EFFECTIVE EXCHANGE RATES AND OTHER EXCHANGE RATE INDICES

by D. JOHANNES JUTTNER*

Introduction We are accustomed to gauge the value of our dollar in terms of its

exchange rate with the US dollar. At times this measure gives an imprecise reading, because at any moment of time a host of exchange rates exist. Our dollar may gain against the US currency but fall or remain steady vis-a-vis the yen, the pound sterling, the Deutschemark and the Swiss franc. In order to express the value of the Australian dollar in terms of some average of several currencies, the Reserve Bank calculates a trade-weighted exchange rate index and, in order to give it more prominence, publishes the trade- weighted exchange rate twice a day.

In the following we analyse the construction of such trade weighted indices and examine their use in economic analysis.

Effective Exchange Rates A Simple Trade-weighted Exchange Rate Index

We commence our discussion by constructing a simplified version of a trade-weighted exchange rate. As the term suggests, some measure of international trade is used as the weighting device. Let us assume Australia only trades with three other countries, namely the US, Japan and West Germany, and their shares in Australian trade (exports plus imports) during a particular time are 45%, 30% and 25%, respectively. The trade weights constitute only one element of the effective exchange rate index, the currencies of the index countries and the base index are the other two. The trade-weighted index of the base year (TWIo) is usually set at 100. The current trade-weighted index (TWIt) is then constructed as follows:

where EUS, EY and EDM are the exchange rates of the three countries, defined as units of foreign currency per one Australian dollar. The subscript “0” refers to the base period and “t” denotes the current period.

Each weight in equation (I) is multiplied by the ratio of the current

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exchange rate to the exchange prevailing at the base period. These ratios are absolute numbers since the currency denominations cancel out: for instance USt0.875

AS 0.875 Et - - - ussol.oo -

A S 0 -0

The ratio of the current US$/A$ exchange rate to the exchange rate of the base period stands at 0.875. In other words, the Australian dollar depreciated between the base period and the current period by 12.5% (1.00-0.875). Similarly, the weights of the two other countries are multiplied by their respective exchange rate ratios of the current to the base year. The terms in the bracket are then multiplied by TWIo ( = 100).

Continuing with our example, we assume Et - - Y131.2/A$, E,Y = Y2001A$, E l M = DM 1.261A$ and E:M = DM 1.60/A$

TWIt = (0.45 x 0.875 + 0.30 x 0.656 + 0.25 x 0.788)lOO = 78.76

to obtain the current value of the trade-weighted index as

Like any index, the trade-weighted exchange rate index is given as an absolute number. It lacks a dimension and does not express the price of one currency in terms of another. However, the index measures the value of our currency in terms of a bundle of other currencies. This exchange rate is also called the effective exchange rate of the Australian dollar vis-a-vis the exchange rates of our trading partners. It is conventional to select a value of 100 for the base trade-weighted index: any other number, such as 1 or 1000 would have fulfilled the same purpose.

In our example, the effective exchange rate of the dollar has depreciated by 21.2% (100-78.6), while it lost 12.5% in terms of the US$, 34.4% (100-65.6) against the yen and 21.2% (100-78.8) vis-a-vis the DM.

Our simple example of an effective exchange rate index encapsulates elements of all the critical issues that the construction of such an index poses. The major analytical problems concern first, the selection of currencies, second, the determination of the weights and third, the adoption of a weighting method. These are discussed in turn.

Selection of Currencies In principle, all of Australia’s trading partners’ currencies ought to be

included in the computation of the TWI. However, such a complete set would include countries with insignificant trade volumes: in addition, often data are unavailable or unreliable for small trading partners. For these reasons all TWIs include only the most important trading partners. For instance, the Reserve Bank’s trade-weighted index includes 19 countries plus the SDR. The latter composite currency is included because some trading partners’ currencies are pegged to the SDR. The International Monetary Fund’s (IMFs) Multilateral Exchange Rate Model (MERM) uses 17 currencies, the indices

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calculated by the Morgan Guaranty ’hst of New York (World Financial Markets] takes account of the currencies of 15 and 40 countries, respectively. The US Federal Reserve Bank Board’s trade-weighted exchange rate index --TWEX) covers the Group of %n countries plus Switzerland. Recently, Cox (1986) developed a comprehensive exchange rate index for the US dollar which is based on the currencies of all 131 US trading partners.

Batten and Belongia (1987) and Hervey and Strauss (1987) provide useful summary characteristics of commonly used effective exchange rates.

The Weights With the exception of the IMF’s MERM all trade-weighted exchange rates

are directly based on some measure of international trade. Two widely used weighting methods are bilateral and multilateral trade weights.

