110 CHAPTER 3. SPOT MARKETS FOR FOREIGN CURRENCY
inflation in Freedonia was lower thanus.
Below, we first show the general relation between the percentage change in theRER
and the changes in the nominal rate, and then a first-order approximation that is
occasionally used:
percentage change in theRER = (1 +st 0 ,t)1 +infl∗t 0 ,t
1 +inflt 0 ,t− 1 (3.15)
≈ st 0 ,t+ [infl∗t 0 ,t−inflt 0 ,t] (3.16)wherest 0 ,tis the simple percentage change in the spot rateSbetween timest 0 andt
whileinflt 0 ,tandinfl∗t 0 ,tdenote inflation at home and abroad, respectively, over the
same time window. The first-order approximation works well if both inflation rates
are low. This is not the case in our Freedonian example:
Example 3.18
In our above story, foreign inflation was zero, us inflation 25 percent, and the
exchange rate changed by minus one-sixth; so theRERchanges by
(1− 1 /6)
1 + 0. 00
1 + 0. 25
−1 = 0. 66667 −1 =− 1 / 3 ,
as computed directly before. In contrast, the first-order approximation would have
predicted a change of –1/6 – 0.25 = –41.67 percent rather than –33.33 percent.
The error is nontrivial because in this example the exchange-rate change and one
inflation rate, theusone, are far from zero.
If theRERis constant—whatever the level— then Relativeppp(RPPP) is said
to hold; and the percentage change in theRERis a standard measure of deviations
fromRPPP. AnRPPPdeviation is most often resorted to if theRERitself cannot be
computed because price-level data are missing. If, indeed, absolute price levels for
identical bundles are not available, there is no way to compute which of the two
countries is the cheaper one. But one can still have an idea whether theRERwent
up or down if one estimates the inflation rates from the standard Consumption Price
Indices (CPI’s) rather than the price levels. ACPIis a relative number vis-a-vis a
base period, and the consumption bundle is typically tailored to the country’s own
consumption pattern rather than being a common, internationally representative
bundle of goods. Still, in most cases this makes little difference to the inflation
rates.
TheRPPPrate relative to some chosen base periodt 0 is the level of the current