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Exchange Rate Variability: Alternative Measures and Interpretation

Author(s):
International Monetary Fund. Research Dept.
Published Date:
January 1982
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IN ASSESSING THE IMPACT of floating exchange rates on the world economy, and in comparing the experience since 1973 with that under the par value system, considerable attention has been focused on the possible negative impact of exchange rate fluctuations and, consequently, on the ways in which an exchange regime could be chosen so as to reduce such fluctuations.1 Prior to 1973, discussion of the “costs” arising from these fluctuations was largely theoretical.2 Since the advent of managed floating, however, the actual experience with floating rates and the interest of many countries in choosing an exchange regime that would limit the fluctuations have stimulated the empirical investigation of such costs. Because these are difficult to measure directly, it is convenient to choose measures of exchange rate variability that can be regarded as indicators of the costs resulting from such variability.

This paper addresses the question of what exchange rate index or indices would be appropriate to use for measuring exchange rate variability. During the past decade a number of methods have been developed to calculate indices that average changes in exchange rates between the currency of an individual country and the currencies of its trading partners. Although alternative weighting schemes for an index to assess the effect of exchange rate changes on the trade balance have been thoroughly compared,3 the relevance of alternative indices for assessing the economic effects of short-run exchange rate fluctuations has not been systematically analyzed. Such an analysis is the purpose of this paper. Section I briefly describes alternative indices of exchange rate variability. Section II discusses the various types of cost that may arise from exchange rate variability and suggests which index may be most relevant for assessing the magnitude of each type. Section III uses alternative measures of nominal rate variability to analyze the experience of 118 countries between 1973 and 1979. Section IV examines the same experience using a nominal index and a price-adjusted index, and Section V summarizes the findings and suggests possible applications of this analysis to exchange rate policy.

I. Alternative Indices of Exchange Rate Variability

For the purposes of this paper, exchange rate “variability” is defined as the standard deviation of either monthly or quarterly percentage changes in exchange rates, depending on the type of measure used. This definition was chosen because it focuses on detrended short-run changes for the period being analyzed and seemed to the authors to be intuitively more appealing than other methods that, for example, are based on moving averages.4 The definition of variability per se, however, is not germane to the purpose of this paper, which is to choose the proper exchange rates and weighting procedures used to construct the index whose variability is being calculated.

The question of how to choose an index related to the costs of exchange rate variability has no definitive answer because there are different types of such costs. (See Section II.) The first problem encountered in attempting to construct an appropriate index is whether the variability of individual bilateral rates should first be calculated and then averaged in some way, or whether the variability of a weighted average of the bilateral exchange rates (an effective exchange rate) should be calculated. The latter method is the more familiar5 and will be referred to as a measure of the variability of the effective exchange rate (VEER). The former approach, first described by Frankel (1975), will be referred to as an index of effective variation (EV). The technical definitions of these indices are given in Section III.

Regardless of which measure is used, a further question of choosing an appropriate weighting scheme arises. For some purposes, the weights might be based on the use of currencies for external transactions, or for certain types of such transactions (e.g., merchandise trade), but the lack of data generally precludes the construction of such weights.6 To assess the impact of exchange rate changes on the trade balance, weights derived from the Fund’s multilateral exchange rate model (MERM) are useful. However, because these weights are available for only 14 industrial countries, they are not used in the calculations presented in this paper. In choosing weights that could be calculated for most Fund members, it is convenient to select trade weights, such as imports, exports, some average of imports and exports, or global trade weights such as those used in calculating the special drawing right (SDR); there are, in fact, many different ways in which import and export data can be used to calculate a set of weights for this purpose. (See Rhomberg (1976).) For convenience, the computations for this paper have been done using import weights only, but, as will be argued in Section II, these are not always the most appropriate weights.

Finally, there remains the question of whether it is more appropriate to examine the variability of an index of nominal exchange rates or the variability of an index that has been adjusted for both domestic and foreign price inflation. In this paper, an index of variability in the effective exchange rate, adjusted by relative movements in domestic and foreign price levels, is referred to as the RVEER index. Again, the relative usefulness of the VEER and RVEER indices depends upon the purpose for which an index of variability is required. The different cases in which either nominal or price-adjusted exchange rate indices appear to be the more relevant are discussed in the following section.

II. Types of Cost Resulting from Exchange Rate Variability

All countries are faced with fluctuations in exchange rates between their currencies and at least some of the major currencies. Despite initial hopes expressed in some quarters that the size of exchange rate fluctuations could be expected to decline as exchange market participants became accustomed to floating rates, large fluctuations in rates among the industrial countries have continued to occur, resulting in greater variability of the effective exchange rates of developing countries than they had faced under the par value system. Evidence on this type of variability has been reported by Kafka (1978) and in IMF (1979 a, pp. 41–43).

The concern with exchange rate variability stems in almost all cases from its impact on the domestic-currency value of international transactions, for the most part the prices of exports and imports. For this reason, the following discussion focuses initially on the effect of exchange rate variations on the prices of traded goods in terms of the domestic currency. Certain other effects— on the real value of international reserves (which is not properly assessed in domestic-currency terms) and the domestic-currency value of various nonmerchandise transactions (such as workers’ remittances and debt payments)—will be discussed later.

The effects of fluctuations on the prices of traded goods can, in the first instance, be divided between the impact on individual transactions taking place within a limited period and the effect on overall levels of wages, prices, or economic activity. If the unit value of an export or import transaction is fixed for the “currency-contract period”7 in terms of a foreign currency against which the domestic currency fluctuates, exchange rate fluctuations result in larger or smaller profits than expected for the exporter or importer. If the exporter or importer is unable to cover himself against such fluctuations, he faces a risk to which he attaches a cost. There is an analogous cost with regard to government foreign currency receipts or expenditures: these may differ from budgeted amounts, resulting, for excess expenditure or a shortfall in receipts, in the administrative and political problems of failing to stay within a prescribed budget. If the private trader or government bureaucrat is a risk averter,8 he will favor systems in which the variance of the difference between actual and expected unit values in terms of domestic currency is minimized. Each transactor is, of course, interested only in the exchange rate for that foreign currency in which his transaction is denominated. For traders as a whole, this variance is measured by the EV index, already described. To take an extreme example, if all trade were denominated in U.S. dollars, a peg to the U.S. dollar within narrow margins would virtually eliminate such variance.

While the type of variability just defined is relevant chiefly within the currency-contract period, it could influence longer-term decisions affecting the volume of exports and imports,9 the allocation of investment, and government sales and procurement policies. Again assuming that the relevant decision-makers are risk averse, a greater variability of unit values in foreign trade could lead to a shift toward sales and purchases in domestic rather than foreign markets. A closely related effect of exchange rate variability consists of the costs of efforts by both the public and the private sectors to offset the impact of variability. Such costs arise, for example, from the use of personnel to decide on changes in the currency composition of portfolios of units engaged in foreign trade; more frequent re-examinations and decisions concerning the invoicing of exports, imports, and other foreign exchange operations than would be necessary under fixed rates; additional banking personnel required to carry out the larger number of foreign exchange transactions resulting from the additional operations; and government personnel required to minimize the impact of foreign exchange fluctuations on the international assets and operations of the central bank as well as on those of other public agencies whose activities involve external payments and receipts. Again, these types of cost are best indicated by an EV index.

