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Relative PPP Facts
For a U.S. dollar to buy as much in the UK as in the U.S., as is assumed
under the law of one price, the price of a basket of goods in pounds in the UK
(denoted as: £P) times the spot exchange rate (denoted as: $/£) should equal the
price of the same basket in the U.S. priced in dollars (denoted as: $P).
£P ($/£)= $P
This implies that the exchange rate that equalizes the value of a dollar of
purchasing power (the PPP exchange rate) is:
($/£)= $P/£P
If the actual spot rate is greater, it suggests that the £ is over-valued
against the $. If the actual spot rate is less, it suggest that the $ is
over-valued against the £.
For example if a "representative" consumption basket costs $1,500 in the U.S.
and £1,000 in the UK the PPP exchange rate would be $1.50/£. If the actual spot
rate was $1.80/£ this would indicate that the pound is overvalued by 20%, or
equivalently the dollar is undervalued by 16.7%.
Relative PPP
Relative PPP relates the inflation rate (the change of price levels) in each
country to the change in the market exchange rate.
where St is the spot rate in Foreign Currency/Domestic Currency and Pt is the
price level in period t (foreign values are marked by an asterisk). This
relation is necessary but not sufficient for absolute purchasing power parity.
According to this theory, the change in the exchange rate is determined by price
level changes in both countries. For example, if prices in the United States
rise by 3% and prices in the European Union rise by 1% the purchasing power of
the USD should depreciate by 2% compared to the purchasing power of the EUR
(equivalently the EUR will appreciate by about 2%)
PPP equalization and the law of one price
The law of one price states that differing prices of a traded good will tend to
equalize in the absence of tariffs, other barriers to trade and prohibitively
high shipping rates. The law of one price can also be stated as: "In an
efficient market all identical goods must have only one price."
The naïve PPP hypothesis is that free trade of goods should revert exchange
rates to their PPP values. However, econometric analysis rejects this
hypothesis, and gives a better prediction of the PPP/exchange rate relationship
(the CPI) based on relative GDPs. Neo-classical economics includes Balassa-Samuelson
effect theory, which explains the PPP model adjustment giving the equilibrium
CPIs.
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