The Reserve Bank’s bilateral trade weights are measured by each trading partner’s share in Australia’s total exports plus imports. For instance, let us assume Australia’s exports plus imports during a given year amount to A$70 billion and Japan takes A$7 billion of our exports and accounts for A$11.2 billion of our imports, that is, its total share of our trade comes to A$18.2 billion: Japan will then be assigned a weight of 0.26. Of course, the weights of all trading partners must add up to one.

TABLE 1 WEIGHTS OF FOREIGN CURRENCIES IN THE AUSTRALIAN DOLLAR’S

EFFECTIVE EXCHANGE RATE

Currency Trade- Weight

Japanese yen United States dollar West German mark UK pound sterling French franc New Zealand dollar Italian lira New Taiwan dollar Chinese renminbi South Korean won Singapore dollar Hong Kong dollar USSR rouble Special Drawing Right (SDR) Canadian dollar Saudi Arabian riyal PNG kina Netherlands guilder Malaysian ringgit Indonesian rupiah

26.3616 21.8887 6.3544 6.1596 5.0966 4.4621 3.9510 3.3337 2.8916 2.8069 2.6036 2.1551 1.9679 1.7973 1.7160 1.4451 1.3618 1.2928 1.2531 1.1013

~

Weights applied to currencies included in the trade-weighted index have been revised from 1 October 1986 to reflect changes in the make-up of Australia’s trade in 1985186.

The previous set of weights was shown in the Reserve Bank Bulletin for October 1985. Source: Reserve Bank of Australia, Bulletin, October 1986.

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The Reserve Bank’s computation of the TWI coincides exactly with the procedure of equation (1). though it includes more countries. While only one exchange rate definition is required (units of foreign currency per one Australian dollar), the Bank uses two exchange rate definitions, which, after multiplication and cancellations of terms, are collapsed into our approach. The Reserve Bank method is unnecessarily complex and it offers scope for simplifications.

The statistical definitions of bilateral trade shares are versions of the following relationship:

w, * x:us+ M:”s X,( L+ MiM) (3)

where Wi = weight of currency i Xius = Australian exports to country i Mius = Australian imports from country i.

A qualification is required. As some countries peg their exchange rates to either the US dollar, the yen, the Deutschemark or the currencies of other major trading nations, the trade shares of these satellite currencies are included in the shares of their respective leading countries. For example, the “pure” weights (without those of the satellites shares) of our four major trading partners are Japanese yen 26.1, US$15.6, DM 5.3 and pound stering 5.4. As a comparison of these figures with the actual weights in Table 1 shows the difference is particularly marked for the US dollar. It obviously has drawn many other minor currencies into its orbit.

Hooper and Morton (1978) assess the conceptual advantages and dis- advantages of bilateral weights. Obviously, bilateral weights are easy to obtain. They focus on the trade between two countries and convey information about their relative competitiveness in export and import substitution industries. Bilaterial weights, however, fail to capture the competitive effects on trade in third countries. For instance a depreciation of the trade-weighted $A-index due to an appreciation of the yen suggests that the demand for Japanese cars falls, but it does not allow for a resulting expansion in the share of, say, Korean cars in the Australian car market. Bilateral weights are also used by Morgan Guaranty, the US Beasury, the Bank of Canada and the Bundesbank.

Multilateral weights measure the percentage of each country’s trade in the sum total of that of all the trading partners whose currencies are included in the index. Let us assume the total trade among the countries in the index amounts to A$500 billion: Japan’s trade share of this total (exports plus imports) equals, say, A$125 billion and the United States’ share comes to A$100 billion. In the same way we calculate the shares of the remaining index countries (except for Australia’s). Using this method, Japan obtains a weight of 0.25 and the US a weight of 0.20 and the weights for the remaining countries are calculated in an analogous fashion. Multilateral trade shares may be defined as

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where Xi = exports from country i to the rest of the countries in the index Mi = imports to country i from the rest of the countries in the

index

Multilateral weighting schemes are used to indicate the competitive position which Australia faces at home and in the markets of the index countries. However, they are far from ideal as Pads and Helkie (1987) have pointed out.

While exchange rate indices based on multilateral trade weights take account of third-country effects amongst index countries, they do not capture the competitive position of Australia vis-a-vis third countries (that is, countries not included in the index). Such third-country effects are explicity considered by weighting schemes developed by the EC and the OECD (see Durand, 1986 and European Community Note, 1986). Durand employs a double weighting scheme in order to capture “the role played by each country as both supplier and market” for other countries’ exports.