Other problems created by exchange rate variability are related to longer periods than the currency-contract period. The individual entrepreneur faces exchange rate fluctuations that may be unrelated to underlying international price and cost differentials. These changes introduce an additional source of profit uncertainty for all export, import-dependent, or import-competing activities. On the national level, these medium-term fluctuations in international competitiveness affect the balance of payments and the level of economic activity. Of perhaps greater concern to national authorities are the corresponding variations in prices for traded goods, especially if wage goods (e.g., food) are imported and if real wages are rigid downward, because, in this case, exchange rate variations could result in general increases in wages and prices, and such increases could be subject to a ratchet effect. This might not occur after every short-run change in import prices, but some fluctuations take the form of medium-term swings, which would then influence wage determination.

A summary measure of exchange rate variability, as it influences competitiveness of domestic firms vis-à-vis the rest of the world and the levels of domestic prices, wages, and activity, is provided by a VEER index. When such an index is used to reflect the relative-price uncertainty faced by exporters and importers, it should be adjusted by movements in domestic and foreign price levels. Such a price-adjusted index of variation is the RVEER index, which indicates the average divergence from a simple measure of purchasing power parity.

Whether the effects of variability on competitiveness of the domestic traded-goods sector is best measured by means of computing a real exchange rate index or by comparing movements in an index of nominal exchange rates with changes in prices is largely a matter of taste and convenience. In some cases, interest is focused on aspects of “currency risk,” or the risk arising from unanticipated changes in profitability arising from changes in nominal exchange rates, while in other cases, interest is focused on aspects of “relative price risk,” or the risk of unexpected changes in profits caused by changes in relative prices at home and abroad that result from the combined effect of price and exchange rate movements (Wihlborg (1978)).

In constructing both the VEER and RVEER indices, a certain amount of information is lost through the averaging of individual nominal or real exchange rate movements that is implicit in a measure based on an index of effective exchange rates. For example, a country whose currency is simultaneously depreciating against one major currency and appreciating against another may find itself with a stable VEER or RVEER index, yet its exporters or importers may be faced with large short-run changes in profits, depending on the extent to which they are tied to trade in specific markets during the relevant period. The presence of high variability of this kind would be picked up by a high EV index. In the medium run, where there is significant substitutability among markets in response to relative-price changes, more interest attaches to the stability of the VEER and RVEER indices, which measure the variability of a country’s competitiveness vis-à-vis the world as a whole.

The trade weights used for exchange rate indices may be of various kinds. Again, which type is chosen depends on the chief reason for which variability is being studied. For example, an import-weighted index may be best suited for studying the effect of exchange rate fluctuations on the domestic price level, while an export-weighted index would be more relevant for the impact of exchange rates on nominal income. Similarly, whether an export-weighted or an import-weighted index is considered more interesting for analyzing the effect of rate changes on the competitiveness of the traded-goods sector depends on whether the export or the import-competing sector is the more responsive to price incentives. There is little problem in choosing weights if the geographical distribution of exports does not differ much from that of imports. If it does differ sharply, and if both sectors are equally responsive and of equal concern, a total trade-weighted index of some sort would be desirable; alternatively, it might be useful to calculate separate export-weighted and import-weighted indices.10 Finally, when the concern with exchange rate variability is focused on its effects on the trade balance, the appropriate measure will be given by an exchange rate index based, where possible, on weights derived from a MERM.11 Stabilization of the trade balance is tantamount to neither income nor price stabilization12 and is no more likely than the last two to be sought as a short-term objective to be achieved through exchange rate policy.

For the purpose of reflecting changes in competitiveness, a trade-weighted VEER index seems superior to an EV index as a broad measure of variability, since it takes into account changes in competitiveness among trading partners.13 If, however, foreign trade markets for the home country are so imperfect that exports and imports are effectively tied to specific trading partners, the VEER index may be no more useful than the EV index. In general, the more rigid is the structure of trade for the period under consideration, the more relevant is the EV index compared with the VEER index, and this is true with regard to the impact of exchange rate variability on both the competitiveness of the traded-goods sector and, more generally, macroeconomic stability.

It has been mentioned that the EV index, relevant as it is to short-term variability of the domestic-currency value of import payments and export receipts within the currency-contract period, would ideally be based on currencies of trading partners.14 Because precise information on currency of denomination is notoriously difficult to obtain, the empirical section of this paper uses import weights instead. The use of trade weights in the EV index leads to an upward bias in the measure of short-term exchange rate variability to the extent that trade is denominated in the domestic currency15 or in another currency to which the domestic currency is either pegged or that serves as an important indicator for exchange rate policy.16 These biases do not arise for the trade-weighted VEER measure, since it is intended to reflect a longer-term impact on competitiveness and macroeconomic variables.

The impact of exchange rate variability on exports and imports may not be the same as its effects on balance of payments items that are not related to trade. For a number of countries, such items as debt service payments and workers’ remittances are important components of the balance of payments. The effect of exchange rate variability on nontraded invisibles and capital transfers depends on the currencies in which external payments are due or receipts are received. As the relative importance of the various foreign currencies may be different for such transactions than for exports or imports, in general it will be impossible to minimize the exchange rate component of fluctuations in the prices of traded goods and at the same time to minimize the impact of exchange rate variations on the variability of the domestic-currency value of nontraded items in the balance of payments.

One special problem that has arisen under floating exchange rates has been the maintenance of the value of international reserves. The principal reason for holding international reserves is, normally, to finance future payments deficits.17 The proper measure of the value of reserves would therefore be in terms of a weighted average of the price of the foreign currencies required for making international payments in terms of those currencies held in reserves; to derive the real value of reserves, this index would have to be adjusted by an appropriate price index. For example, if only U.S. dollars were held as reserves and all international payments were for imports, the value of the reserves would properly be measured by an import-weighted effective exchange rate index for the U.S. dollar (using the import weights of the country holding the reserves), and the real value would be derived by adjusting this index by an import-weighted index of the export prices of the country’s suppliers.18

Although the exchange rates between the domestic currency and the currencies of trading partners would not provide a measure of fluctuations in the real value of reserves, there are, in practice, reasons why central banks have been especially concerned about the stability of nominal rates between their own currencies and other currencies. One reason for this is that most central banks play a major part in foreign exchange markets, either engaging directly with the public in sales and purchases of foreign exchange—as is true in many developing countries—or acting as residual buyers or sellers of foreign exchange in transactions with commercial banks. As a result of these operations, central banks experience accounting losses or gains resulting from the effect of exchange rate fluctuations on the book value of their international reserves. It may be argued that these accounting losses or gains are in lieu of losses or gains accruing to either the private sector or other departments of the public sector, and thus represent no additional losses or gains for the society as a whole.19 Nevertheless, central bankers may, for political reasons or administrative convenience, tend to favor exchange arrangements that reduce the risk that large exchange or valuation losses will appear on their books. For this purpose, stabilizing an EV index may be more helpful than stabilizing a VEER index, but in either case the key to stabilizing the book value of reserves would be that the weights used in such an index reflect the currency makeup of the reserves themselves in addition to the currency composition of international payments.

