Effective exchange rate

The effective exchange rate or multilateral exchange rate measures the performance of the domestic currency against several other important currencies and is methodologically comparable with a price index . Exchange rates indicate the exchange ratio between currencies. If one compares two currencies with one another and uses this to determine their exchange rate, one speaks of the bilateral exchange rate . Based on the bilateral exchange rate, changes in the exchange rate can only be read off against one currency. The effective exchange rate is used to express the average change in the exchange rate against all other currencies. Among other things, it serves as an indicator for the international competitiveness of a country or a currency zone.

Definition of terms

To determine an effective exchange rate, the exchange rate between a currency and a so-called currency basket is considered.

The currency basket is formed from the currencies of the most important trading partners. The effective exchange rate is determined by taking the average of all bilateral exchange rates in the currency basket. Each bilateral exchange rate is weighted with the share of the respective country in foreign trade . If weighting is carried out with the export share , one speaks of the export exchange rate, if, on the other hand, weighting is carried out with the import share , then one speaks of the import exchange rate. Usually the average is formed from the export and import share, in this case the effective exchange rate is also referred to as the external value of the currency.

When calculating the effective exchange rate, as with the bilateral one, there is a subdivision into a nominal and a real exchange rate.

Demarcation		Inclusion of the price level
		nominal	real
Number of countries	bilateral	nominal bilateral exchange rate	real bilateral exchange rate
	effectively	nominal effective exchange rate	real effective exchange rate

Determination of the effective exchange rates

method

Effective exchange rates for the currency of a country or currency area are determined as the weighted average of bilateral exchange rates vis-à-vis the main trading partners, with the partner countries being weighted according to their importance for the base country.

1. Identify the main trading partners of the base country
2. Calculation of the bilateral exchange rates between the partner countries and the base country
3. Determination of the price level / price indices for each partner country with the same reference values
4. Weighting of the individual trading partners according to their importance for the base country
5. Calculation of the real effective exchange rate
6. Determination of the base period

weighting

German world trade by region, 2007

Countries / regions	Exports to		Imports to
	Billion euros	percent	Billion euros	percent
The 27 EU countries	628	65	460	60
Other European countries	103	11	91	12
United States	73	8th	46	6th
Southeast Asian emerging economies	32	3	33	4th
China	30th	3	55	7th
Japan	13	1	24	3
Near and Middle East	24	2	6th	1
Other	66	7th	55	7th
Total	969	100	770	100

Each partner country is given a weight that usually represents the importance of the country in the foreign trade of the base country. The partner countries can be weighted according to the import or export shares of the partner country in the base country (bilateral weighting procedure). Since it is tedious to track two different exchange rates, the weighting of the effective exchange rate is usually used as the average of export shares and import shares.

For example, according to the adjacent table: "German world trade by region" , the US dollar would have a weight of

${\displaystyle \left({\frac {8\,\%+6\,\%}{2}}\right)=7\,\%}$

receive.

In addition to this bilateral weighting method, the global weighting method and weighting based on world trade models are also common.

With a global weighting, the shares of individual countries in world exports are considered. The world export shares of the trading partners to the base country are not taken into account. A weighting on the basis of world trade models can, for example, take place via the Multilateral Exchange Model (MERM) of the IMF .

Weighting of the ECB

The European Central Bank determines the weights of the individual partner countries based on the proportions of finished products as defined in Sections 5 to 8 of the Standard International Trade Classification (SITC) .

For the weights, the ECB uses the values ​​from exports and imports, without taking into account trade within the euro area. The imports are weighted according to the simple share of the partner countries in total imports into the euro area. Exports, on the other hand, are weighted twice because of the so-called “third market effects”. This captures the competition between European exporters in foreign markets versus domestic producers and exporters from third countries. The weightings of the individual trading partners by the European Central Bank are available on its website.