The Base Periods The construction of effective exchange rates involves the selection of two

base periods. First, the TWI for period 0 in equation (1) was set at 100. May 1970 was chosen as the base period for the effective exchange rate of the $A. Care has to be exercised that the trade-weighted exchange rate of the base year is neither substantially over- or undervalued. Ideally, the base rate should reflect an equilibrium exchange rate, say, in terms of purchasing power parity. Second, the base period for the trade weights should reflect the longer run trade shares. However, international trade patterns tend to shift over time, making it necessary to redefine weights. For instance, the Reserve Bank updates the weights from time to time; the last such revision occurred in October 1986. In order to avoid frequent adjustment to the weights, base weights are calculated as averages over several years. At the other end of the spectrum, Cox (1986) uses a moving- average weighting scheme. In this case, weights are updated almost continuously.

Capital-Weighted Indices As the balance on current account mirrors the balance on capital account,

it is conceivable to use capital imports and exports between Australia and the index countries as the basis for the construction of weights. Ott (1987) computes weights based on capital flows.

Trade and capital weighted exchange rate indices have one thing in common: they are based on flow variables. However, nations do not only trade with each other or move capital across borders, they also own foreign assets and are indebted to each other. It is therefore conceivable to construct

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effective exchange rates with weights that are related to stocks of assets and liabilities.

Debtor and creditor countries obtain useful information from exchange rate indices that are weighted by the currency-denominations of their stocks of external liabilities and assets. An index that is based on the currency composition of the stock of foreign debt contains useful information. Movements in such an index reflect changes in domestic currency vis-a-vis the currencies in which our debt is denominated. Such index movements measure revaluation and devaluations of the outstanding debt and indicate whether the debt burden has increased or fallen.

Arithmetic or Geometric Averages The Reserve Bank’s averaging technique is arithmetic: it shares this

feature with the IMF’s Special Drawing Rights. Most trade-based indices use the geometric weighting method. With geometric weights, equation (1) has to be written as:

TWI, = [(;d 1-1 E; >”] 100

Using the same numerical values, we obtain

that is, a slightly lower exchange rate value than with the arithmetic weighting technique.

The advantages of geometric weights as compared to arithmetic averages, are pointed out by the United States Federal Reserve Board:

The previously used arithmetic average had an undesirable property; namely, a s currencies diverged from each other over time, changes in currencies that rose against the dollar had a reduced impact on the index while changes in currencies that fell against the dollar had a n increased impact on the index. As a result. arithmetic averaging imparted a systematic upward bias to the measurement of changes in the dollar’s average exchange value. The geometric averaging technique now being adopted is free from this problem since essentially it averages the percentage changes in the individual exchange rates to determine the percentage change in the index. (1978, p. 700)

The TWI of the Reserve Bank suffers from the same bias although it was, in recent years, relatively small in practical terms. This is so because the domestic dollar fell in value almost uniformly against the currencies of our major trading partners.

TWI, = 0.7818

Real Effective Exchange Rates If purchasing power parity always prevailed, there would be no need to

adjust effective exchange rates for relative price changes; real exchange rates would fluctuate in line with nominal exchange rates. Purchasing power parity, however, is often violated; therefore inflation-adjusted effective exchange rates have to be constructed. Such real effective exchange rates

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contain valuable information about the international competitiveness of a country.

Real Effective Exchange Rates An index of inflation-adjusted effective exchange rates is obtained by

weighting price-deflated exchange rates of the index countries. Equation (1) may be converted into a real trade-weighted exchange rate index by dividing the nominal index by the ratio of weighted foreign to home price indices, using the same trade weights. Employing the CPIs of the respective countries, the real trade-weighted exchange rate index (RTWI) becomes:

The notion of the RTWI is based on purchasing power parity (PPP). We demonstrate this by analysing only one of the three real exchange rates. The composite term (EUS/E~s).(PAus/PUS) measures the real USdollar- Australian-dollar exchange rate relative to a base year. Let us assume the average price levels are PAUS = 137 and Pus = 100. The absolute levels of prices in both countries are irrelevant for our argument: only relative price levels matter, that is, the ratio of the domestic to the foreign price level. Let us further assume that we started off with a base year exchange rate of Eo = US$l.OO/A$ and we now ask what the current exchange rate has to be when PPP holds. PPP requires that a domestic dollar, when converted into foreign currency, buys the same amount of goods overseas as a dollar at home. Therefore, the PPP exchange rate is E = US$O.73OO/A$. As an example, when a consumer has to pay A$1370 for a camera at home helshe may also convert this amount into US$lOOO ( = A$1370 x US$O.73/A$) and order one at this price from the US. If PPP holds, the composite term above as well as the remaining two in equation (5) each become one, giving RTWI = 100.