An additional problem of national governments, sometimes mentioned as being complicated by exchange rate fluctuations, concerns the closely related tasks of external debt management and development planning. A rational approach to decisions on the amounts, terms, and currency-denomination of foreign borrowing may be made more difficult by floating rates among the major currencies because of the unpredictability of the domestic-currency, or effective trade-weighted foreign-currency, costs of debt service. The related development planning exercise, which involves, inter alia, projections of import and external financing requirements, is also said to be complicated by exchange rate fluctuations. It could be argued that the effect of variability on debt-servicing requirements is best measured by an index weighted by the currencies in which the debt is denominated, while the variability of the value of the foreign exchange component of development expenditures could be calculated using an exchange rate index weighted by the sources of development-related imports.

In summary, there are a number of different types of cost that may be associated with exchange rate variability, and, correspondingly, the calculation of different indices of exchange rate variability would be of interest in order to monitor the effect of exchange rate changes on various activities of the private and public sectors. The empirical sections of this study are based on the notion that the authorities of member countries might choose their exchange regimes so as to minimize, or at least to reduce, the variation in one or more of such indices. Where this occurs, it seems reasonable to assume that the effects of exchange rate variability on foreign trade and overall economic activity are principal factors determining the selection of the regime. An EV index, described earlier, would appear to be the best indicator of fluctuations affecting the short-run risks faced by those engaged in foreign trade, while some type of VEER index—either nominal or price-adjusted—seems more relevant for the medium-term profit variations and the effects on prices and the level of economic activity arising from exchange rate fluctuations. The following sections discuss recent exchange rate experience in terms of an EV index, a (nominal) VEER index, and a (price-adjusted) RVEER index, and examine how this experience appears to be related to the actual choices of exchange regimes made by member countries.

III. Alternative Measures of Variability of Nominal Exchange Rates: Definitions and Country Experience

In the previous section, two measures of the variability of nominal exchange rates were discussed: the effective variability of exchange rates (EV) and the variability of effective exchange rates (VEER). In this section, the two measures are given a precise definition and are used to interpret the exchange rate experience of a wide range of countries since the onset of floating exchange rates in 1973. The focus of the discussion is on the effect of the choice of exchange rate regime on the magnitude of exchange rate variability.

DEFINITIONS

Effective variation (EV)

The effective variation in exchange rates (EV) is defined as the weighted sum of the variabilities of bilateral exchange rates, where the variability of an exchange rate is defined as the standard deviation of monthly percentage changes in the rate over the relevant period.20 For a particular country i, therefore, the EV index is given as

where wij is j’s share of i’s imports (Σwij = 1), and σj is the variability of the exchange rate between i and j, expressed as units of i’s currency per unit of j’s currency. Ideally, the weights should be the proportion of total transactions conducted in each currency, but because of the unavailability of such data, import shares are used in the calculations made for this paper.

Variability of effective exchange rate (VEER)

The variability of an effective exchange rate (VEER) is defined as the standard deviation of the quarterly percentage changes in an effective exchange rate. For a particular i, let the effective exchange rate be defined as

where Rij is the bilateral rate between countries i and j. The effective exchange rate can be linearized in terms of the logarithms of the exchange rates

Thus, ΔXRiEṘi = the quarterly percentage change in the effective exchange rate over the relevant period. VEER is then defined as the standard deviation of the quarterly percentage change in the effective exchange rate

where T is the number of quarters being observed.

Changes in the VEER index arise from both changes in the individual country’s bilateral rates and changes in the bilateral rates among other currencies. This can be shown by using equation (3) and squaring the VEER index. Letting rij = ln(Rij) and Δrijij, one obtains

where VAR = variance and COV = covariance. The covariance term can be interpreted as “exogenous” influences on the country’s effective exchange rate over which the country has no influence. VEER can be greater (less) than the weighted sum of the variances of the country’s bilateral exchange rates if the covariance term is positive (negative).21

COUNTRY EXPERIENCE

To assess how the choice of exchange arrangement can affect the two indices just described, simulated EV and VEER indices are calculated for each currency assuming six alternative pegs, namely, to the U.S. dollar, deutsche mark, French franc, pound sterling, Japanese yen, and SDR. For each calculation, it was assumed that all actual exchange rate changes took place, except that the exchange rate between the domestic currency and the unit to which the domestic currency was assumed to be pegged was held constant. For example, when the EV index for currency i is calculated assuming a peg to the U.S. dollar, the exchange rate between the U.S. dollar and currency i is assumed to be constant, and thus its variability is zero; the actual exchange rates between the U.S. dollar and all other currencies are then used to calculate the variabilities of currency i vis-à-vis those currencies.

The calculations for the six alternative pegs are compared with the actual EV and VEER indices for the currency in question, which are derived by direct application of equations (1) and (2), respectively, using actual exchange rate data for all currencies.

Thus, even for a country that fixes its currency in terms of one of the six alternative pegs for which simulations were performed, the actual EV or VEER index may differ somewhat from the corresponding simulated index, because, over the period under examination, the currency may have been adjusted discretely against its unit of peg or permitted to fluctuate within declared margins, or the exchange arrangement itself may have been changed.

The calculations just described were carried out using monthly exchange rate data from March 1973 through December 1980 for 118 countries—117 Fund member countries plus Switzerland. Since, as explained in the previous section, the principal usefulness of the EV index is to measure short-term fluctuations, the variability of EV is calculated on the basis of monthly exchange rate averages. In calculating the VEER index, which is relevant chiefly for indicating medium-run changes in international competitiveness, quarterly averages are used.22

The calculations given in Table 1 for EV and VEER are, for each country, the actual value of the index and the minimum of the simulated values for each index among the six alternative pegs. All the calculations are given in percentage terms. The countries are listed by their declared exchange arrangements as of June 30, 1980. At that time, 7 participated in the cooperative exchange arrangements under the European Monetary System (EMS); 13 were industrial countries with other types of exchange arrangements; 10 were pegged to the SDR; 13 were pegged to the French franc; 34 were pegged to the U.S. dollar; and the remaining 41 were developing countries with other exchange arrangements.

