Relative PPP posits that the exchange rate will change to offset differences in the rates of product
price inflation in different countries. In symbols, (et/e0) = (Pt/P0)/(Pf,t/Pf,0), where the subscript 0
indicates the initial year values and the subscript t indicates values in a subsequent year. The text
presents evidence on the relative version of PPP by examining inflation rates (rates of change of
product prices) in different countries and the rates of the change of the exchange rate between the
countries’ currencies. A relationship consistent with relative PPP is clear—low-inflation countries
tend to have appreciating currencies and high inflation countries tend to have depreciating
currencies. In addition, examination of the dollar-mark and dollar-yen exchange rates shows that
there is a tendency to follow relative PPP in the long run, but that there are also substantial
deviations from relative PPP in the short run.
If exchange rates follow national price levels in the long run, what determines national price
levels in the long run? In the long run the national money supply (or its growth rate) determines
the national price level (or the national inflation rate), through the equilibrium between money
supply and money demand. In the text we use the demand for money that follows the quantity
theory of money, in order to draw out the relationships in the most direct manner possible.
Money is held to facilitate transactions, so that money demand is based on the annual turnover of
transactions that require money, and this turnover is proxied by the level of (nominal) domestic
product (PY, where Y is real GDP). The quantity theory then says that, for each country, Ms =
kPY, where Ms is the national money supply, which is controlled by national monetary policy,
and k is a behavioral parameter.
Combining PPP and the quantity theory equations for two countries, we obtain a basis for the
monetary approach to explaining or predicting exchange rates in the long run: e = P/Pf =
(Ms/Msf)(kf/k)(Yf/Y). If the ratio of the k’s is steady, then the exchange rate will change over
the long run as the money supplies change and as real GDPs grow, with elasticities of one. Other
things equal, in the long run a lower level (or slower growth over time) of a country’s money
supply, or a higher level (or faster growth) of its real GDP, tend to result in a higher value (an
appreciation over time) of the country’s currency, because each implies a lower level (or slower
rate of increase) in the country’s price level.
How do we get from the short run in which portfolio adjustments by international investors place
the major pressures on exchange rates to the long run of PPP? We can view this as a process in
which the exchange rate overshoots (relative to the value consistent with PPP) in the short run,
and then (gradually) reverts to PPP in the long run. This can be seen most clearly by considering
an abrupt change in the domestic money supply. The additional (and presumably realistic)
assumption is that product price levels adjust slowly toward the level consistent with the quantity
theory equation. If the domestic money supply increases abruptly, then, at first, the domestic
price level does not rise much, but eventually it will. With the increase in the money supply (and
not so much of an increase in money demand at first), domestic interest rates decrease. In
addition, investors expect that eventually the foreign currency will appreciate (the domestic
currency will depreciate) relative to its initial value, because the domestic price level eventually
will be higher (PPP in the long run). For both of these reasons (lower interest rate and expected
appreciation of the foreign currency relative to its initial value), investors shift their investments
toward foreign-currency assets. This causes an abrupt, large appreciation of the foreign currency