate and T˙euc the percentage change in the rate applying to copper exports, the supply shift effect of the Chilean devaluations was set equal to ηs(αT˙cucT˙c), where α was given the value of 0.87 over the period 1971-73 and of 0.78 in 1974, when wages were not adjusted fully for domestic inflation.

The approach suggested by Ridler and Yandle (1972) postulates that changes in exchange rates are fully reflected in relative prices. Even though this may be a reasonable simplification if the changes are small enough, it clearly becomes unrealistic for large changes—in. particular, for exporters, if mechanisms exist that link production costs to such changes in exchange rates either directly or indirectly (for example, through their effect on domestic inflation). The “supply shift” effect of Chile’s devaluations was modified accordingly to take into account the increases in production costs (from imported and domestically produced materials and supplies, and wages in the copper mining industry) related to the devaluations as well as the application by the Chilean authorities of a special exchange rate for copper. If we let Ṫc represent the percentage change in the dollar/escudo rate and T˙euc the percentage change in the rate applying to copper exports, the supply shift effect of the Chilean devaluations was set equal to ηs(αT˙cucT˙c), where α was given the value of 0.87 over the period 1971-73 and of 0.78 in 1974, when wages were not adjusted fully for domestic inflation.

Table 2.Table 2. Zaïre: Notional Changes in World Export Prices Expressed in U.S. Dollars, Second Half 1971-First Quarter 1975(In per cent over the preceding period)
EffectSecondFirstSecondFirstSecondFirstSecondFirst
AfterHalfHalfHalfHalfHalfHalfHalfQuarter
ProductYear19711972197219731973197419741975
Copper11.692.440.113.893.30−3.20−3.640.82
21.942.97−0.034.383.43−3.46−2.961.34
31.852.780.024.213.38−3.37−3.201.16
Coffee12.023.354.734.44−3.300.943.71
20.882.48−0.333.953.67−3.65−0.042.55
30.522.21−0.443.703.43−3.76−0.352.18
Cobalt10.320.59−0.130.750.42−0.46−0.050.39
20.510.92−0.201.170.65−0.71−0.080.61
30.661.19−0.261.510.84−0.92−0.100.80
Other agricultural commodities2.604.81−0.215.753.60−3.750.030.55
Other primary commodities2.554.73−0.135.683.61−3.600.040.86
Manufactures2.454.50−0.175.513.53−3.440.021.27
Total111.732.990.014.173.24−3.10−2.220.98
21.833.27−0.104.433.28−3.31−1.861.24
31.763.16−0.084.333.24−3.28−2.031.12

Weighted average with weights equal to the share of each category in total exports. Proportionate changes in the prices of other agricultural and primary commodities as well as manufactures (which, as mentioned earlier, were obtained from intermediate results generated by MERM) were assumed to take place in their entirety during the first year. This relatively fast speed of adjustment is consistent, for manufactures, with recent findings on the adjustment of export unit values to exchange rate changes—see Artus (1974)—and, even for primary commodities, would appear to be borne out by the calculations reported for copper, whose price does not vary substantially after two and three years of adjustment from the level reached after only one year. Coffee would not, however, lend itself so well to this simplification, owing to the absence of supply response during the first year. At any rate, the relatively smaller weight of these commodity groups in total export receipts would not make for significant changes in results.

Weighted average with weights equal to the share of each category in total exports. Proportionate changes in the prices of other agricultural and primary commodities as well as manufactures (which, as mentioned earlier, were obtained from intermediate results generated by MERM) were assumed to take place in their entirety during the first year. This relatively fast speed of adjustment is consistent, for manufactures, with recent findings on the adjustment of export unit values to exchange rate changes—see Artus (1974)—and, even for primary commodities, would appear to be borne out by the calculations reported for copper, whose price does not vary substantially after two and three years of adjustment from the level reached after only one year. Coffee would not, however, lend itself so well to this simplification, owing to the absence of supply response during the first year. At any rate, the relatively smaller weight of these commodity groups in total export receipts would not make for significant changes in results.