A fall of the RTWI implies a devaluation of the A$ vis-a-vis the index countries in real terms. It represents an improvement in Australia’s inter- national competitiveness. A decline may be caused by a less rapid rise in domestic relative to foreign prices, a devaluation of the nominal exchange rate vis-a-vis those of the index countries of a combination of price and exchange rate movements.

Figure 1 contains information about nominal and real effective exchange rates of the Australian dollar. The Reserve Bank’s nominal exchange rate index (TWI-nominal) has declined almost continuously since mid-1981; the steepest fall occurred between 1984 and 1986. A similar picture emerges for the domestic dollar in terms of Morgan Guaranty’s nominal exchange rate index (MG15-nominal) which is calculated against 15 major industrialised countries. Morgan Guaranty’s real exchange rate index (MGlSreal), however, shows a slight appreciation of the Australian dollar until the end of 1984. From then onwards to the third quarter of 1986 the

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real effective exchange rate fell rapidly. Since then it has recovered somewhat.

FIGURE 1

MM NOMINAL AND REAL EXCHANGE RATES 110,

1980 1981 1982 1983 1985 1986 1987

The pronounced fall of the real effective rate was due to the fact that our nominal exchange rate depreciated by more than the inflation differential between Australia and the 15 other industrial countries. For instance, a depreciation of the $A by 12% when our inflation rate exceeded those of the rest of the industrialised world by 7 % implies a 5% fall in the RTWI, that is, a real depreciation by 5%.

Unlike the nominal effective exchange rate, the real effective exchange rate index indicates whether a currency is over- or undervalued relative to the base year. An index number above 100 suggests overvaluation and one below 100 undervaluation in terms of purchasing power parity. Thus, since about 1985 the downward movement in the real rate has conferred increased competitive advantages on Australian exporters and import competing industries. It is worth noting that competitive gains due to undervaluation are cumulative. That is, exports still benefit today from the improvements in our competitive position which have occurred since about 1985.

Hooper and Morton (1978) caution against using the real exchange rate index as a measure of international competitiveness in an uncritical fashion. The RTWI may give misleading signals due to the incorrect measurement of prices, the use of inappropriate weighting methods and the failure to take account of sectoral shifts in productivity. In addition they stress the importance of non-price factors. Success in export markets hinges

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importantly on the quality of goods and services as well as reliability and promptness of service. However, as these non-price elements only change slowly, movements of real exchange rates as an indication of competitiveness would not be grossly distorted by these factors. However, the value of real effective exchanges may be most seriously impaired by the selection of an inappropriate price index. This issue therefore deserves further consideration.

Before leaving this section, we add a further caveat. For a commodity exporting country such as Australia, movements in real exchange rates may give conflicting signals to the manufacturing and the primary sectors. Both require, therefore, separate RTWIs, each with its own weights and price deflators. The Federal Treasury (1987) has recently developed an index of commodity export competitiveness, thus providing more accurate information to the commodity export industry.

Such measures of international competitiveness, however, have to be dis- tinguished from effective exchange rates. An international competitive index is commonly defined as a ratio between current domestic costs or prices to those of a country's competitors. The relative costs or prices thus obtained are adjusted for exchange rate changes and trade weights, similar to those employed for effective exchange rates, are used. Unlike effective exchange rates, indices of competitiveness do not relate the values of the current exchange rates to that of a base period.

Choice of Price Indices The consumer price index is generally deemed to provide a good measure

of the prices of a broad range of domestically produced final goods and services. This index is collected on a consistent basis across countries and made available oil a timely basis. However, it suffers from a serious drawback: the index includes the prices of non-traded goods such as housing costs, mortgage payments and various services. This limits its value as a deflator because our aim is to develop a measure of international competitiveness in traded goods and services.

The wholesale price index covers more narrowly the goods sector but, as is well known, the range of wholesale goods covered may vary from country to country. Hooper and Morton (1978) point out that the weights assigned to commodities diverge across countries and often their prices are not representative of underlying domestic cost and manufacturing output prices.

