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I'm having troubles to understand the difference between the Real Exchange Rate and the PPP rate.
I know the first one is calculated using a basket of goods and services so that the non-tradeable basket costs the same in 2 countries (imagining a 2-country world). Now, isn't that the rate that would hold if PPP applies?
I think I'm wrong if I say that the real exchange rate is the one that makes PPP become valid. Any help appreciated.
Both answers here are giving really good definitions of the concepts, but I think it's important to additionally talk about the relation between the two to clarify the justified confusion and to compare them.
tl;dr RER is combining PPP theory with the current exchange rate to produce a rate that is taking purchase power into account. Read the two last paragraph to understand the confusion.
From Wikipedia:
Purchasing Power Parity (PPP) is a theory that measures prices at different locations using a common basket of goods.
PPP is giving us a ratio (rate) that is fair in purchase power between different locations (according to the basket of goods).
The market exchange rates are not following PPP. This is why the RER exists. We apply PPP theory to the current exchange rates to get a "real" rate that takes purchase power into account. In other words, RER is using PPP.
From Wikipedia:
The real exchange rate (RER) is the purchasing power of a currency relative to another at current exchange rates and prices
This is confusing because, at least in online litterature, we don't seem to be explicitly mentioning their relation. For example, when we talk and teach about PPP, we often associate it with simple price indices to give usage examples (e.g. the Big Mac Index). These indices are using the current exchange rate to compare between countries, so they are simply RERs normalized to one currency and using a specific good basket for the comparison (in this case one single item, the Big Mac). Since this is not mentionned and one leads to the other, the distinction often becomes unclear.
Another confusion factor is that you can easily find PPP rates, exchange rates and price indices online, but not RERs.
There are several exchange rate concepts that need to be distinguished. There are bilateral and multilateral (aka "effective") exchange rates, nominal and real exchange rates, and market-price versus PPP (purchasing power parity) exchange rates.
Let's start with the simplest concept: A bilateral nominal exchange rate, e.g., 117 yen/(US dollar), 0.8 pounds/euro, 7.7 (Swedish krona)/(Swiss Franc), etc. These are the exchange rates that are commonly reported in newspapers and in any number of online outlets.
A bilateral real exchange rate is the bilateral nominal exchange rate multiplied by a ratio of price indices of the two currencies. (How the ratio is taken depends on whether the currency pair is quoted in the E or R method.) Naturally, many different price indices can be used; most common, though, is the use of headline CPIs (consumer price indices). Because CPI series are generally monthly (or even lower frequency) time series, real exchange rates too are generally monthly time series. The home currency appreciates in real terms against a foreign currency either if the home currency appreciates in nominal terms or if the home country's inflation rate is lower than that in the foreign currency.
While bilateral exchange rates are straightforward to report, interest often centers on multilateral exchange rates. The home economy has trade and financial ties not just with one other economy but (usually) with many different economies. To form an index of the multilateral exchange value of the home currency, it's necessary to weight the various bilateral exchange rates according to the importance of the foreign economies. Again, many different weighting schemes are possible; a common scheme uses merchandies trade weights based on imports and/or exports between the home economy and the most important foreign economies. Because bilateral exchange rates are ratios of relative prices, an exchange rate index (aka a multilateral or efffective exchange rate) is computed as a Tornqvist index (a geometric rather than arithmetic average).
Up to now, we've mainly dealt with market prices for both nominal and real exchange rates. While that's perfectly OK for many applications, it's not the most helpful way to proceed if one wants to make comparisons of standards of living across countries. Purchasing power parity (PPP) tries to facilitate such comparisons by figuring how much a standard "basket of goods" -- frequently, but not always, the goods in the CPI baskets -- costs in various countries.
A famous case of a bilateral PPP exchange rate is the "Big Mac Index" of The Economist magazine: Since a Big Mac is pretty much the same in all countries where it's sold, one can work out the PPP-based bilateral exchange between the U.S. dollar (say) and all other countries as the exchange rates that would make the cost of purchasing a Big Mac the same. (Obviously, The Economist makes no claim that the Big Mac features prominently in anybody's consumption basket.)
By comparing nominal and PPP-based exchange rates it is possible to make statements such as "currency A is overvalued (or undervalued) against currency B". Of course, different choices of consumption baskets will lead to different PPP exchange rates. Hence, depending on the choice of basket, conflicting answers may arise as to whether a currency is over- or undervalued.
For more about the Big Mac index, check out the Economist Magazine's own website.
For a non-technical discussion of the dollar indices used by the staff of the U.S. Federal Reserve Board see, e.g, the 2005 article Indexes of the Foreign Exchange Value of the Dollar in Federal Reserve Bulletin.
Effectively RER is calculated by converting currency from Country A to country B first, than purchasing the same goods in Country B, whereas PPP is the ratio of the price of goods in each country.
From the Wikipedia article:
If all goods were freely tradable, and foreign and domestic residents purchased identical baskets of goods, purchasing power parity (PPP) would hold for the exchange rate and GDP deflators (price levels) of the two countries, and the real exchange rate would always equal 1
Unfortunately, barriers to trade (as well as potential Ricardian advantages in production) often mean one good is "cheaper" in a given country than another, so RER and PPP can and do differ.
Edit: As Mico pointed out in the comments, $PPP = RER$ is only true if all goods are freely tradable, fungible, and there are no capital flows between the two countries.