Table 3.zaïre: Notional Changes in Export Receipts Expressed in U.S. Dollars, Second Half 1971-First Quarter 1975(In per cent over the preceding period)
EffectSecondFirstSecondFirstSecondFirstSecondFirst
AfterHalfHalfHalfHalfHalfHalfHalfQuarter
ProductYear19711972197219731973197419741975
Copper11.982.860.134.563.87−3.75−4.270.96
22.493.790.115.624.43−4.46−3.921.67
32.563.850.045.834.69−4.67−4.451.60
Coffee12.023.354.734.44−3.300.943.71
21.363.28−0.335.084.73−4.440.184.60
30.903.09−0.525.054.69−4.92−0.283.48
Cobalt11.292.34−0.502.971.65−1.81−0.201.58
22.003.64−0.784.622.57−2.82−0.312.46
32.614.73−1.016.013.34−3.67−0.403.21
Other agricultural commodities12.604.81−0.215.753.60−3.750.030.55
23.025.58−0.246.674.18−4.350.030.64
33.256.01−0.267.194.50−4.690.040.69
Other primary commodities12.554.73−0.135.683.61−3.600.040.86
22.965.49−0.156.594.19−4.180.051.00
33.195.91−0.167.104.51−4.500.051.08
Manufactures13.386.21−0.237.604.87−4.750.031.75
23.947.25−0.278.875.68−5.540.032.04
34.297.88−0.309.646.18−6.020.042.22
Total111.973.374.773.70−3.56−2.621.16
22.384.22−0.065.794.27−4.30−2.461.76
32.484.42−0.136.154.57−4.55−2.841.71

Weighted average with weights equal to the share of each category in total exports during the preceding year.

Weighted average with weights equal to the share of each category in total exports during the preceding year.

The proportionate changes in import prices (measured in the numeraire currency) resulting from all exchange rate adjustments that have taken place during each six-month period were computed from Zaïre’s import matrix (showing commodity and country detail) and MERM calculations of changes in the export prices (with commodity detail) of all 23 countries and groups of countries that are currently included in the MERM. (See Table 4.)

The model for Zaïre17 was then solved under the assumption of

“Keynesian neutral” 18 monetary and fiscal policies in order to isolate the effect of exchange rate changes from other policy actions that the authorities may wish to take to strengthen or soften the impact of exchange rate adjustments. The resulting changes in Zaïre’s balance of trade, and hence in its effective exchange rate, proved to be determined primarily by changes originating from the export side, as can be seen from Table 5.

Table 4.Zaïre: Notional Changes in Import Prices Expressed in U.S. Dollars, Second Half 1971-First Quarter 1975(In per cent over the preceding period)
SecondFirstSecondFirstSecondFirstSecondFirst
HalfHalfHalfHalfHalfHalfHalfQuarter
Product19711972197219731973197419741975
Food2.585.16−0.026.134.19−4.350.512.59
Crude materials2.274.28−0.105.093.51−3.370.231.68
Fuel2.294.19−0.085.174.14−3.300.503.51
Manufactures2.715.09−0.096.214.76−4.510.923.98
Total2.655.02−0.076.094.57−4.360.803.62
Table 5.Zaïre: Notional Changes in the Balance of Trade, Second Half 1971-First Quarter 1975(In millions of U.S. dollars)
SecondFirstSecondFirstSecondFirstSecondFirst
HalfHalfHalfHalfHalfHalfHalfQuarter
19711972197219731973197419741975
Exports17.2530.56−0.9263.8047.37−60.84−37.8717.41
Imports
Export-induced8.7514.11−0.2323.2117.40−24.51−15.4612.03
Price-induced5.4011.47−0.1711.348.51−12.512.2913.85
Balance of trade3.104.98−0.5229.2521.46−23.82−24.70−8.47

Zaïre’s effective exchange rate is thus much more sensitive to changes in the world price of its major export commodities (in particular, copper) and hence to changes in the exchange rates of major suppliers and consumers of these commodities19 than to changes in import prices. (See Table 6.)