Weighting of the Japanese central bank

Japan real and nominal effective exchange rates

The Japanese Central Bank determines the weights based on the export and import values ​​or the total export and import values. The choice of weights to be used depends on the effects to be investigated. If, for example, the “competitiveness of Japanese exports” is examined, the weights are based on Japanese exports to the individual countries and regions (trading partners).

The weighted values ​​of the exports are calculated on the basis of the average shares of the individual trading partners in the current calendar year. As a trading partner, Japan has 27 countries and regions, which corresponds to 15 currency areas. The data source is the Trade Statistics released by the Japanese Ministry of Finance.

Weighting of the Federal Reserve System

US real and nominal effective exchange rates

The FED , the United States ' central banking system , weights the individual countries or currency areas with a combination of three different bilateral weights. It weights imports, exports and third-market transactions. The combination of these three weightings is the weighting of the FED.

Three weights

1. bilateral weighting according to imports of goods into the USA = import weight of the country in the period = share of the country in the total US goods imports in the period
   
   ${\displaystyle \mu _{\text{US,j,t}}={\frac {M_{\text{US,j,t}}}{\sum _{j=1}^{N(t)}M_{\text{US,j,t}}}}}$
   
   ${\displaystyle \mu _{\text{US,j,t}}}$ ${\displaystyle j}$ ${\displaystyle t}$
   ${\displaystyle M_{\text{US,j,t}}}$ ${\displaystyle j}$ ${\displaystyle t}$
   
   
2. bilateral weighting according to exports of goods from the USA = export weight of the country in the period = share of the country in the total US goods exports in the period
   
   ${\displaystyle \epsilon _{\text{US,j,t}}={\frac {X_{\text{US,j,t}}}{\sum _{j=1}^{N(t)}X_{\text{US,j,t}}}}}$
   
   ${\displaystyle \epsilon _{\text{US,j,t}}}$ ${\displaystyle j}$ ${\displaystyle t}$
   ${\displaystyle X_{\text{US,j,t}}}$ ${\displaystyle j}$ ${\displaystyle t}$
   
   
3. bilateral weighting of the “third market effects” = third market weight of the country in the period = export weight of the country in the period = share of the economy in the imports of the country in the period (where ) = multiplicative factor (1 - weight of imports in the country from the USA in the period ) [sum of the weights becomes 1]
   
   ${\displaystyle \tau _{\text{US,j,t}}=\sum _{k\neq 1;k\neq US}^{N(t)}\epsilon _{\text{US,k,t}}{\frac {\mu _{\text{k,j,t}}}{(1-\mu _{\text{k,US,t}})}}}$
   
   ${\displaystyle \tau _{\text{US,j,t}}}$ ${\displaystyle j}$ ${\displaystyle t}$
   ${\displaystyle \epsilon _{\text{US,k,t}}}$ ${\displaystyle k}$ ${\displaystyle t}$
   ${\displaystyle \mu _{\text{k,j,t}}}$ ${\displaystyle k}$ ${\displaystyle j}$ ${\displaystyle t}$ ${\displaystyle k\neq j}$
   ${\displaystyle (1-\mu _{\text{k,US,t}})}$ ${\displaystyle k}$ ${\displaystyle t}$

Linking the weights

The coefficients of the three partial weights were chosen to give equal weight to competition from imports into US markets and competition from US exports in overseas markets. In addition, the bilateral export weights and the weights for recording competition in third-party markets are given the same meaning.

${\displaystyle w_{\text{j,t}}={\frac {1}{2}}\mu _{\text{US,j,t}}+{\frac {1}{2}}\left({\frac {1}{2}}\epsilon _{\text{US,j,t}}+{\frac {1}{2}}\tau _{\text{US,j,t}}\right)}$

Trading partner

The US central bank calculates the effective exchange rates with a broad group (The Broad Index) of trading partners. This is split into a main group (The Major Currencies Index) and a subsidiary group (OITP - Other important trading partners).