Table 1.Average Variability of Bilateral Exchange Rates (EV),1 April 1973-December 1980, and of Effective Exchange Rates (VEER),2 Second Quarter 1973-Fourth Quarter 1980(In per cent)
EVVEER
ActualMinimum3ActualMinimum3
Industrial countries
Cooperative exchange arrangements
Belgium1.681.67D*1.782.01S*
Denmark1.721.65D*1.802.01S*
France2.071.81D*2.571.68S
Germany, Fed. Rep. of2.071.86S*2.881.56S
Ireland1.631.20£1.921.86£*
Italy2.551.92S3.071.56S
Netherlands1.771.68D*1.761.79S*
Other industrial countries
Australia2.681.64$2.981.25S
Austria1.392.00D*1.431.62D*
Canada1.380.54$1.860.59$
Finland1.781.71D*1.631.89S*
Iceland4.321.66D5.841.92S
Japan2.851.27$4.491.03$
New Zealand2.561.73S2.931.29S
Norway1.721.75D*1.561.89S*
Spain2.901.74$3.921.16S
Sweden1.881.68D*2.091.81S*
Switzerland2.321.52D3.472.15S
United Kingdom2.391.82S3.571.44S
United States1.741.85S*1.381.19S*
Developing countries
Pegged to SDR
Burma4.171.84S4.861.69S
Iran1.981.87S*2.101.50S
Jordan2.121.81$*1.511.30S*
Kenya2.241.74S2.311.41S
Malawi1.921.84S*1.921.86S*
Mauritius3.861.78S4.191.31S
Sierra Leone1.881.61S*2.431.36S
Uganda2.241.70S1.711.67S*
Zaϊre10.401.69D10.721.90S
Zambia3.641.71S4.341.36S
Pegged to French franc
Benin1.411.41F*1.891.89F*
Cameroon1.061.10F*1.341.34F*
Central African Republic1.101.10F*1.311.31F*
Chad0.620.61F*0.830.83F*
Congo0.980.97F*1.161.16F*
Gabon0.640.63F*0.790.79F*
Ivory Coast1.231.23F*1.611.61F*
Madagascar1.211.20F*1.551.55F*
Mali0.460.45F*0.600.60F*
Niger0.940.94F*1.341.34F*
Senegal1.311.30F*1.651.65F*
Togo1.301.30F*1.691.69F*
Upper Volta0.780.78F*1.051.05F*
Pegged to U.S. dollar
Bahamas0.790.79$*0.850.85$*
Barbados1.821.38$2.001.21S
Burundi2.591.83S2.891.63S
Chile27.962.37$18.692.40S
Costa Rica3.021.26$3.581.25S
Dominican Republic0.870.87$*0.900.90$*
Ecuador1.731.73$*1.741.25S
Egypt8.591.81S8.211.35S
El Salvador1.171.17$*1.131.13$*
Ethiopia2.041.91S*2.231.45S
Guatemala1.241.24$*1.211.15S*
Guyana1.641.50$*1.451.33S*
Haiti0.800.79$*0.820.82$*
Honduras1.101.10$*1.061.06$*
Iraq2.361.99D*2.661.80S
Jamaica5.310.71$5.560.87$*
Liberia1.681.68$*2.251.30S
Libyan Arab Jamahiriya2.251.95S*2.911.90S
Nepal2.681.56S3.661.70S
Nicaragua4.621.08$5.321.02$
Oman1.731.66S*2.211.37S
Pakistan1.821.81S*1.841.19S
Panama0.770.77$*0.700.70$*
Paraguay3.303.30$*4.373.47S
Romania2.372.00S*9.571.54S
Rwanda2.201.78S2.601.63S
Somalia1.891.67S*2.661.80S
Sudan3.301.80S4.501.45S
Suriname1.481.48$*1.981.19S
Syrian Arab Republic2.151.88S*2.291.61S
Trinidad and Tobago2.111.18$2.491.14$
Venezuela1.601.60$*1.681.08S
Yemen Arab Republic1.781.70S*1.981.23S
Yemen, People’s Democratic Republic of1.661.58S*2.011.25S
Other developing countries
Afghanistan2.381.72Ұ3.432.07S
Algeria1.901.68F*1.331.90S
Argentina15.262.07$15.291.55S
Bahrain1.321.29$*1.390.99S
Bangladesh6.781.49$6.201.80S
Bolivia4.133.00$4.392.85S
Brazil4.061.80$5.601.36S
Colombia2.451.66$2.881.17S
Cyprus1.811.95S*0.771.46S
Fiji1.891.84S*1.251.72S
Gambia, The1.611.61£*3.651.83S
Ghana7.401.78S9.311.41S
Greece2.421.95S2.841.64S
India2.041.64$1.941.03S
Indonesia3.661.72S5.021.54S
Israel7.371.81S7.881.53S
Korea3.321.58$4.381.80S
Kuwait1.831.86S*1.491.39S
Lebanon3.131.85S4.551.47S
Malaysia1.901.69S*2.031.41S
Malta1.811.86£*0.781.84S
Mauritania2.070.99F2.301.25F
Mexico7.090.93$6.461.05$
Morocco1.841.75F*1.431.73S
Nigeria2.251.87S*3.221.77S
Peru6.281.49$6.941.07S
Philippines1.911.52$2.051.45S
Portugal2.921.94S3.261.43S
Qatar2.171.82S*2.471.74S
Saudi Arabia1.851.65$*1.651.17S
Singapore1.691.45$*1.601.19S*
South Africa2.681.84S3.541.56S
Sri Lanka9.631.34$8.460.98S
Tanzania2.841.78S3.461.60S
Thailand1.811.75S*2.241.66S*
Tunisia2.131.64F1.671.93F*
Turkey8.091.74S8.961.41S
United Arab Emirates1.931.78S*2.231.51S
Uruguay4.012.54$5.922.41S
Western Samoa3.841.88S4.051.87S
Yugoslavia3.991.81D4.421.74S
Sources: International Monetary Fund, International Financial Statistics (various issues).

EV is defined as the import-weighted sum of the standard deviations of monthly percentage changes in monthly average bilateral exchange rates.

VEER is defined as the standard deviation of the quarterly changes in the quarterly average import-weighted effective exchange rate.

The letter next to the minimum value indicates which peg calculation yielded that value. An asterisk(*) indicates that the observed minimum value is not significantly different from the actual value. The abbreviations are S (SDR), $ (U.S. dollar), F (French franc), D (deutsche mark), £ (pound sterling), and ¥ (Japanese yen).

Sources: International Monetary Fund, International Financial Statistics (various issues).

EV is defined as the import-weighted sum of the standard deviations of monthly percentage changes in monthly average bilateral exchange rates.

VEER is defined as the standard deviation of the quarterly changes in the quarterly average import-weighted effective exchange rate.

The letter next to the minimum value indicates which peg calculation yielded that value. An asterisk(*) indicates that the observed minimum value is not significantly different from the actual value. The abbreviations are S (SDR), $ (U.S. dollar), F (French franc), D (deutsche mark), £ (pound sterling), and ¥ (Japanese yen).

The following results should be interpreted cautiously. Both indices depend on the variances of the bilateral rates, which in turn depend on the period analyzed. The results, therefore, should not be viewed as prescriptive, but only as indicative, of the range of choice that countries have with regard to their exchange arrangements. Certain possibilities, such as managed floating, were not considered unless they were the actual arrangements chosen.

Results for EV index

The figures given in Table 1 clearly indicate that the value of the EV index is strongly affected by the choice of exchange arrangement. Of the 118 countries, in 27 the actual EV value was equal to the calculated minimum value,23 and in another 37, there was no significant difference between the actual value of EV and the minimum value of EV.24 The cases where the actual EV is the minimum include 12 of the 13 countries that peg to the French franc, 13 that peg to the U.S. dollar, one that pegs its currency to the pound sterling, and one that participates in cooperative exchange arrangements. There are, thus, 53 countries in which the actual EV value differs significantly from the minimum EV value.

For the six alternative pegging arrangements for which the EV index was simulated, most of the countries actually using one of those arrangements have a lower EV than if they had chosen one of the five others. This is true for 19 of the 34 countries pegging to the dollar; 8 of the 10 countries pegging to the SDR; and all the 13 countries pegging to the French franc.

The two remaining groups of countries—the developed and the other developing countries—have declared exchange arrangements that are widely diverse, and, in general, are not pegged. Within these two groups, the minimum value of the EV index is generally given by the peg calculation that corresponds to trading patterns. Of the 20 industrial countries, 10 have their minimum EV given by the deutsche mark-peg simulated values, of which only 2 are significantly different from the actual EV values. These are all European countries and have a large portion of their trade with the members of the EMS. For Canada and Japan, with their relatively larger trade with the United States and countries that peg to the dollar, the dollar-peg simulations yield the minimum value. For analogous reasons, Ireland’s minimum EV value is produced by the pound-peg simulation.