Table 6.Zaïre: Index of Effective Exchange Rate, First Half 1971-First Quarter 19751
FirstSecondFirstSecondFirstSecondFirstSecondFirst
HalfHalfHalfHalfHalfHalfHalfHalfQuarter
197119711972197219731973197419741975
100.098.997.597.693.290.093.797.799.4

The appreciation shown for the first quarter of 1975 does not take into account the restrictions imposed at the end of January 1975 to tailor import payments to incoming export receipts. Their inclusion would result in the effective rate remaining (approximately) at the level reached when the restrictions were introduced.

The appreciation shown for the first quarter of 1975 does not take into account the restrictions imposed at the end of January 1975 to tailor import payments to incoming export receipts. Their inclusion would result in the effective rate remaining (approximately) at the level reached when the restrictions were introduced.

zambia

The parameter values required for application of the model to Zambia were obtained from estimating the following simplified econometric model:

where Tnx and Tx represent, respectively, nonexport and export taxes; other symbols have their usual interpretation. The two behavioral equations were estimated by 2SLS.

The specification of the consumption function, distinguishing between disposable income originating from the export and domestic sectors, was adopted as a simplification of the “true” consumption relationship in Zambia, which exhibits significantly different propensities to spend out of wage and nonwage income.20 Since yearly fluctuations in nonwage income are determined primarily by fluctuations of export prices, the lower propensity to spend out of profits is reflected in the lower propensity to consume out of export rather than “domestic” income.

Price controls administered by the Government of Zambia and backed by extensive subsidization of certain essential consumer goods have, in recent years, prevented domestic prices from responding fully to demand and supply pressures. Available evidence indicates that increases in the price of imports have not always been fully passed on to the consumer and have not, therefore, been fully reflected in the domestic price indices.21 As a first approximation, the elasticity of domestic prices with respect to import prices was assumed to be equal to the import content of domestic production, thus reflecting the cost/ push element of higher import prices. However, in view of the argument presented above, this is probably an overestimate, as least for some years.

The elasticity of copper supply for Zambia was obtained from the following equation relating copper production to capital stock and copper prices:

whereQ is the volume of production in thousands of metric tons
Kadj is the capital stock at constant 1965 prices adjusted for losses of productive capacity in 1966-67 (following Rhodesia’s unilateral declaration of independence) and in 1970-72 (the disastrous flooding of the Mufulira mine). Estimates of losses in productive capacity were derived independently.
P* is the “settlement and cash sellers’ price” (according to the London Metal Exchange) in thousands of kwacha per metric ton deflated by an index (1964 = 1.0) of wage rates in the Zambian mining sector.

In the absence of better information, domestic supply elasticities for other exports (which, however, accounted for less than 7 per cent of total exports, on average, during the period 1970-74) were set equal to those used for Zaïre.

Tables 7 and 8 show the percentage changes in Zambia’s export receipts and import prices, respectively. The model was again solved under the assumption of “Keynesian neutral” monetary and fiscal policies. Changes in the effective rates of the kwacha are also dominated (although to a somewhat lesser extent than for Zaïre) by changes originating from the export side and, in particular, by copper prices.

