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# Explanation of the Effective Exchange Rate (Nominal, Real)

August 14, 2009

Bank of Japan

Research and Statistics
Department

## Basic information

Compilation section : Research and Statistics Department

Frequency of compilation : monthly basis

Time of release : basically the second business day of the following month

Method of release : Bank of Japan Internet web site

Publications : Financial and Economic Statistics Monthly, Bank of Japan Statistics

Commencement of data : January 1970

## 1. Concept and Calculation Method of the "Effective Exchange Rate (Nominal, Real)"

The effective exchange rate is an indicator to grasp Japan's international competitiveness in terms of its foreign exchange rates that cannot be understood by examining only individual exchange rates between the yen and other currencies.

Note: There are two main cases in terms of the "appreciation of the Japanese yen." One case occurs when the yen is appreciating only against the U.S. dollar; and the other case occurs when the yen is also appreciating against other foreign currencies. Even though the exchange rate between the yen and U.S. dollar is the same in both cases, the price competitiveness of Japan and the effect on its balance of trade differ between these cases.

The effective exchange rate is calculated as follows. The weighted average (geometric mean) of the yen's exchange rates against other major currencies is calculated using the annual value of Japan's trade with the respective countries and regions as its weights. It is then converted into an index using a base period. This type of indicator is called the "nominal effective exchange rate."

International competitiveness is affected not only by the exchange rate but also by domestic and foreign price movements. For example, even when the nominal effective exchange rate of the yen remains unchanged, the relative competitiveness of Japanese goods increases when the inflation rate of its trading partner is higher than that of Japan. Taking this into account, the nominal effective exchange rate is adjusted to incorporate inflation rate differences.This type of indicator is called the "real effective exchange rate."

The real effective exchange rate is calculated as follows. Each of the yen's exchange rates against other major currencies (i.e. nominal exchange rates) is deflated by the price indices of Japan and the corresponding countries and regions to calculate the real exchange rate. The, weighted average (geometric mean) of the real exchange rates is then calculated using the annual value of Japan's trade with the respective countries and regions as its weights. It is then converted into an index using a base period.

## 2. Data and Methodology

### (1) Selection of Currencies

The criterion for selecting the currencies to be included in the effective exchange rates is that they must have had an individual share of no less than 1 percent of Japan's total exports in 2005. From January 2000, the following 15 currencies comprise the nominal and real effective exchange rates:

US dollar / Chinese yuan / EMU Euro / Korean won / New Taiwan dollar / Hong Kong dollar / Thai baht / Singapore dollar / Pound sterling / Malaysian ringgit / Australian dollar / Indonesian rupiah / Philippine peso / Canadian dollar / Mexican peso

As for the Euro area, it is regarded as a single region when selecting currencies regardless of the individual share of each member country. Accordingly, with Slovakia having adopted to the Euro from January 2009, the selected countries and regions became 30 with the 16 countries of the Euro area included, as of January 2009.

The exchange rate of each currency is quoted from the official reference rate released by International Department, Bank of Japan, which is equal to a monthly average of actual exchange rate (For the latest month, a preliminary figure calculated by Research and Statistics Department, Bank of Japan is quoted).

### (2) Country Weights for Exports from Japan

Various kinds of weighted value of trade (such as export or import value, or the total value of exports and imports) are commonly used according to the purpose of calculating the effective exchange rate (e.g., whether the impacts on Japan's exports, or imports, or balance of trade, is of interest). Here, for the purpose of measuring the "competitiveness of Japan's exports," we use the weighted value of Japan's exports to the individual countries and regions.

The weighted value of exports to the trading partner is calculated based on the average export share of each trading partner among the 30 countries and regions selected above during the current calendar year. The data source is the Trade Statistics released by the Ministry of Finance (Individual shares in 2005 are shown in Table 1).

With the release of the newest figures of the effective exchange rate, the current year's weighted value of exports is not available. Preliminary estimates are therefore calculated using the weighted values of exports of the latest annual data available at the time of release. After the current year's trade data become available, the preliminary estimates are finalized.

For example, the effective exchange rates from January to December in 2009 are preliminarily released and then revised accordingly.

### (3) Index Formula and Base Period

The effective exchange rates are chain-linked indices aggregated from individual exchange rates with the corresponding year's weighted values.

The nominal effective exchange rate in month m of year t (CI_{t,m}),
is given by the following formula.

where is the change rate of the effective exchange rate from January year t-1 to January year t calculated with the year t-1's weighted value of trade and is the change rate from January year t to month m of year t with year t's weighted value of trade. The formula for is given by the following geometric mean.

where e_{j,t,m} is the nominal exchange rate of the yen in terms of
foreign currency j at month m of year t, and w_{j,t} is the weight of
exports to country (or region) j in year t.

Replacing the nominal exchange rate with its real exchange rate by deflating them with the price indices of Japan and the corresponding countries and regions yields the formula for the real effective exchange rate. The base period is March 1973, just after Japan's adoption of the floating exchange rate system. The effective exchange rates are indexed by March 1973 = 100.

### (4) Price Index Used for Calculation of the Real Effective Exchange Rate

Price indices for domestically produced trading goods are ideal in deflating the nominal exchange rates to calculate the real effective exchange rates, because relative prices of trading goods between Japan and its trading partners determine the competitiveness of Japan's exports. In principle, the producer price indices (PPI), or the wholesale price indices (WPI) for domestic products either for domestic demand, or for domestic demand and exports, are used to calculate the real effective exchange rate (for Japan, Domestic Corporate Goods Price Index is used). However, several countries where these kinds of price indices are not included in the International Financial Statistics (released by IMF), other indices such as consumer price indices (CPI) are used instead. The sum of export shares to the countries and regions where PPI or WPI is used amounts to 94 percent in CY 2005. Price indices used for individual countries and regions are shown in Table 2 (for China's price index, it is estimated by using a year-to-year change data of Price Index of Industrial Products released by National Bureau of Statistics, People's Republic of China).

## 3. Figures Before CY2000

Figures from CY1970 to CY1979 have been based on 23 currencies, excluding the New Taiwan dollar and the Chinese yuan, while those from CY1980 to CY1986 have been based on 24 currencies excluding the Chinese yuan. Figures from CY1987 to CY1999 have been based on 25 currencies including the Chinese yuan.

Exchange rates for the New Taiwan dollar and the Chinese yuan are quoted from the rates released by the former Dai-ichi Kangyo Bank and the IMF, respectively. The exchange rates of the other currencies are quoted from the customer exchange rates released by the former Bank of Tokyo-Mitsubishi (selling rate; monthly average).

Price indices used before CY2000 for individual countries and regions are shown in Table 3.

## 4. Notice on Usage

The effective exchange rate is based on a specific base period. It does not indicate the absolute level of competitiveness of any country or region including Japan.

## 5. Next Revision Schedule

Effective exchange rates are revised every five years in principle. The next revision is scheduled in 2011 when 2010 trade data become available.

## Country Weights, Japan's Exports, 2005 (Table 1)

- These countries and regions cover 87.32% of Japan's total exports in 2005.

## Price Index Used for Calculating the Real Effective Exchange Rate(Table 2)