# Real exchange rate

The real exchange rate is an economic indicator . It describes the ratio at which a representative basket of goods in one currency area can be exchanged for a representative (ideally the same) basket of goods in another currency area. Thus the real exchange rate is a measure for the comparison of goods - prices at home and abroad. Mathematically, the real exchange rate is a nominal exchange rate adjusted for the ratio of the price levels of the currency areas involved .

The exchange rate is one of the central prices of an economy . For methodological reasons, it is usually calculated as an index in practice. The terms of trade can be represented as the reciprocal of the real exchange rate.

## Different definitions

In principle, the real exchange rate can be derived in two ways:

1. Derivation from the purchasing power parity theory .
2. Derivation from the distinction between tradable and non-tradable goods (see Balassa-Samuelson effect ).

In the nominal exchange rate, a distinction is made between volume quotation (number of units of foreign currency in exchange for one unit of domestic currency) and price quotation (number of units of domestic currency in exchange for one unit of foreign currency).

## calculation

Since the real exchange rate is usually not calculated for individual goods but for (representative) shopping baskets or groups of goods, it is usually shown as an index.

independent variables:

• ${\ displaystyle e_ {t} ^ {n}}$the nominal exchange rate at the time in volume quotation,${\ displaystyle t ^ {}}$
• ${\ displaystyle e_ {0} ^ {n}}$ the nominal exchange rate of the base year in volume quotation,
• ${\ displaystyle P_ {t} ^ {*}}$the foreign price index at the time related to the base year,${\ displaystyle t ^ {}}$
• ${\ displaystyle P_ {t} ^ {}}$the domestic price index at the time related to the base year.${\ displaystyle t ^ {}}$

The base year must be identical in each case. The index of the real exchange rate then results:

${\ displaystyle e_ {t} ^ {r} = {\ frac {e_ {t} ^ {n}} {e_ {0} ^ {n}}} \ cdot {\ frac {P_ {t} ^ {*} } {P_ {t}}} \ cdot 100}$

The real exchange rate for individual goods is calculated as follows:

${\ displaystyle e_ {t} ^ {r} = e_ {t} ^ {n} \ cdot {\ frac {p_ {t}} {p_ {t} ^ {*}}} \ quad}$,

with as the price of the goods abroad, as the price of the goods in Germany and as the nominal exchange rate in volume quotation. ${\ displaystyle p_ {t} ^ {*}}$${\ displaystyle p_ {t} ^ {}}$${\ displaystyle e_ {t} ^ {n}}$

If one considers the changes in the real exchange rate in a period, then this results for low inflation rates approximately as

${\ displaystyle \ Delta \% e ^ ​​{r} = \ Delta \% e ^ ​​{n} + \ pi - \ pi ^ {*}}$

${\ displaystyle \ Delta \% e ^ ​​{r}}$is the percentage change in the real exchange rate, the percentage change in the nominal exchange rate in each case in terms of quantity. denotes the inflation rate in Germany, the inflation rate abroad. ${\ displaystyle \ Delta \% e ^ ​​{n}}$${\ displaystyle \ pi}$${\ displaystyle \ pi ^ {*}}$

## Consequences of changes in the real exchange rate

A change in the real exchange rate takes place when the dependent variable changes . According to the calculation above, this is triggered by a change in the value of one or more of the independent variables listed above. Given domestic and foreign prices, nominal and real appreciation and depreciation take place in parallel. This case can be viewed as decisive in the short term, since the volatility of the nominal exchange rate is higher than that of the price indices, especially in the short term. ${\ displaystyle e ^ {r}}$

### Real appreciation

When using the quantity quotation , a rising real exchange rate indicates a real appreciation ; Consequences:

• Exports fall as domestic goods become expensive compared to foreign ones.
• Imports increase because foreign goods become relatively cheaper.

As a result, the real appreciation for the domestic market leads to a loss of competitiveness and higher purchasing power compared to abroad and improved terms of trade.

### Real devaluation

A falling real exchange rate in the volume quotation indicates a real devaluation ; Consequences:

• Exports are increasing as domestic goods become cheaper compared to foreign ones.
• Imports are falling because foreign goods become relatively more expensive.

For the domestic market, the real devaluation leads to an increase in competitiveness combined with lower purchasing power compared to foreign countries and worsened terms of trade.