Table 7.Zambia: Notional Changes in Export Receipts, Second Half 1971-First Quarter 1975(In per cent over the preceding period)
ProductEffect After YearSecond Half 1971First Half 1972Second Half 1972First Half 1973Second Half 1973First Half 1974Second Half 1974First Quarter 1975
(In U.S. dollars)
Copper12.173.040.143.253.24−3.70−4.210.95
22.493.70−0.043.833.39−4.00−3.421.55
32.383.460.023.633.33−3.90−3.701.34
Agricultural commodities12.604.81−0.215.753.60−3.750.030.55
23.025.58−0.246.674.18−4.350.030.64
33.256.010.267.194.50−4.690.040.69
Other primary commodities12.554.73−0.135.683.61−3.600.040.86
22.965.49−0.156.594.19−4.180.051.00
33.195.91−0.167.104.51−4.500.051.08
Total112.203.200.113.393.26−3.70−3.930.93
22.523.87−0.053.993.44−4.02−3.191.49
32.443.693.843.40−3.94−3.451.31
(In kwacha)
Total12.203.200.11−4.11−0.39−3.70−3.930.93
22.523.87−0.05−3.51−0.21−4.02−3.191.49
32.443.69−3.66−0.25−3.94−3.451.31

Weighted average with weights equal to the share of each category in total exports.

Weighted average with weights equal to the share of each category in total exports.

Table 8.Zambia: Notional Changes in Import Prices Expressed in U.S. Dollars, Second Half 1971-First Quarter 1975(In per cent over the preceding period)
ProductSecond Half 1971First Half 1972Second Half 1972First Half 1973Second Half 1973First Half 1974Second Half 1974First Quarter 1975
Food2.614.73−0.097.103.94−3.13−0.620.93
Crude materials2.494.51−0.035.463.81−3.460.241.89
Fuel2.294.19−0.095.174.07−3.330.493.48
Manufactures2.574.72−0.485.453.38−3.720.012.41
Total2.564.68−0.415.593.49−3.64−0.012.33

The results presented in Tables 9 and 10 abstract from the impact of the restrictive import licensing system introduced by the Zambian authorities in June 1972. Taking it into account would result in a smaller response of payments to changes in export receipts and import prices and, consequently, in a much sharper depreciation of the kwacha in 1973.

Table 9.Zambia: Notional Changes in the Balance of Trade, Second Half 1971-First Quarter 1975(In millions of U.S. dollars)
SecondFirstSecondFirstSecondFirstSecondFirst
HalfHalfHalfHalfHalfHalfHalfQuarter
19711972197219731973197419741975
Exports16.3728.0643.7138.70−52.49−45.9612.76
Imports
Export-induced2.023.166.865.73−6.80−5.922.09
Price-induced9.5317.84−1.5732.7919.33−21.62−0.0912.77
Balance of trade4.827.061.574.0613.64−24.07−39.95−2.10
Table 10.Zambia: Index of Effective Exchange Rate, First Half 1971-First Quarter 1975 1
FirstSecondFirstSecondFirstSecondFirstSecondFirst
HalfHalfHalfHalfHalfHalfHalfHalfQuarter
197119711972197219731973197419741975
100.098.095.194.593.088.196.0110.2111.1

The effective exchange rate index with the impact of the import licensing restrictions taken into account would be as follows:

FirstSecondFirstSecondFirst
HalfHalfHalfHalfQuarter
19731973197419741975
87.879.687.8101.4102.2

The effective exchange rate index with the impact of the import licensing restrictions taken into account would be as follows:

FirstSecondFirstSecondFirst
HalfHalfHalfHalfQuarter
19731973197419741975
87.879.687.8101.4102.2

III. Conclusion

The framework used in this paper to evaluate changes in the effective exchange rate of primary producers’ currencies was derived as an alternative to the various trade-weighted concepts that are often used as synthetic indicators of the relationship of a given currency to all other currencies. Even though the analysis required is more complex, its usefulness for analytical and policy-making purposes would seem to warrant the additional effort, as no adequate alternative appears to be available for assessing, even partially, the impact of exchange rate changes on a given country’s external position. This would appear to be true especially for producers of primary commodities, because the relative homogeneity of those commodities makes “third market” effects particularly important and trade-weighted concepts more unreliable indicators of the effect of exchange rate changes on export receipts than for industrialized countries, whose exports are more differentiated and, as a result, less substitutable for similar products of a different origin.

