SUGGESTED READINGS
4.5 THE REAL EXCHANGE RATE
Expected change in the spot exchange rate Expected inflation differential
t
Interest rate differential
(1 + id)t (1 + E[pd])
(1 + E[pf])
E[Std/f] S0d/f (1 + if)
Forward-spot differential
International Fisher relation
Unbiased forward expectations Interest rate parity Uncovered RPPP
interest parity
Ftd/f S0d/f
FIGURE 4.9 The International Parity Conditions.
the realized real return in each currency. Real interest parity and the international Fisher relation do not hold over short horizons largely because of inflation volatility.
Real rates are seldom equal across currencies.
Uncovered Interest Parity
Figure 4.9 summarizes the international parity conditions. Note that the ratios that lie diagonally across the figure also must be equal in equilibrium. Because interest rates are tied to the forward premium and the forward premium is a (long-run) predictor of changes in spot rates, then
E[Std/f] S0d/f =
(1+id) (1+if)
t
(4.10) This is calleduncovered interest parityand relates nominal interest rates to expected spot rate changes, and vice versa.7
Similarly, the other diagonal in Figure 4.9 should hold in equilibrium.
Ftd/f S0d/f =
(1+E[pd]) (1+E[pf])
t
(4.11) The inflation differential should predict future changes in the spot rate of exchange.
This completes the circuit of international parity conditions.
what if the inflation rate in pounds sterling was 8 percent during the year? Solving the Fisher equation, your real rate of return during the year was £ =(1+i£)/(1+ p£)−1=(1.05/1.08)−1= −0.028, or−2.8%. In real or purchasing power terms, you are worse off at the end of the year than you were at the beginning of the year.
And you are a year older, if no wiser.
A similar phenomenon occurs with exchange rate changes. If you look only at nominal changes, you’ll miss real changes in purchasing power across currencies. In order to identify real, as opposed to nominal, changes in spot rates of exchange, we need to adjust nominal exchange rates for the effects of inflation in the foreign and domestic currencies.
Real Changes in Purchasing Power
Suppose the spot rate is S0¥/$=¥100/$, as in Figure 4.10. Expected inflation is E[p¥]
= 0 in Japan and E[p$] = 10 percent in the United States. If nominal spot rate changes reflect changes in the relative purchasing power of the yen and the dollar, the expected spot rate in one period should be
E[S¥1/$]=S¥0/$(1+E[p¥])
(1+E[p$]) =(¥100/$)(1.00)
(1.10)=¥90.91/$ according to RPPP in Equation 4.5.
Suppose that one year later the inflation estimates turn out to be accurate but the dollar has appreciated to S¥1/$=¥110/$. This is a 10 percent dollar appreciation in nominal terms. In fact, this represents a 21 percent real (inflation-adjusted) appreciation of the dollar relative to the expected spot rate of ¥90.91/$.
(Actual−Expected)/Expected= (¥110/$−¥90.91/$)
¥90.91/$ =0.21
This 21 percent real (inflation-adjusted) surprise in purchasing power is shown in the right panel of Figure 4.10. In this example, the dollar has experienced a 21 percent appreciation in purchasing power relative to the yen. The real exchange rate captures changes in the purchasing power of a currency relative to other currencies by backing out the effects of inflation from changes in nominal exchange rates.
The Real Exchange Rate
We used the law of one price as our guiding principle in deriving the international parity conditions. This faith is well founded for actively traded financial contracts, such as currencies and Eurocurrencies traded in the interbank markets. For these assets, arbitrage is quick to eliminate deviations from PPP. For less actively traded assets, especially those with many barriers to trade such as land or labor, deviations from PPP can persist for many years.
The real exchange rate Xtd/f is the nominal exchange rate Std/f adjusted for relative changes in domestic and foreign price levels (i.e., adjusted for differential inflation) since an arbitrarily defined base period at time t=0.