The main group contains the following seven currency areas:

• Euro
• Canadian dollar
• Japanese yen
• British pound
• Swiss franc
• Australian dollar
• Swedish crown

The US dollar index

US dollar index

The US Dollar Index (USDX) has been determined by ICE Futures US , a subsidiary of the Intercontinental Exchange , a commodity and index exchange based in Atlanta (USA), since 1973 after the Bretton Woods agreement was terminated .

The US Dollar Index shows the ratio of six currencies to the USD, taking into account the euro with the trading volume from twelve EU countries. These make up 57.6% of the index. The other currencies are the Japanese yen (13.6%), the British pound (11.9%), the Canadian dollar (9.1%), the Swedish krona (4.2%) and the Swiss franc (3, 6%).

The trade-weighted Trade Weighted US Dollar Index (also known as "The Broad Index") of the US Federal Reserve (FED) is comparable to the geometrically weighted US Dollar Index . Compared to the US Dollar Index, the FED's index measures the value of the US dollar much more accurately, as the weighting of the FED represents the competitiveness of US goods compared to other countries and trading partners.

The Euro Currency Index

Euro Currency Index

The Euro Currency Index (EUR_I) represents the arithmetic ratio of four key currencies in comparison to the euro: US dollars , British pounds , Japanese yen and Swiss francs . All currencies are expressed in units of measure of currency per euro. The index was launched in 2004 by the Stooq.com stock exchange portal. The base value is 100 points on January 4, 1971. Before the European common currency was introduced on January 1, 1999, an exchange rate of 1 euro = 1.95583 German marks was calculated.

The trade-weighted Euro Effective Exchange Rate Index of the European Central Bank (ECB) is comparable to the arithmetically weighted Euro Currency Index . Compared to the Euro Currency Index, the ECB's index measures the value of the euro much more accurately, as the weighting of the ECB represents the competitiveness of European goods compared to other countries and trading partners.

Other companies also published Euro Currency Indices. However, the calculation was discontinued after a few years. Examples are the Dow Jones Euro Currency Index from Dow Jones & Company from 2005 to 2009 and the ICE Euro Currency Index from the futures exchange ICE Futures US , formerly the New York Board of Trade (NYBOT), from 2006 to 2011.

The US Dollar Index and the Trade Weighted US Dollar Index use a calculation method similar to the Euro Effective Exchange Rate Index .

Nominal effective exchange rate

Nominal effective exchange rates between the EU and EER 22 and EER 42

Nominal effective exchange rates ( nominal effective exchange rate (NEER) ) or nominal multilateral exchange rates are weighted averages of the bilateral exchange rates against the currencies of the most important trading partners. The determination of this effective exchange rate neglects the foreign price level of all countries in the currency basket.

When calculating the nominal multilateral exchange rate, it should be noted that the bilateral exchange rates are used uniformly in the quantity or price quotation . Depending on the quotations used, there is a nominal effective exchange rate.

${\displaystyle NEER=E_{1}^{g_{1}}\cdot E_{2}^{g_{2}}\cdot E_{3}^{g_{3}}\cdot \ldots \cdot E_{n-1}^{g_{n-1}}=\prod _{i=1}^{n-1}E_{i}^{g_{i}}}$

${\displaystyle {\text{mit}}\quad g_{i}>0\quad {\text{und}}\quad \sum _{i=1}^{n-1}g_{i}=1}$

${\displaystyle E_{i}}$	= nominal bilateral exchange rate of the domestic currency to the respective foreign currency ${\displaystyle i}$
${\displaystyle g_{i}}$	= Weight of the respective country
${\displaystyle NEER}$	= nominal multilateral exchange rate

The ECB publishes the nominal EER indices for the euro against the other currencies for a narrow ( EER- 23 group ) and a broad group ( EER-42 group ) of trading partners. The weights used reflect the share of the individual partner countries in trade in the euro zone.