Within the group of 41 developing countries classified under “other arrangements,” the minimum EV is generally related to economic and historical ties. The 15 countries whose minimum EV results from the dollar-peg simulation have close economic ties to the United States; they are all Latin American, Asian, or oil exporting countries. The four countries whose minimum EV is given by the franc-peg simulation—Algeria, Mauritania, Morocco, and Tunisia—all have strong economic ties to France. Analogously, the minimum EVs of The Gambia and Malta are produced by the pound-peg simulation. For the overwhelming majority of the remaining countries in the group with “other arrangements,” the minimum EV values correspond to a simulated peg to the SDR, suggesting that these countries have relatively diversified trading patterns.

Results for VEER index

The figures given in Table 1 for the VEER calculations show that this index is also sensitive to the choice of peg. For 19 of the 118 countries, the actual VEER is equal to the minimum of the values calculated, and for another 18 countries, there is no significant difference between the actual and minimum VEER values. Thus, for 81 countries the actual VEER value differs significantly from the minimum calculated value.

The alternative-peg calculations of the VEER index show that the SDR-peg simulation yields the minimum value for 89 of the 118 countries. All the 10 countries pegging to the SDR have their minimum VEER given by the SDR-peg simulation.25 The SDR-peg simulation yields the minimum value for 25 countries pegging to the dollar, for 38 developing countries having other exchange arrangements, and for 16 industrial countries. For all 13 countries that peg their currencies to the French franc, the actual and minimum VEER values are equal to the franc-peg simulation. The dollar-peg simulation yields the minimum value for only 9 countries that peg to the U.S. dollar, a sharp contrast to the results obtained from the EV calculations.

Possible implications of results for choice of exchange arrangement

The figures given in Table 1 illustrate that the choice of exchange arrangement does affect exchange rate variability. It remains to be examined whether these calculations offer an indication of the criteria that countries might employ, or actually have employed, in choosing an exchange arrangement.

A potential difficulty arises when there is no exchange arrangement that will yield minimum values for both EV and VEER. In such a case, the country faces a policy conflict and would have to choose an arrangement that would minimize only one of these measures, or, alternatively, one that yields a reasonably satisfactory result for both without minimizing either. A comparison of the results obtained using the simulations for the six alternative pegs for both EV and VEER shows that there are 44 countries for which the peg yielding the minimum EV value differs from the peg yielding the minimum VEER value (Table 2). If, however, the latter peg yielded an EV value not significantly different from the minimum EV value, or the VEER value for the peg yielding the minimum EV value did not differ significantly from the minimum VEER, or some other peg could be found whose EV and VEER values were both not significantly different from the respective minimums, it would then be exaggerated to say that a policy conflict exists.

Table 2.Countries with Possible Policy Conflict if Pegging Currencies and Minimizing EV or VEER1
Minimum EVMinimum VEER
Industrial countries
Cooperative exchange arrangement
BelgiumD*S*
DenmarkD*S*
FranceD*S*
NetherlandsD*S*
Other industrial countries
Australia$S
FinlandD*S*
IcelandDS
NorwayD*S*
Spain$S
SwedenD*S*
SwitzerlandDS
Developing countries
Pegged to SDR
Jordan$*S*
ZaϊreDS
Pegged to U.S. dollar
Barbados$S
Chile$S
Costa Rica$S
Ecuador$*S
Guatemala$*S*
Guyana$*S
IraqD*S
Liberia$*S
Paraguay$*S
Suriname$*S
Venezuela$*S
Other developing countries
Afghanistan¥S
AlgeriaF*S
Argentina$S
Bahrain$*S
Bangladesh$S
Bolivia$S
Brazil$S
Colombia$S
Gambia, The£*S
India$S
Korea$S
Malta£*S
MoroccoF*S
Peru$S
Philippines$S
Saudi Arabia$*S
Singapore$*S*
Sri Lanka$S
Uruguay$S
YugoslaviaDS
Source: Table 1.

EV is defined as the import-weighted sum of the standard deviations of monthly percentage changes in monthly average bilateral exchange rates. VEER is defined as the standard deviation of the quarterly changes in the quarterly average import-weighted effective exchange rate.

An asterisk (*) indicates that the observed minimum value is not significantly different from the actual value. The abbreviations are S (SDR), $ (U.S. dollar), F (French franc), D (deutsche mark), and £ (pound sterling).

Source: Table 1.

EV is defined as the import-weighted sum of the standard deviations of monthly percentage changes in monthly average bilateral exchange rates. VEER is defined as the standard deviation of the quarterly changes in the quarterly average import-weighted effective exchange rate.

An asterisk (*) indicates that the observed minimum value is not significantly different from the actual value. The abbreviations are S (SDR), $ (U.S. dollar), F (French franc), D (deutsche mark), and £ (pound sterling).

To find how many countries had a significant conflict in the latter sense, a simple statistical test using the F-statistic was performed.26 Using this test, it was found that for 43 of the countries in Table 2 neither the EV nor the VEER index would be significantly different from their minimum values if at least one of the following exchange arrangements was employed: the actual exchange arrangement being used; the peg that minimizes either EV or VEER; or pegging to the SDR. Thus, for 117 of the 118 countries examined in this paper, it is possible for a policy conflict, as defined here, to be avoided.

A final question to be examined was whether the actual exchange arrangements chosen by the 118 countries appeared to be related to an attempt to minimize the two measures of exchange rate variability. Table 3 shows for each category of exchange arrangement the number of countries for which the actual exchange arrangement, or the alternative pegging arrangements enumerated in the preceding paragraph, resulted in values for both indices that were either minimum or not significantly different from the minimum. From this table it is possible to determine how many countries have chosen an exchange arrangement that came significantly close to minimizing the value of both measures of exchange rate variability. Countries pegging to the French franc or to the SDR have an overwhelming correspondence between their declared arrangement and the peg that yields minimum values for both the EV and VEER indices. All 13 countries pegging to the franc have both of their minimums given by the franc-peg simulation, and 9 of the 10 countries pegging to the SDR have both of their minimums given by the SDR. Of the 34 countries whose declared arrangement is that of pegging to the U.S. dollar, 12 (all in Latin America) have both their minimum EV and VEER values given by the U.S. dollar-peg simulation, while 21 have their minimum EV and VEER values given by the SDR calculations. The latter countries are mainly in Asia, Africa, and the Middle East; 2 of them also have minimum EV and VEER values with the U.S. dollar-peg simulation.

