The idea of purchasing power parity (PPP) is quite simple. A menu of common prices is used to determine at what exchange rate the same basket of goods costs the same amount in all countries. This exchange rate is called purchasing power parity or parity exchange rate.
Thus, for the exchange rate , purchasing power parity applies, i.e. is a value for the nominal exchange rate, so that
So on average, goods cost the same in both countries if the nominal exchange rate is .
The purchasing power parity represents a natural equilibrium level for the exchange rate. The law of uniform price says that (under certain conditions, such as the absence of transport- and trade- costs) a good has the same price everywhere, otherwise arbitrage would occur.
What does this mean? Let’s imagine we have a good that is sold cheaper in country A than in country B. Then traders would buy the good cheaply in country A and sell it more expensively in country B and thus make a profit. This would have three effects on (1) the market in A, (2) the market in (B) and (3) the currency market. All three effects work towards an alignment of prices.
Thus, the prices converge: the cheap good in A becomes more expensive, the expensive good in B becomes cheaper and from the point of view of country A, the increase in currency value makes the good in B even cheaper (or from the point of view of country B, the good in A becomes more expensive because the currency of B is now worth less). This process continues until the prices have converged.
Although the arbitrage idea behind the purchasing power parity theory is very simple, clear and intuitive, empirical evidence often provides very weak results. The PPP is only considered a long-term relationship, since the underlying assumptions are violated several times:
Another important limiting factor is the volume of capital-market-induced currency transfers. This is many times higher than the goods-induced volume and thus, at least in the short term, has a stronger influence on exchange rate developments than PPPs. This means that there can be systematically frequent and larger short-term deviations from the purchasing power parity, especially in the case of freely floating exchange rates.
Logs and differences
The use of purchasing power parity in macroeconomic models requires the presentation in a formal way. In addition, we always consider the representation in level values as well as in logarithmic values. Purchasing power parity means that the nominal exchange rate exactly compensates for the difference in price levels:
or in log form
where lower case letters denote logarithmic variables. The real exchange rate is:
With purchasing power parity, of course, the following applies:
If you now look at the change compared to the previous year (here we limit ourselves to the log display, as this is simpler), you will see that
where is the difference of the variable to the previous period. If is a logarithmic value, then represents the rate of change of the level value .3 is thus the domestic inflation rate , , correspondingly, the foreign inflation rate, and is the depreciation rate of the exchange rate. So, we get
Thus, the rate of depreciation corresponds exactly to the difference between the inflation rates.
The formalization of transaction costs for level values happens by means of a factor , which enters the model as a surcharge on the foreign prices and becomes as a log value an additive term .
Tradable and non-tradable goods
If non-tradable goods are explicitly included, the price index must reflect them.
3 is the absolute change of relative to the initial value.