APPENDIX:
derivation of import demand equation

Following Armington (1969), and Artus and Rhomberg (1973), the percentage change in the value (expressed in the numeraire currency) of the demand by the kth country for the ith good produced by country i can be written as follows:

where

i, nare used to refer to goods (the mth, or last, good being the nontraded good)
j, k, lare countries

and where

X˙ijk=proportionate change in the value of demand (measured in the numeraire currency) for product ij in market k
P˙ij=proportionate change in the price of the ith good supplied by country j (in the numeraire currency)
T˙k=proportionate change in the exchange rate of country k’s currency in terms of the numeraire currency
Dk=proportionate change in the money expenditures on all goods and services (for final and intermediate demand) in country k (in local currency)
εik=expenditure elasticity of country k’s demand for the ith good
ηij/ilk=price elasticity of demand (in volume terms) in market k for the ith good produced by country j with respect to the price of the ith good produced by country l
ηi/nk=price elasticity of demand (in volume terms) in market k for the ith good in general, irrespective of the source of supply, with respect to the price of the nth good in general
Snlk=share of country l in supply of good n to market k
Snk=share of good n in total expenditures in market k

Using the Slutzky equation, we also write the demand elasticities (η) in terms of the corresponding income-compensated price elasticities (λ) and expenditure elasticities (ϵ), that is,

Substituting from equations (24) and (25) in equation (23) we have

where

If we also assume, following Artus and Rhomberg (1973), that the utility functions governing choices between goods of various kinds exhibit fixed coefficients, the income-compensated cross-price elasticities, λi/n n≠i, can be set equal to zero and the last term dropped altogether.24

To achieve further economies in the number of parameters included in equation (26), the procedure suggested by Armington (1969) is adopted and the income-compensated own-price and cross-price elasticities for the jth product are defined as follows:

whereCijk|0Cijk1 represents the proportion of a given trade flow (Xijk) “effectively competing” in the kth market with other products of the same kind at the uniform elasticity of substitution σik, 25 We also make the assumption that imports are fully competitive, that is,

or, in other words, that no imported product of a given kind is so differentiated that it could not be replaced by a similar product of a different origin. Substituting from equations (27), (28), and (29) in equation (26), we get (after some rearrangement of terms)

The percentage change in total imports of the ith good can then be obtained from the weighted sum of import flows from all j|jk origins with weights equal to their respective shares in total imports of the ith good by the kth country, namely, Sijk/(1Sikk) Hence,

Further uses of this equation in the main text exclude the last term on the basis that, in most developing countries, import substitutes are either nonexistent or are protected from outside competition, so that Cikk (the proportion of domestic production of the ith good “effectively competing” in the local market against imports of the same kind) is quite small and the last term vanishes as Cikk approaches zero, that is,

The percentage change in the total imports of the kth country can then be obtained from the weighted sum of imports of goods i, i = 1,…, m − 1, with weights o£

ωi,Mk equal to the share of each in total imports:

with real imports a function of real expenditures. Under the additional assumption of proportionality between total and final demand, allowing us to give k either of the two interpretations, behavioral equation (32) describing the demand for imports reduces to the one used in the main text.

solution for effective exchange rate

The equation in the text representing the change in the trade balance

can be simplified as follows when Ṫj = 0, jk

On the export side, the percentage change in the price of exports reduces to

since there is no demand shift (the exchange rates of all importing countries remaining unchanged), while the supply of the kth country has changed by − ηsikT˙k, representing a shift in the world supply curve of − Vi,xkηsikT˙k The percentage change in export receipts (measured in the numeraire currency) thus equals

On the import side, we have

As a result of the relatively small size of most countries to which the foregoing framework could be applied, devaluation (or revaluation) of the country’s currency will have little or, in most cases, no effect on the export prices of the countries from which it imports, that is,