Table 3.Most Satisfactory Exchange Arrangements with Respect to Minimizing Both EV and VEER Indices1(Number of countries by category of exchange regime)
Industrial Countries
AlternativePeggedPeggedPegged
ExchangeEMS2to U.S.toto French
ArrangementsmembersOthersDollarSDRFrancOtherTotal
Pegged to
U.S. dollar212519
Pound sterling11
French franc13316
Deutsche mark314
Japanese yen
SDR352193573
Actual arrangement (if other than pegs shown)3431213
Total71436111345126
Memorandum items
Number of countries in each category of exchange arrangement713341013401173
Number of countries for which an SDR peg yields minimum or near-minimum values for both EV and VEER indices6923103785

This table shows the results of carrying out the tests for the existence of a policy conflict, as described in footnote 26. When the actual peg (or other exchange arrangement) yields minimum EV and VEER values, or values that are not significantly different from those minimums, that peg or arrangement is the one reported in this table. When the peg (other than the actual arrangement) yielding the minimum EV value also yields a VEER value not significantly different from the minimum, or the peg (other than the actual peg) yielding the minimum VEER value also yields an EV value not significantly different from the minimum, either or both of these pegs are reported if the actual peg (or arrangement) has not been reported. Because for some countries the EV and VEER indices are minimized by different pegs (neither of them the actual exchange arrangement), each of which yields a value for the other index that is not significantly different from the minimum, more than one peg yielding a “minimum value for both EV and VEER index” is reported for those countries; consequently, the totals add up to more than 117. When neither the actual arrangement nor a peg yielding minimum values for either the EV or the VEER index satisfies the requirement that both EV and VEER indices are significantly close to the minimums, a test was done for the SDR peg (if not already tested as the actual arrangement) and was reported if it yielded satisfactory values for both indices.

European Monetary System.

Peru is not included in this table, because for this one country neither the actual arrangement nor the other pegs examined here yielded a minimum value for both EV and VEER.

This table shows the results of carrying out the tests for the existence of a policy conflict, as described in footnote 26. When the actual peg (or other exchange arrangement) yields minimum EV and VEER values, or values that are not significantly different from those minimums, that peg or arrangement is the one reported in this table. When the peg (other than the actual arrangement) yielding the minimum EV value also yields a VEER value not significantly different from the minimum, or the peg (other than the actual peg) yielding the minimum VEER value also yields an EV value not significantly different from the minimum, either or both of these pegs are reported if the actual peg (or arrangement) has not been reported. Because for some countries the EV and VEER indices are minimized by different pegs (neither of them the actual exchange arrangement), each of which yields a value for the other index that is not significantly different from the minimum, more than one peg yielding a “minimum value for both EV and VEER index” is reported for those countries; consequently, the totals add up to more than 117. When neither the actual arrangement nor a peg yielding minimum values for either the EV or the VEER index satisfies the requirement that both EV and VEER indices are significantly close to the minimums, a test was done for the SDR peg (if not already tested as the actual arrangement) and was reported if it yielded satisfactory values for both indices.

European Monetary System.

Peru is not included in this table, because for this one country neither the actual arrangement nor the other pegs examined here yielded a minimum value for both EV and VEER.

For the two remaining groups of countries—the industrial countries and the developing countries classified under other arrangements—there appears to be a correspondence between the currency that yields a minimum value for both EV and VEER and actual exchange rate policies. Within the group of 20 industrial countries, Canada and Japan have their minimum EV and VEER given by the U.S. dollar-peg simulation, while Ireland has its minimum values given by the pound sterling-peg simulation; as discussed earlier, these results correspond to the trade patterns of these countries. Analogously, Austria and Switzerland both have minimum EV and VEER values given only by the deutsche mark-peg simulation. The largest number of industrial countries (8) have both minimum values given by the SDR-peg simulation—a fact that reflects their diverse trading patterns and is consistent with exchange rate policies that are not closely linked to a single foreign currency.

Within the group of developing countries classified under other arrangements, the majority have both minimum EV and VEER values given by the SDR calculations. These countries are predominantly Asian, African, and Middle Eastern, and have diverse trading patterns. Of the five countries in this group with both minimum values given by the U.S. dollar-peg simulation, three are in Latin America (Bolivia, Mexico, Uruguay). The three countries in the group—Algeria, Mauritania, and Tunisia—for which minimum values are given by the French franc calculations have strong economic ties to France.

These considerations suggest that, in the large majority of cases, countries have chosen the exchange arrangement that, among the alternatives presented here, has come close to minimizing the variability of both their EV and VEER indices. There exist, to be sure, other possible arrangements specific to each country—for example, an import-weighted basket of currencies— that would result in an even lower value of variability than the calculations that are given here.

IV. Variability of Nominal and Price-Adjusted Exchange Rates

An alternative measure of exchange rate variability is an index of the real effective exchange rate. Such a measure is especially useful for assessing changes in the international competitiveness of local producers.

It has been argued that just as the decision whether to minimize the EV or the VEER index may affect the choice of exchange arrangements, so does the decision of whether to minimize fluctuations in either nominal or real exchange rates. Lipschitz (1979) and Lipschitz and Sundararajan (1980) suggest that a country should minimize fluctuations in the real effective exchange rate, which they use to define an “equilibrium” rate. They show that a currency basket can be found to minimize fluctuations in a nominal effective exchange rate, but to the extent that changes in bilateral rates affect the corresponding relative price levels, the equilibrium rate will change.

The discussion that follows deals with an adjustment for changes in relative price levels for the VEER index only. A relative price adjustment to the EV index is not warranted because the usefulness of this index lies principally in indicating the degree of risk faced during the currency-contract period, during which prices are fixed.

To convert the effective exchange rate from nominal to real terms, a relative price index is constructed. Using logarithmic notation, let the relative price index be given as

where wij are the import shares as defined previously, and Pij = ln(Pi/Pj), where P is the price index. The percentage change in the real effective exchange rate (RXR) can then be expressed in logarithmic form as

and the variability of the real effective exchange rate as

Equation (8) expresses the standard deviation of quarterly percentage changes in the real effective exchange rate. The relationship between the variability of the real and nominal effective exchange rate is

27

If the changes in nominal exchange rates exactly offset the changes in relative prices, COV(ΔXRi, ΔRPi) = VAR(ΔXRi) = VAR (ΔRPi) and RVEERi = 0. It is possible, therefore, for RVEER to be minimized while VEER is positive. If VEERi = 0, and at the same time COV(ΔXRi,ΔRPi) = 0 and VAR(ΔRPi) is greater than zero, then RVEERi will be positive.

The covariance term shows the relationship between changes in the nominal effective exchange rate and in the relative price level and gives the effect of the relative size and direction of these changes on the variability of the real effective exchange rate. If prices and exchange rates move together (an appreciation of i’s currency relative to j’s is associated with a decline in i’s prices relative to j’), the covariance term will be positive. If the magnitude of the positive covariance term is sufficiently large, RVEER will be less than VEER. If the covariance term is positive, but not sufficiently large to make RVEER less than VEER, it shows that exchange rate changes have been in the right direction but not large enough to offset changes in relative prices. If the covariance term is negative—and, thus, RVEER is greater than VEER—exchange rate movements have been in the opposite direction to that of changes in relative price levels.

Simulations for RVEER were calculated for the six alternative pegs utilized in the previous section of this paper. The minimum values resulting from these calculations, together with the actual values, are given in Table 4. These figures show that for 20 countries28 the minimum value of RVEER is given by the actual value and that for another 63 countries there is no significant difference between their actual and minimum RVEER values.