## Calculation problems

### Choice of price index

In practice, various price indices can be used to calculate the real exchange rate, e.g. B. Export price index, GDP deflator, consumer price index, labor cost index, etc. The problem is that the individual indices in different countries do not contain the same goods and / or services, which is particularly relevant with regard to the distinction between tradable and non-tradable goods. In addition, the use of indices that contain closely related tradable goods is criticized, since purchasing power parity usually applies to such groups of goods and therefore the value of the real exchange rate calculated in this way has little informative value with regard to the competitiveness of the countries under consideration.

### Choice of the base year

The choice of the base year is obviously decisive for the interpretation of ongoing exchange rate developments. A point in time should therefore be chosen as the base year at which the economies under consideration are in an internal and external equilibrium (which creates renewed problems with regard to the definition of such a point in time). Alternatively, however, the indices can be calculated for different base times and compared with one another.

### Real and real effective exchange rate

Usually countries have multiple trade links, which is why the calculation of a real exchange rate for a trading partner hardly allows a comprehensive interpretation of competitiveness. This requires the calculation of a real effective exchange rate , which can be determined as the average of the bilateral real exchange rates for all trading partners (or at least the relevant ones) weighted with the respective trading shares.

### Other problems

Different legal systems or tax rates as well as differences in the implementation of fiscal and monetary policy measures or in the development of the financial markets can be the reason for movements in real exchange rates. At least permanent changes in the terms of trade should also be reflected. However, these causes are sometimes difficult to determine or quantify and can therefore easily lead to misinterpretations of developments in real exchange rates.

## Comparison of the development of nominal and real exchange rates

The aim here is to compare the development of nominal exchange rates in comparison to real exchange rates using four of the most important currencies. For this purpose, the development of these courses in the period 1975–2002 was examined. In the graphics for the euro area and Japan, indices are shown with the base year: 1995 = 100.

Comparison of nominal vs. real exchange rate of the EU-27 zone (1975–2002), 1995 index = 100

Both exchange rates tended to be similar in the euro area - however, the real rate fell from 108 to 82 between 1977 and 1982, while the nominal rate only fell from 1980 (starting from 109) and did not end its strongly negative trend until 1985 a value of 1979. The real rate had recovered again in 1982 and rose continuously up to 1987 up to a value of 100. By 1990 the two rates had converged and since then have followed a similar trend, between 1992 and 1997 synchronously and from 1997 again with a similar trend Tendency.

Comparison of nominal vs. Japan's real exchange rate (1975–2002), 1995 index = 100

In the period from 1975 to 1982, the exchange rates in Japan ran in opposite directions. While the real exchange rate fell to a value of 50, the nominal exchange rate rose to 42. Thereafter, both exchange rates tended to run in the same direction until 1994, when they both reached the value 96. From 1994, both exchange rates are approximately synchronous.

The exchange rates in the currency area of ​​the United Kingdom (UK) ran from 1977 with the same tendency but different values. Up until 1995, the nominal exchange rate was always higher than the real exchange rate. This changed from this year on - now the real exchange rate showed higher values. While the nominal exchange rate stagnated at a value of 115 from 1997, the real exchange rate rose to a value of 145 by 2002, thus its level had increased by 60 points since 1975.

In the US currency area , both rates tended to be the same from 1978 onwards. From 1989 to the end of the observation period 2002, the nominal and real exchange rates were completely synchronized, apart from minor deviations. In general, a connection between real and nominal exchange rates can be seen - based on the currency areas considered here. However, this assumed relationship has not yet been sufficiently empirically proven at this point; this requires further, more extensive research and empirical analysis. The examples UK and especially the USA show a tendency (partly also synchronously) of the two courses to be similar. However, the examples of Japan and the euro area show that both courses can develop differently from one another.

## literature

• Olivier Blanchard, Gerhard Illing: Macroeconomics. 4th updated edition. Pearson Studium, Munich 2006, ISBN 3-8273-7209-7 .
• Michael C. Burda, Charles Wyplosz: Macroeconomics. 2nd, completely revised edition. Franz Vahlen Verlag, Munich 2003.
• Paul R. Krugman, Maurice Obstfeld: International Economy - Theory and Politics of Foreign Trade. 7th, updated edition. Pearson Studium, Munich 2006, ISBN 3-8273-7199-6 .
• Laurence Copeland: Exchange Rates and International Finance. 4th edition. Pearson Education, London et al. 2005.