What is the difference in value between goods from a country and those of other countries, groups of countries or the rest of world at the current exchange rate?
How can one tell if a currency is fundamentally overvalued or undervalued? This question is at the heart of international economics as well as many trade disputes.

George Soros knew the answer once, in 1992 when he placed $1 billion on the British pound. This was the beginning of a new age in currency speculation. Soros and other speculators believed the British currency was too expensive, leading to the collapse of the British currency. This led to the dramatic exit of the United Kingdom from the European Exchange Rate Mechanism, which was the precursor for the common European currency, euro. The United Kingdom never reverted to the common currency.

However, Soros and his fellow speculators failed to repeat the feat over the years. The economics profession lacks a reliable method for determining when a currency has been properly valued. This is remarkable considering that the exchange rate is an important price in economics. However, there is an answer that could be found and plenty of data available: the real exchange rates (RER).

What does it really cost to buy certain things?

The nominal exchange rate is the price of one currency in relation to another. Most people know this. The nominal exchange rate is usually expressed as the currency’s domestic price. The nominal rate for a dollar is 0.735 euros. So, if one euro costs $1.36 to purchase from the United States Dollar holder, then it would cost $1.36 to buy one Euro. The nominal exchange rate is only one part of the story. A person or company buying another currency is also interested in the possibilities of purchasing it. Is it better to have euros or dollars? The RER is here to help. It measures the value of goods in a country against the goods of other countries, groups of countries or the rest at the current nominal exchange rate.
What is the real exchange rate of currency?

The real exchange rate between two currencies (RER), is the sum of the nominal exchange rates (the dollar cost per euro, for instance) and the ratio between prices. The core equation of RER is RER =eP*/P. In our example, P* is an average price for a good in Europe and P is an average price in the United States.

E = 1.36 in the Big Mac example. If the German price for a Big Mac is 2.5 Euros and the U.S price is $3.40 then (1.36) X (3.40) = 1.36, which gives an RER of 1. If the German price was 3 euros and the U.S. cost $3.40, then the RER would be 1.36X3 / 3.40 for a RER of 1.2.

The real exchange rate between two countries can be measured using a single representative product, such as the Big Mac or McDonald’s sandwich. A nearly identical version of the Big Mac is available in many countries. If the real currency rate is 1, a burger would be the same price in the United States and Germany if the price is in a common currency. This would hold true if the Big Mac costs $1.36 US and 1 euro in Germany (or in any other European country that uses the euro). This one-product world, in which prices equal exchange rates, has the purchasing power parity of $1.36 and 1 euro respectively. The RER is 1.

Imagine that the burger is sold in Germany for 1.2 Euros. This would make it 20 percent more expensive in the euro zone, indicating that the euro is 20% overvalued relative the dollar. The nominal exchange rate will need to adjust if the real rate of exchange is not in line with its 1.2 level. This is because the same product can be bought cheaper in one country than the other. It would be economically sensible to purchase dollars and use them to purchase Big Macs in the United States for the equivalent of 1 euro. Then, you can sell them in Germany at 1.2 euros. Arbitrage is the act of taking advantage of price differences. Arbitrageurs purchase dollars to buy Big Macs in Germany. The nominal exchange rate rises until the dollar price in Germany and the US is the same. There are many costs in the real world that can prevent a direct price comparison, such as transportation and trade barriers.

The basic idea is that currencies are subject to pressure to change if RERs diverge. Overvalued currencies will be under pressure to depreciate, while those with lower values will face increased pressure to appreciate. This can become more complex if government policies prevent normal equilibration, which is often a problem in trade disputes.
Many products

What about comparing the purchasing power of countries that sell more than one product? Economists often measure the real exchange rate using a wide range of goods to do this. The price of such a basket is usually expressed in an index number, such as the consumer price index. This index includes both goods as well as services. RER can also be used to benchmark the index to any time period. Referring to the dollar-euro example above, an RER index of 1.2 means that the average Cambio Euro Real in Europe is 20% higher than the US, relative to the benchmark. Indexes do not measure absolute prices, such as the Big Mac’s price, but only changes in overall prices relative the base year. If the index is 100 in 2000 and 120 in 2011, the average price of the Big Mac will be 20 percent higher in 2011 than it was in 2000.

It can be very important to compare RER indexes between countries. The huge U.S. trade deficit against China has become a political issue and an economic problem. It is unclear if its roots lie in a fundamentally misaligned currency.

Economists and policymakers, however, are most interested in the real effective currency rate (REER), which measures a currency’s overall alignment. The REER is the average of all bilateral RERs between a country and its trading partners. It is weighted by each partner’s trade shares. It is an average. A country’s REER can be considered “equilibrium” if its currency is not undervalued relative the currencies of any one or more trading partners.

The REER series can be used to determine if a currency has been misvalued over time. If the currencies are in equilibrium, then there shouldn’t be any changes to the relative and absolute RERs. However, because consumption patterns and transport costs can change more quickly than the market baskets that statisticians create–as well as trade policies and tariffs–decreases in REERs do not necessarily mean fundamental misalignment.

Despite the fact that transportation costs and tariffs are down sharply in recent years and national consumption baskets becoming more uniform, REERs have seen their fluctuations increase. In the past century, fluctuations in REER were limited to a 30% range among advanced economies. The United States saw swings in its REER of up to 80 percent during the 1980s. Similar experiences have been had by other countries.
Other things at work

However, not all REER fluctuations are indicative of misalignment. Some large REER adjustments are remarkable smooth. This suggests that other factors, such as transportation costs, tastes, and tariffs, may play a significant role in determining the REER of a currency not misaligned.

Technological changes that result in productivity increases in goods traded between countries are called tradables. To maintain equilibrium, the REERs will rise because productivity increases result in lower production costs. However, not all goods within a market basket are tradable and therefore subject to international competition. International price competition is minimal for non-tradable goods, like houses and personal services. Prices of tradables should be equal across countries, unless there are currency controls or trade barriers. However, nontradable prices can vary widely. Data support and economic theory suggest that a large part of the REER variation across countries is due to fluctuations in non-tradable price levels.

Changes in terms of trade (such that oil producers often experience) as well as differences in fiscal policies and tariffs and financial development may explain why REERs vary across countries. In estimating the REER “equilibrium”, analysts such as the IMF take into account real exchange rate fundamentals. If there is no misalignment, the actual REER should be centered around this figure.

It can be difficult to estimate equilibrium RERs because prices tend to be sticky and the nominal rate of exchange is not in countries where market rates are determined. It’s no surprise that REERs are subject to significant short-run volatility due to news and noise trading. This makes it easy for policymakers and market participants alike to make mistakes, sometimes very serious. This can cause massive realignments that have devastating consequences, such as the 1992 ERM crises. Despite being imperfect, REERs have indicated large exchange rate overvaluations during the rise of many financial crises. It is important that the IMF and other international organizations monitor both bilateral and multilateral RERs.