As long as there are no high and diverging inflation rates between individual countries, changes in the nominal effective exchange rates can be regarded as identical to the real effective exchange rates. Otherwise, however, the two sizes fall apart. In this case, nominal effective exchange rate changes do not provide any useful pointers for assessing changes in international competition.

Real multilateral exchange rate

Real effective exchange rates between the EU and EER 22 and EER 42

The real effective exchange rate (REER) or the real multilateral exchange rate is a measure of the change in a country's competitiveness, taking into account the change in costs or prices compared to other countries.

Real effective exchange rates are deflated nominal effective exchange rates with a weighted average of foreign prices and costs compared to domestic prices or costs. This means nothing else than that the price level is taken into account in the courses. They are therefore a measure of the competitiveness of prices and costs.

The price level can be determined in different ways, which ultimately leads to different real exchange rates and thus also has an effect on the real effective exchange rate. The following price indices can be used for the price level:

US real effective exchange rate based on two different indices

• Consumer price indices (CPI),
• Producer price index (PPI),
• Gross domestic product ( GDP deflator ),
• Unit labor costs in manufacturing (ULCM)
• Unit Labor Costs in the Overall Economy (ULCT)
• Export price indices

• internationally non-traded goods and internationally traded goods (called internal terms of trade)
• domestic export goods and domestic import goods (called external terms of trade)

The ratio between the domestic export goods and the domestic import goods (from different countries) is a special real effective exchange rate. This ratio is the reciprocal of the terms of trade , which correspond to the ratio of export to import prices. Real exchange rates on a broader basis are considered when comparing consumer price indices or when comparing GDP deflators.

When calculating the real multilateral exchange rate, a distinction must be made between volume quotation and price quotation .

Quantity quotation

If the initial value, i.e. the nominal bilateral exchange rate, is given in the quantity quotation, the following formula should be used:

${\displaystyle REER=\left(E_{1}\cdot {\frac {P}{P_{1}^{*}}}\right)^{g_{1}}\cdot \left(E_{2}\cdot {\frac {P}{P_{2}^{*}}}\right)^{g_{2}}\cdot \ldots \cdot \left(E_{n-1}\cdot {\frac {P}{P_{n-1}^{*}}}\right)^{g_{n-1}}=\prod _{i=1}^{n-1}\left(E_{i}{\frac {P}{P_{i}^{*}}}\right)^{g_{i}}}$

${\displaystyle {\text{mit}}\quad g_{i}>0\quad {\text{und}}\quad \sum _{i=1}^{n-1}g_{i}=1}$

${\displaystyle E_{i}}$	= nominal bilateral exchange rate of the domestic currency to the respective foreign currency (quantity quotation) ${\displaystyle i}$
${\displaystyle g_{i}}$	= respective weight of the foreign currency ${\displaystyle i}$
${\displaystyle P}$	= domestic price index
${\displaystyle P_{i}^{*}}$	= foreign price index (with comparable goods / groups of goods)
${\displaystyle REER}$	= real multilateral exchange rate

Price quotation

If, on the other hand, the initial value, i.e. the nominal bilateral exchange rate, is specified in the price quotation , the domestic price index swaps positions with the foreign price index.

${\displaystyle REER=\prod _{i=1}^{n-1}\left(E_{i}{\frac {P_{i}^{*}}{P}}\right)^{g_{i}}}$

${\displaystyle {\text{mit}}\quad g_{i}>0\quad {\text{und}}\quad \sum _{i=1}^{n-1}g_{i}=1}$

${\displaystyle E_{i}}$	= nominal bilateral exchange rate of the domestic currency to the respective foreign currency (price quotation) ${\displaystyle i}$
${\displaystyle g_{i}}$	= respective weight of the foreign currency ${\displaystyle i}$
${\displaystyle P}$	= domestic price index
${\displaystyle P_{i}^{*}}$	= foreign price index (with comparable goods / groups of goods)

