Indexes of the Foreign Exchange Value of the Dollar

By Loretan, Mico; Mazda, Autria et al. | Federal Reserve Bulletin, Winter 2005 | Go to article overview

Indexes of the Foreign Exchange Value of the Dollar


Loretan, Mico, Mazda, Autria, Subramanian, Sarita, Federal Reserve Bulletin


At the end of 1998, the staff of the Federal Reserve Board introduced a new set of indexes of the foreign exchange value of the U.S. dollar. (1) The staff made the changeover, from indexes that had been used since the late 1970s, for two reasons. First, five of the ten currencies in the staff's previous main index of the dollar's foreign exchange value were about to be replaced by a single new currency, the euro. Second, developments in international trade since the late 1970s called for a broadening of the scope of the staff's dollar indexes and a closer alignment of the currency weights with U.S. trade patterns.

Exchange rate indexes aggregate and summarize information contained in a collection of bilateral foreign exchange rates. Choices concerning the exchange rates to include, the formula to use in combining the component exchange rates into a single number, and the weights to assign the exchange rates in an index all depend importantly on the objectives of the index. The main objective of the staff's current indexes is to summarize the effects of dollar appreciation and depreciation against foreign currencies on the competitiveness of U.S. products relative to goods produced by important trading partners of the United States. The staff also uses some of the indexes--those that track the dollar's moves against only the major foreign currencies--to gauge financial market pressures on the dollar.

To capture the evolving nature of international trade patterns, the staff's current exchange rate indexes allow changes in the component exchange rates and their weights. The currency weights in the dollar indexes are based on annual trade data, vary by year, and have been updated annually since 1998. Although the set of exchange rates in the indexes has remained unchanged so far, the staff will continue to review whether changes in composition or methodology are needed to ensure that the indexes adequately reflect ongoing developments in international trade patterns.

Several practical aspects of the design and implementation of the current indexes--the choice of index formula, the design of currency weights, and the selection of currencies--are discussed in this article. The article also reviews the performance of the indexes over the past twenty-five years and discusses the three minor methodological changes that the indexes have undergone since their introduction.

CHOICE OF INDEX FORMULA

The practice followed by the staff of the Board and by that of several other central banks, international organizations, and private-sector financial institutions is to use exchange rate indexes that are geometrically weighted averages of bilateral exchange rates. (2) The Board staff's nominal dollar exchange rate index at time t, [I.sub.t], is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

where [I.sub.t-1] is the value of the index at time t - 1, [e.sub.j,t] and [e.sub.j,t-1] are the prices of the U.S. dollar in terms of foreign currency j at times t and t - 1, [w.sub.j,t] is the weight of currency j in the index at time t, N(t) is the number of foreign currencies in the index at time t, and [[summation of].sub.j][w.sub.j,t] = 1. (3) Because the weights are based on annual data on international trade, they are constant within a calendar year, as is explained later in more detail.

The staff chose geometric rather than simple arithmetic averaging for its exchange rate indexes because under geometric averaging, proportionately equal appreciation and depreciation of a currency has the same numerical effect (though of opposite sign) on the index. In an arithmetically averaged exchange rate index, such changes result in an upward bias in the index for the dollar. The upward bias is less of a problem if major components move in the same direction, but this condition is often not met by bilateral exchange rates. (4)

If a currency depreciates persistently--for example, because of high domestic inflation--an exchange rate index that includes that currency will increase markedly even if the currency's weight is small. …

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