At first sight, an export price index appears to provide a suitable measure for a country's price competitiveness. However, this price measure includes only currently traded goods and services and ignores prices of potentially traded goods and services. For instance, import substitutes in Australia and those of the index countries (which compete with our exports) may become tradable goods. Furthermore, export prices are less influenced by exchange rate changes in the short than in the longer run. In the case of an appreciation of the domestic currency, exporting firms often refrain from

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raising the foreign-currency prices of exported goods. Obviously, as a result of such a pricing policy, the prices of exports in domestic currency fall and profit margins are squeezed. Conversely, with a depreciating currency, the temptation exists that exporting firms do not reduce the prices of goods and services in foreign markets in order to enjoy greater profits. In this case, export prices in domestic currency rise (fall when an appreciation occurs), wrongly indicating a worsening [an improvement) in the competitive position of the home country. Of course, in the longer run, below-normal and fat profit margins are not sustainable in a competitive environment.

Finally, unit labour costs may be used to construct real exchange rates. Since labour costs form a large part of total production costs, they reflect broad trends in the costs of domestic production. They are not distorted by the problems arising from short-run fluctuations in profit margins which are associated with exchange rate changes. But what about costs of capital and costs of raw material which form two other important components of total production costs? Financial markets are now characterised by almost perfect international capital mobility: marginal, usually large, borrowers continuously scan global financial markets for comparatively low-cost sources of capital. Therefore, capital costs tend to be equalised across countries. This, of course, applies only to capital costs in real terms; nominal costs of capital which include inflation premia of the respective countries differ, often quite substantially. Real, that is, inflation-adjusted interest rates, are frequently taken as a proxy for real capital costs.

The prices of raw material inputs tend to be determined in world markets, and are therefore the same for producers wherever they are located. Concluding Remarks

Trade weighted or effective exchange rate indices are an indispensable yardstick to gauge the value of a currency in terms of the average of the country’s major trading partners. Movements in real effective exchange rates indicate whether a currency is over- or undervalued and they thus provide some guidance for the central bank’s intervention operations and other policy decisions. In view of the great relevance of such indices, it is surprising that the Reserve Bank only computes a nominal effective exchange rate index which is unnecessarily complex: to boot, it employs a crude weighting method. Simplification and improvements of the existing index and the development of real effective exchange rates that are based on relative consumer prices and unit labour costs should therefore rank high on the agenda of the monetary authorities. In order to measure the valuation effects of exchange rate changes on our huge foreign debt, a novel exchange rate index is required. The weights of this index should be based on the currency composition of our outstanding debt.

REFERENCES Artus, J.R. and Rhomberg, R.R. (1973), “A Multilateral Exchange Rate Model”, IMF Staff Papers,

Australia. Treasury (1987), Round-up of Economic Statistics, June. November, 591-611.

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Batten, D.S. and Belongia, MX (1987), “Do the New Exchange Rate Indices Offer Better Answers to Old Questions?”, Federal Reserve Bank of St Louis Review, May, 5-17.

Cox, W.M. (1986). “A New Alternative Pade-Weighted Dollar Exchange Rate Index”, Federal Reserve Bank of Dallas Economic Review, September, 20-28.

Durand, M. (1986). “Methods of Calculating Effective Exchange Rates and Indicators of Competitiveness”, OECD Working Paper, February.

EEC (1986), “The Influence of Exchange Rate Changes on Prices: A Study of 18 Industrial Countries: Bchnical Annex. The Calculation of Effective Exchange Rates and Indices of Competitiveness”, European Community Note, September.

Hervey, J.L. and Strauss, W.A. (1987), “The International Value of the Dollar: an Inflation Adjusted Index”, Economic Perspectives, Federal Reserve Bank of Chicago, JanuarylFebruary. 17-28.

Hervey, J.L. and Strauss. W.A. (1987), “The New Dollar Indexes Are No Different From the Old Ones”, Economic Perspectives, Federal Reserve Bank of Chicago, JulylAugust, 3-22.

Hooper. I? and Morton, I. (1978), “Summary Measures of the Dollar’s Foreign Exchange Value”, Federal Reserve Bulletin, October, 783-89.

Morgan Guaranty ’Rust. World Financial Markets, various issues. Ott. M. (1987). “The Dollar’s Effective Exchange Rate: Assessing the Impact of Alternative

Weighting Schemes”, Federal Reserve Bank of S t . Louis Review, February, 5-14. Pauls. &D. and Helkie, W.L. (1987), “A Reassessment of Measures of the Dollar’s Effective

Exchange Value”, International Financial Discussion Papers, April. Reserve Bank of Australia (1984). “The 2adeWeighted Index of Value of the Australian Dollar”,

Reserve Bank of Austmlia Bulletin. April, 69697. Weight revisions are published in October 1985 and 1986 issues of the Bulletin.

US Federal Reserve Bank (1978). “Index of the Weighted-Average Exchange Value of the US. Dollar: Revision”, Federal Reserve Bulletin, August, 200.

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