Table 4.Variability of Price-Adjusted Effective Exchange Rates, Second Quarter 1973-Fourth Quarter 19801
RVEER1
ActualMinimumVRP2Covariance3
Industrial countries
Cooperative exchange arrangements
Belgium1.922.08S*0.780.038
Denmark2.322.27S*1.27-0.264
France2.601.68S0.650.139
Germany, Fed. Rep. of2.961.66S0.46-0.134
Ireland2.372.27£*1.410.038
Italy2.921.86S1.141.090
Netherlands1.921.89S*0.67-0.060
Other industrial countries
Australia2.901.68S1.210.958
Austria1.571.75D*0.54-0.068
Canada1.750.75$0.630.398
Finland1.871.77S*0.930.011
Iceland5.283.27S3.148.024
Japan4.511.54$1.390.874
New Zealand2.791.41S1.081.043
Norway1.642.09S*0.840.225
Spain3.731.53S1.421.741
Sweden1.872.41S*1.131.078
Switzerland3.552.20D0.940.157
United Kingdom3.832.00S1.490.135
United States1.571.46S*0.840.072
Developing countries
Pegged to SDR
Burma6.895.00£5.372.510
Iran3.713.28S*3.00-0.183
Jordan3.333.14$*2.93-0.120
Kenya2.881.66S1.800.150
Malawi3.523.58S*2.76-0.522
Mauritius3.853.55S*3.286.737
Sierra Leone5.235.62£*5.584.829
Uganda10.339.70F*10.17-0.216
Zaϊre9.706.59F6.6032.203
Zambia4.342.51S2.192.387
Pegged to French franc
Benin2.041.91F*0.69-0.057
Cameroon2.492.49F*1.97-0.261
Central African Republic2.872.87F*2.35-0.487
Chad2.332.33F*2.06-0.255
Congo3.163.16F*2.73-0.575
Gabon3.243.24F*2.99-0.474
Ivory Coast4.034.03F*3.740.157
Madagascar2.262.26F*2.471.702
Mali8.588.57F*8.610.435
Niger3.743.74F*3.620.457
Senegal4.743.83$*4.03-0.724
Togo4.044.04F*3.770.409
Upper Volta6.906.48S*6.63-1.236
Pegged to U.S. dollar
Bahamas2.342.34$*2.380.466
Barbados3.202.82S*2.570.197
Burundi5.204.73S*4.671.541
Chile6.9412.84£*14.26252.278
Costa Rica5.433.49S*3.24-3.109
Dominican Republic2.672.67$*2.32-0.469
Ecuador1.931.93$*1.781.233
Egypt8.182.39S2.062.399
El Salvador1.791.79$*1.720.526
Ethiopia4.544.02S*3.990.148
Guatemala2.872.87$*2.740.375
Guyana2.442.62S*1.980.044
Haiti3.293.29$*3.250.226
Honduras2.122.12$*1.80-0.062
Iraq3.953.93S*3.291.170
Jamaica3.943.09$*3.2613.025
Liberia2.982.63S*2.511.240
Libyan Arab Jamahiriya3.092.37S*2.141.721
Nepal4.463.53S*1.710.425
Nicaragua4.065.86S*5.7722.587
Oman2.201.33S0.740.301
Pakistan2.902.84S*2.981.911
Panama1.591.59$*1.490.083
Paraguay4.834.83$*4.9410.102
Romania9.551.60S0.800.463
Rwanda3.582.82S*2.710.646
Somalia5.414.86S*4.48-1.065
Sudan6.756.54S*6.679.623
Suriname3.052.45S*2.360.095
Syrian Arab Republic4.633.68S*4.31-2.244
Trinidad and Tobago3.301.67$1.62-1.035
Venezuela2.441.96S*1.66-0.183
Yemen Arab Republic3.933.32S*3.34-0.207
Yemen, People’s Democratic Republic of2.341.94S*1.911.109
Other developing countries
Afghanistan7.836.20¥*6.55-3.282
Algeria2.463.99S*2.430.817
Argentina9.1210.97£*11.84145.495
Bahrain3.503.22S*3.340.432
Bangladesh10.005.34$5.49-15.694
Bolivia5.856.13F*6.5614.064
Brazil3.393.36S*3.9317.639
Colombia3.332.48S*2.341.325
Cyprus1.571.99S*1.410.062
Fiji2.032.04S*1.57-0.042
Gambia, The4.784.46£*4.103.637
Ghana13.6411.14S*11.0511.229
Greece4.393.40F*2.55-2.328
India3.963.56$*3.690.872
Indonesia5.462.96¥2.170.088
Israel5.665.80F*5.6430.950
Korea4.292.82S2.293.002
Kuwait2.162.12S*1.650.136
Lebanon4.591.45S0.940.263
Malaysia2.471.73S1.15-0.344
Malta1.852.02S*1.58-0.148
Mauritania3.692.71F2.58-0.820
Mexico5.442.28$2.018.125
Morocco1.592.05F*1.721.234
Nigeria4.083.66S*3.352.473
Peru5.834.17$4.3316.445
Philippines3.382.88S*2.33-0.876
Portugal4.253.78F*3.532.511
Qatar2.351.59S0.920.700
Saudi Arabia4.514.23£4.02-0.732
Singapore2.842.52$*2.26-0.186
South Africa3.561.67S1.200.645
Sri Lanka8.372.59$2.450.764
Tanzania5.124.08S*4.191.671
Thailand2.712.37S*1.690.247
Tunisia2.402.54D*1.770.087
Turkey5.545.90S*5.7941.508
United Arab Republic2.241.39S0.920.402
Uruguay6.114.39S4.7810.296
Western Samoa5.103.26S2.81-0.872
Yugoslavia4.402.95D2.162.428
Sources: International Monetary Fund, International Financial Statistics (various issues).

RVEER is the standard deviation of the effective exchange rate (VEER) adjusted for changes in relative domestic and foreign levels of the consumer price index. This measure is calculated from the first quarter of 1973 to the fourth quarter of 1980.

The abbreviations are S (SDR), $ (U.S. dollar), F (French franc), D (deutsche mark), £ (pound sterling), and ¥ (Japanese yen). An asterisk (*) indicates that the observed minimum value is not significantly different from the actual value.

This column gives the standard deviation of quarterly percentage changes in the import-weighted effective relative price index. These numbers correspond to the actual exchange rate variability calculations.

The covariance term corresponds to the actual exchange rate calculations. The relationship is given by COV = (VEER2 + VRP2 - RVEER2)/2. Owing to rounding, the sum of the three terms may not exactly yield the given covariance.

Sources: International Monetary Fund, International Financial Statistics (various issues).

RVEER is the standard deviation of the effective exchange rate (VEER) adjusted for changes in relative domestic and foreign levels of the consumer price index. This measure is calculated from the first quarter of 1973 to the fourth quarter of 1980.

The abbreviations are S (SDR), $ (U.S. dollar), F (French franc), D (deutsche mark), £ (pound sterling), and ¥ (Japanese yen). An asterisk (*) indicates that the observed minimum value is not significantly different from the actual value.

This column gives the standard deviation of quarterly percentage changes in the import-weighted effective relative price index. These numbers correspond to the actual exchange rate variability calculations.

The covariance term corresponds to the actual exchange rate calculations. The relationship is given by COV = (VEER2 + VRP2 - RVEER2)/2. Owing to rounding, the sum of the three terms may not exactly yield the given covariance.

Of the 118 countries studied, there are only 9 for which the peg yielding the minimum VEER value differs significantly from the peg yielding the minimum RVEER. It is possible, however, to find a single peg that minimizes the variability of both VEER and RVEER for these countries. These results indicate very clearly that the decision of whether to minimize the variability of a nominal effective exchange rate or that of a real effective exchange rate need not, in itself, entail a policy conflict in the choice of exchange arrangements.