We will, in fact, assume it to be exactly equal to zero. Also,

after substituting for (P˙dkT˙k)=θ(P˙MkT˙k)andP˙Mk=0, reduces to

Substituting from equations (35) and (36) for X˙kandP˙Mk, the percentage change in import payments (measured in the numeraire currency) reduces (after some rearrangement of terms) to

Substituting for k and k from equations (35) and (40) in the expression for Δβ¯k we have

which can be solved for T˙k*, the change in Tk that would have the same effect, Δβ¯k, on the trade balance:

The preceding expression may also be used to investigate the conditions under which the system will be stable, that is, the conditions under which a devaluation (Ṫk < 0) will improve the balance of trade Δβk > 0) measured in the numeraire currency. With trade originally balanced (i.e., X0 = M0 and αx = αM),26 the condition for stability can be written as follows:

Since it is not possible for the exchange system to be stable when the whole economy is dynamically unstable, we must have

as required for dynamic stability of the postulated income expenditure system.27 The condition for stability of the exchange rate then reduces to

that is, a depreciation will improve the trade balance (measured in the numeraire currency) if it leads to an increase in foreign exchange receipts from exports (also measured in the numeraire currency), provided that the propensity to spend is less than unity.

The restrictive nature of this condition for exchange stability depends in a crucial way on some of the assumptions used earlier. It can be easily verified, for example, that the presence of substitution between imports and domestically produced goods (i.e., Cikk0 for at least some goods) would make the condition for stability less restrictive. We also neglected the possible influence of the money supply and its “price” in checking the expansion of domestic demand.28 In addition, in practice, an original surplus of imports over exports will make it easier to fulfill the necessary and sufficient condition for a devaluation to improve the trade balance.

BIBLIOGRAPHY

    ArmingtonPaul S. (1969) “A Theory of Demand for Products Distinguished by Place of Production,”Staff PapersVol. 16 (March1969) pp. 15976.

    ArtusJacques R. (1974) “The Behavior of Export Prices for Manufactures,”Staff PapersVol. 21 (November1974) pp. 583604.

    ArtusJacques R. and Rudolf R.Rhomberg (1973) “A Multilateral Exchange Rate Model,”Staff PapersVol. 20 (November1973) pp. 591611.

    BanksFerdinand E. (1974) The World Copper Market: An Economic Analysis (Cambridge, Massachusetts1974).

    Charles River Associates (1969) Economic Analysis of the Cobalt Industry Prepared for the General Services Administration (Cambridge, Massachusetts1969).

    DixonPeter B. (1974) “The Fund Multilateral Exchange Rate Model—A Review” (unpublishedInternational Monetary FundAugust151974).

    FisherFranklin M.Paul H.Cootner and MartinNeil Baily (1972) “An Econometric Model of the World Copper Industry,”Bell Journal of Economics and Management ScienceVol. 3 (Autumn1972) pp. 568609.

    OtaniIchiro (1975) “Inflation in an Open Economy: A Case Study of the Philippines,”Staff PapersVol. 22 (November1975) pp. 75074.

    RidlerDuncan and Christopher A.Yandle (1972) “A Simplified Method for Analyzing the Effect of Exchange Rate Changes on Exports of a Primary Commodity,”Staff PapersVol. 19 (November1972) pp. 55975.

    RhombergRudolf R. (1976) “Indices of Effective Exchange Rates,”Staff Papers.Vol. 23 (March1976) pp. 88112.

    TimmsDaniel E. (1973) World Demand Prospects for Coffee in 1980 with Emphasis on Trade by Less Developed CountriesDepartment of Agriculture, Foreign Agricultural Economic ReportNo. 86 (Washington1973).

    TsiangS. C. (1961) “The Role of Money in Trade Balance Stability: Synthesis of the Elasticity and Absorption Approaches,”American Economic ReviewVol. 51 (December1961) pp. 91236.Reprinted in International Finance: Selected Readingsed. by R. N.CooperPenguin Modern Economic Readings (Harmondsworth, England1969).