Individual evidence

1. ↑ Blanchard, Olivier; Illing, Gerhard (2006): Macroeconomics . 4th updated edition. Munich: Pearson Studium, p. 522
2. ↑ Exchange rate - Article in the Gabler Wirtschaftslexikon.
3. ↑ Jarchow, Hans-Joachim (2002): "Monetary Foreign Trade - II. International Monetary Policy", 5th, revised and significantly expanded edition, Göttingen: Vandenhoeck & Ruprecht Verlag, p. 272
4. ↑ Federal Statistical Office, special trade by country group and country, 2007
5. ↑ Belgium a. Luxembourg, Denmark, Finland, France, Greece, Ireland, Italy, Netherlands, Austria, Portugal, Sweden, Spain, United Kingdom and from May 2004: Estonia, Latvia, Lithuania, Malta, Poland, Czech. Republic, Slovakia, Hungary, Slovenia, Cyprus and from January 2007: Bulgaria, Romania.
6. ↑ Hong Kong, Singapore, South Korea, Taiwan, Brunei, Indonesia, Malaysia, the Philippines and Thailand.
7. ↑ Weighting of the individual currencies of the ECB
8. ↑ Explanation of the Effective Exchange Rate (Nominal, Real) ( Memento from January 22, 2011 in the Internet Archive ) Retrieved on April 28, 2008 21:47 (CET)
9. ↑ ^{a b} Board of Governors of the Federal Reserve System Indexes of the Foreign Exchange Value of the Dollar (PDF; 74 kB) Accessed: May 14, 2008 10:14 am CET
10. ^ Federal Reserve Bank of St. Louis: Trade Weighted Exchange Index: Major Currencies
11. ↑ ICE Futures US: US Dollar Index (PDF; 476 kB)
12. ↑ European Central Bank: nominal effective exchange rate Processing status: April 1, 2008. (Accessed: April 2, 2008, 10:33 am CET)
13. ↑ nominal effective exchange rate (EER) Nominal euro EERs are weighted averages of bilateral euro exchange rates against the currencies of the euro area's main trading partners. The ECB publishes nominal EER indices for the euro against the currencies of a narrow and a broad group of trading partners. The weights used reflect the share of each partner country in euro area trade.
14. ↑ Shams, Rasul (1985): Exchange rate theory and policy: an introduction Munich: Oldenbourg, p. 10
15. ↑ European Central Bank: real effective exchange rate Processing status: April 1, 2008. (Accessed: April 2, 2008, 10:39 CET)
16. ↑ real effective exchange rate (EER) Real euro EERs are nominal euro EERs deflated by a weighted average of foreign, relative to domestic, prices or costs. They are, thus, measures of price and cost competitiveness.
17. ^ Rübel, Gerhard (2002): Fundamentals of monetary foreign trade , Munich: Oldenbourg
18. ↑ Burda, Michael C .; Wyplosz, Charles (2003): Macroeconomics . 2nd, completely revised edition. Munich: Franz Vahlen Verlag

literature

• Blanchard, Olivier; Illing, Gerhard (2006): Macroeconomics . 4th updated edition. Munich: Pearson Studies, ISBN 3-8273-7209-7 .
• Burda, Michael C .; Wyplosz, Charles (2003): Macroeconomics . 2nd, completely revised edition. Munich: Franz Vahlen Verlag, ISBN 3-8006-2856-2 .
• Rübel, Gerhard (2002): Fundamentals of monetary foreign trade , Munich: Oldenbourg, ISBN 3-486-25840-0 .
• Shams, Rasul (1985): Exchange rate theory and policy: an introduction Munich: Oldenbourg, ISBN 3-486-29961-1 .
• Willms, Manfred (1995): International Monetary Policy . 2nd, revised and expanded edition, Munich: Franz Vahlen Verlag, ISBN 3-8006-1999-7 .

Web links

• Weighting of the individual currencies of the European Central Bank
• Weighting of the individual currencies of the Federal Reserve
• Composition of the US dollar Index® (Engl.)

This version was added to the list of articles worth reading on May 20, 2008 .