The calculated covariance terms are also given in Table 4. The covariance term is negative for only 35 countries, implying that exchange rate and relative price movements have been perverse in only a relatively few cases. Of the remaining 83 countries having a positive covariance term, for 25 countries29 this term was sufficiently large to result in the RVEER being less than the VEER. For the other 58 countries, movements in exchange rates have only partially offset relative movements in price levels.

V. Conclusions

This paper has discussed the relevance of measures of exchange rate variability for assessing the economic impact of exchange rate fluctuations and has compared three such measures under alternative assumptions as to exchange rate regime. The three measures simulated were an index of effective variability (EV), the import-weighted sum of the standard deviations of the monthly percentage changes in a country’s bilateral exchange rates; an index of the variability of the effective exchange rate (VEER), the standard deviation of the quarterly percentage changes in a country’s import-weighted effective exchange rate; and the variability of a price-adjusted effective exchange rate (RVEER).

The results of the simulations show that the magnitude of exchange rate variability is influenced by the choice of exchange arrangements, and that the majority of countries could have simultaneously minimized all three measures of variability with a common arrangement. With regard to the specific question of whether a country should aim at minimizing the variability of its real or its nominal rate, the results show that, in most cases, minimizing the variability of either the real or the nominal rate also minimizes the other.

The fact that many countries did not in fact choose exchange regimes that simultaneously minimized the three different measures of exchange rate variability suggests the unsurprising conclusion that other important considerations affect exchange arrangements. These considerations probably include historical tradition, the convenience of pegging to a dominant currency in trade and exchange market intervention, and the appreciation or depreciation in the real effective exchange rate expected in the medium term as the result of a particular peg. It is nevertheless significant that most countries chose exchange arrangements under which exchange rate variability, as defined by one or more of the three measures, did not differ significantly from the minimum as defined in this paper.

BIBLIOGRAPHY

Mr. Lanyi, Chief of the Developing Country Studies Division of the Research Department, is a graduate of Harvard University and the University of California at Berkeley. He has taught at Princeton University.

Ms. Suss, economist in the North American Division of the Western Hemisphere Department, is a graduate of the University of Pittsburgh. She has been a member of the faculties of the University of Virginia and George Washington University.

See Rhombefg (1976).

See footnote 20 for a brief argument in favor of this preference. For further discussion of the advantages and disadvantages of the alternative definitions, see Frankel (1975), Suss (1976), and Bigman (1978).

See, for example, Crockett and Nsouli (1975), Suss (1976), and Kafka (1978).

Some estimates of the use of “vehicle currencies” have been carried out on a global basis or for major industrial countries. See, for example, Page (1977) and Magee and Rao (1980).

See Clark (1973).

The choice of relevant index has been discussed by Rhomberg (1976).

As noted earlier, because such weights are available only for the 14 industrial countries and (on the basis of a somewhat different type of calculation) for a small group of developing countries, they were not used in calculations in succeeding sections of this paper. On the derivation of such weights for developing countries, see Feltenstein, Goldstein, and Schadler (1979).

An index using bilateral trade weights has a drawback to the extent that exports compete against those of third countries. For discussion of a “double-weighted” index, which takes into account third-country competitors in the home country’s export markets, see Rhomberg (1976) and Spitäller (1980). This problem is tackled for exporters of primary products by Bélanger (1976) and Feltenstein, Goldstein, and Schadler (1979).

Also, see Lipschitz (1979) for the possibility of using the “price currency,” namely, the currency in which world prices for the traded commodities are quoted.

The denomination of trade in the domestic currency is relevant not only to industrial countries but also to those developing countries that conduct a substantial portion of their trade under bilateral payments agreements with other nonindustrial countries; such trade is, in effect, denominated in the currency of one of the trading partners.

For instance, through a large weight in a currency basket.

For the relatively small number of “capital surplus” countries, reserves are regarded principally as a form of investment.

Ben-Bassat (1980) uses the country composition of payments in defining the value of international reserves for the purpose of determining the optimal currency composition of reserves.

See Lanyi (1969) for a related argument.

The use of a quadratic form to measure exchange rate variability is most appropriate because variability is viewed as a proxy for exchange rate risk, and percentage changes are used so that changes in various rates can be expressed in a common unit. There are several reasons why the average monthly (for EV) or quarterly (for VEER) percentage change over the period analyzed was used in calculating the standard deviation rather than either a moving average or a trend. First, if a moving average is used, a decision must be made as to the length of the moving average; this injects an element of arbitrariness into the calculation. Second, the use of a moving average may understate the actual costs of exchange rate changes by smoothing the movements too much. Third, using deviations from a trend passed through the level of the rate would imply that expectations are based only on the level of the rate rather than on past changes in the rate. Thus, it is felt that using the average monthly percentage change provides the most appropriate way of removing the trend in changes in the exchange rate when using them to calculate the variability of exchange rates.

A similar expression for the EV index can be obtained by squaring EV and writing it as

where σj, is the standard deviation as defined previously. Each of the terms in the EV index is related only to the bilateral exchange rates of the country and can be influenced by the country. The second term of the EV2 expression, the weighted sum of the product of standard deviations, is always nonnegative, so that there are no offsetting influences to the weighted sum of the variances.

It could, indeed, be argued that the VEER index would be properly measured by semiannual and annual fluctuations, but the relatively few observations used in such calculations would reduce the statistical meaningfulness of the results.

Those countries for which the difference between the two values was only 0.01 were included in this category because there were reasons to believe that this difference represented a purely statistical discrepancy.

To test if the actual figures are significantly different from the minimum figures, an F-test is used: the ratio of the actual value to the minimum value is calculated and squared, and if the squared ratio is greater than 1.52 for EV or 1.84 for VEER, it is assumed that the two figures are significantly different. These tests are approximations, because not all the necessary assumptions underlying the F-test hold. However, these ratios give a benchmark for comparing the different magnitudes of the various calculations.

For 7 of these countries, however, the minimum and actual VEER are significantly different because of adjustments in the level of the pegged exchange rate during the period studied.

Footnote 24 gives the definition of statistical significance used in this paper. The test was performed as follows. For a country whose minimum EV and VEER values were given by different pegs, the ratio of the actual to the minimum value for each index for each of those pegs was tested. (The ratio is always the larger to the smaller value.) If for at least one of these pegs neither of these ratios was significantly different from the critical value (1.52 for EV or 1.84 for VEER), there was judged to be no policy conflict. If, however, for each of these pegs one of the ratios was significantly different from the critical value, the ratios of the SDR-peg VEER and EV to the minimum VEER and EV, respectively, were tested. If neither of these two ratios was significant, there was no policy conflict; the SDR could be used for both measures. The test was not conducted for other alternative pegs.

BecauseVAR(ΔXRi) = VEER2i, one obtains equation (9).

Those countries for which the difference between the two values was only 0.01 were included in this category because there were reasons to believe that this difference represented a purely statistical discrepancy.

Argentina, Australia, Brazil, Canada, Chile, Egypt, Iceland, Israel, Italy, Jamaica, Korea, Mauritius, Mexico, New Zealand, Nicaragua, Oman, Peru, Qatar, Romania, Spain, Sri Lanka, Sweden, Turkey, Yugoslavia, and Zaire. One may note that Argentina and Chile have at times pursued an active exchange rate policy attempting to move from a “vicious” to a “virtuous” circle and that several other of these countries have been pursuing a policy of frequent changes in the exchange rate.

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