    United Nations Conference on Trade and Development“Survey of Commodity Demand and Supply Elasticities” (mimeographedUNCTAD/RD/70, GE. 74-45107March191974).

Mr. Bélanger, economist in the African Department when this paper was prepared, is currently in the Trade and Payments Division of the Exchange and Trade Relations Department. He holds degrees in economics from the Universities of Montreal and Western Ontario and is presently completing a dissertation for his doctorate from the University of Western Ontario.

This paper draws heavily on the earlier work of Artus and Rhomberg (1973) and of Ridler and Yandle (1972).

This view is also presented in Rhomberg (1976).

The proposed definition is thus the same as that used in the MERM calculations for the industrial countries and Australia. See Artus and Rhomberg (1973) and Rhomberg (1976).

This simplified model of world trade is based on the twin assumptions of perfectly competitive markets and the absence of nonprice incentives in the choice of trade partners. These can, however, be easily modified to incorporate some forms of market imperfections. (See Ridler and Yandle (1972) for a general discussion of institutional rigidities and similar problems.) Application of this framework to Zaïre, for example, deals with cobalt in the context of a dominant supplier (Zaïre) maximizing its profits subject to the conditions imposed by market demand and the supply response of other producers.

One measure of effective exchange rate often used to assess the impact of exchange rate changes on the prices received by a given country is the “export-weighted effective exchange rate” with weights based on the direction of trade, that is, Σjωjk(T˙iT˙k),

where ωjk is the share of £’s total exports going to j. That this method will, in most cases, fail to provide correct answers can easily be seen from the foregoing analysis, since, in particular, it leaves out both the role played by demand and supply responses in determining ultimate price effects and the influence of changes in the exchange rates of other suppliers and demanders with which a given exporter may not itself trade. It will, in fact, provide correct answers only under the joint assumption of zero supply responses and of complete market segmentation for the exports of a given country, a condition that is certainly not satisfied for primary producers except in the very short run. Little, if any, significance could, however, be given to such measurement of short-run impact.

This “empirical” simplification may, in some cases, be judged inappropriate and could be modified accordingly. If easy enough conceptually, this could create serious empirical difficulties, since the requirement of consistency of the specification with the main features of MERM would require a disaggregation of the demand for imports by commodity. See the Appendix for a mathematical illustration of the requirements.

See the Appendix for its derivation and the implied assumptions.

In the model, k is used as a subscript to indicate that a variable is measured in the local currencey of the kth country, while as a superscript (where necessary) it indicates that the relevant magnitude, even though measured in the numeraire currency, pertains to the kth country.

Ṗ the percentage change in the demand deflator (measured in local currency), could be written alternatively as

where D* represents total, as opposed to final, demand and (k- Ṫk) represents the percentage change in the local currency price of domestically produced and consumed goods (whether nontradables or import substitutes). The advantage for operational purposes of this second way of writing is that it separates one component that can be readily computed from available information (M/TkDk*)(P˙MT˙k) and one on which more information is required, namely, (1M/TkDk*)(P˙dT˙k) An equation for (d—Ṫk) would, in fact, have to be added to the simplified income determination system presented in equations (8)-(10) in order to close it. For present purposes, we will simply assume the change in the price of domestically produced and consumed goods to be proportional to the change in import prices

leaving further discussion to specific application of the model to Zaïre and Zambia.

See the Appendix for details of calculations and for a brief discussion of conditions for stability.

The data for 1962-67 were based on estimates prepared by the United Nations and those for 1968-73 on those prepared by the International Bank for Reconstruction and Development.

The price of domestically produced goods on the markets of Kinshasa, published by the Institut de Recherches Economiques et Sociales of the University of Lovanium, was used as a proxy for Pd.

See Otani (1975) and references cited therein for a further discussion of this specification.

It can be shown that, in the case at hand where available evidence reveals the supply response of other producers to be zero, the percentage changes in world cobalt prices and Zaïre’s receipts resulting from a set (Ṙ) of changes in the exchange rates of cobalt consumers can be written, respectively, as

where λ is the coefficient describing the response of the dominant supplier’s asking price to changes in world demand (in our case, λ = 0.552) andVi,xz is Zaïre’s share in the world supply of cobalt. The underlying analysis is based on the study of the world cobalt market by the Charles River Associates (1969).

Made up of equations such as equations (10)(12) in the text plus an equation for the percentage change in consumer prices equal to the weighted average of changes in the prices of imports and domestically produced and consumed goods (see footnote 10 and using equation (17) for the relationship between domestic prices and import prices), and incorporating the dynamic features of the equations for consumption and prices. Because of our inability to estimate an investment function (probably because investment expenditures, over the period of observation, were dominated mostly by a few important spending decisions whose determinants could be captured only to a limited extent by our simplified model), investment expenditures were assumed to remain unchanged in real terms.

“Keynesian neutrality,” as coined by Tsiang (1961) for monetary policy, is used to characterize a situation where the authorities undertake to neutralize the effect that changes in monetary and fiscal aggregates induced by exchange rate changes (as they affect the availability and cost of credit and/or money as well as the size of the budget) would have on economic activity and hence on the external position of the country. The absence of any explicit mention of monetary factors ensures this result for monetary policy. For fiscal policy, this was done by forcing the authorities to adjust spending just enough to offset the impact of higher (or lower) tax receipts induced by exchange rate changes, thus keeping unchanged the net effect of the budget on economic activity. These assumptions could clearly be modified in other cases where a certain “automaticity” in policy making (in the form of monetary and/or fiscal policy reaction functions) allows the analysis to be more precise as to the direction of policy response.

The effect of exchange rate changes on the price of copper during most of the period under review was dominated by the appreciation of consumer countries’ currencies relative to the U.S. dollar followed by the appreciation of the dollar in 1974. Only in the second half of 1974 did the supply effect (led by a further substantial Chilean devaluation) dominate.

where W and NW represent, respectively, wage and nonwage income. DUM is equal to 1 over the period 1969-73, and zero otherwise.

This tends to be confirmed by the following regression of the domestic demand deflator on import prices and the ratio of actual to “normal” output:

which shows an elasticity of domestic with respect to import prices that is inferior to the import content of domestic production. The coefficient on import prices is probably biased downward, however, as import prices have a relatively strong exponential trend over the period and are thus highly collinear with the time variable.

22

This equation is based on the following assumptions: (1) the marginal rate of substitution between any two products of the same kind is independent of the quantities demanded of products of other kinds; and (2) the index functions governing choices among products of the same kind are linear homogeneous. See Armington (1969) and references cited therein for a more complete discussion of these two assumptions.

23

Since the assumption of linear homogeneity of the product index functions ensures that εij = εi for all j.

This assumption appears somewhat more restrictive than the ones introduced previously and, where the availability of data permits, could be dispensed with.

See Armington’s appendix to Artus and Rhomberg’s paper (1973). The concept of “effectively competing and noncompeting” trade flows is suggested by Armington as an alternative to the CRESH function that still allows for the relaxation of the assumption that the elasticiy of substitution between the products of any two countries supplying the kth market is equal to that between any other pair of products competing in the same market.

The condition would be different if we started from a position of trade imbalance. The basic condition for stability remains, however, the condition under initial trade balance. See Tsiang (1961), especially p. 156, for a cogent discussion of this point.

See Tsiang (1961), p. 151, for a brief discussion of the implications of the correspondence principle in this context.

On this, see Tsiang (1961). Our choice of assumptions with respect to monetary and fiscal policies is discussed in more detail in the sections in the text that deal with specific application of the model to Zaïre and Zambia.

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