¥90/$
time 1
0
Change in the nominal exchange rate
¥120/$
¥110/$
¥100/$
90%
time 1
0
Expected real exchange rate E[X1¥/$] = 100%
Change in the real exchange rate
120%
110%
100%
St¥/$ Xt¥/$
Actual spot rate S1¥/$ = ¥110/$
is 21% higher than the expected spot rate
Expected spot rate E[S1¥/$] = ¥90.91/$
Actual real exchange rate X1¥/$ = 121%
is 21% higher than the expected real rate
FIGURE 4.10 Change in the Real Exchange Rate.
Real exchange rates reflect changes in purchasing power.
Xtd/f=(Std/f/S0d/f){[(1+p1f)/(1+p1d)][(1+p2f)/(1+p2d)]. . .[(1+ptf)/(1+ptd)]}
=(Std/f/S0d/f)
t
τ=1
!(1+p
τ
f)/(1+p
τ d)"
#
(4.12)
The nominal spot exchange rate Std/f at time t divided by the base period spot rate S0d/f equals one plus the percentage in the spot exchange rate. The inflation adjustment indicates whether this change in the nominal exchange rate reflects the accumulated inflation differential between the two currencies. If change in the nominal spot rate of exchange exactly offsets the mean inflation differential, then the real exchange rate will remain at 100 percent of its base level. Thus, the real exchange rate provides a measure of the purchasing power of two currencies relative to a base period.
The formula for the percentage change in the real exchange rate during a single period is
(1+xtd/f)=(Xtd/f/X
t−1
d/f)=(Std/f/S
t−1
d/f)[(1+ptf)/(1+ptd)] (4.13) The percentage change in the real exchange rate depends only on change in the nominal exchange rate and the inflation differential during the period.
It is somewhat misleading to retain the currencies on the symbols for the real exchange rate, because the currency units cancel from the ratio (Std/f/S0d/f) in Equations 4.12 and 4.13. Inflation rates also are unit-less. The measure Xtd/f is a number, such as 1.21, that represents the real value of the currency in the denominatorrelative to the base period. Currencies are retained as a reminder that this is a measure of the relative purchasing power of the currency in the denominator.
Let’s return to Figure 4.10. The ratio (S1¥/$/S0¥/$) =(¥110/$)/(¥100/$)=1.10 indicates that the dollar increased 10 percent in nominal terms during the period.
This was despite the fact that dollar inflation was 10 percent higher than yen inflation. By construction, the level of the real exchange rate in the base period is X0¥/$=1.00. Equation 4.13 yields
(1+x¥1/$)=(X¥1/$/X¥0/$)=[(¥110/$)/(¥100/$)][(1.10)/(1.00)]=1.21 or a real exchange rate that is 21 percent higher than at the start of the period. This represents a 21 percent increase in the purchasing power of the dollar during the period.
It is convenient to pick a base period in which the purchasing power of the two currencies is close to equilibrium. In this case, PPP holds and S0d/f=Pd0/Pf0for a wide range of assets. Because any base period can be chosen, the level of the real exchange rate is not necessarily informative. In particular, it is inappropriate to claim that a currency is overvalued simply because the level of the real exchange rate is greater than 1. It may be that the currency was undervalued in the base period and remains undervalued. For example, the real exchange rate may have risen by 10 percent from 1.00 to 1.10, but if the ‘‘true’’ value of the currency in the base period was only 0.80 (80 percent of equilibrium), then a 10 percent real appreciation of the currency only brings it up to 0.88 (88 percent of its equilibrium value) and it remains undervalued relative to its equilibrium value. Further, there are cross-currency differences in asset prices, so that a currency can have more purchasing power in some assets than in others. Change in a real exchange rate is more informative than the level of the real exchange rate because of cross-currency differences in individual or national consumption baskets (and hence measures of inflation) and the arbitrary choice of the base period.
It is often convenient to place the domestic currency in the denominator:
(1+xtf/d)=(Xtf/d/X
t−1
f/d)=(Stf/d/St−1
f/d)[(1+ptd)/(1+ptf)] (4.13) to measure the relative purchasing power of the domestic currency. If currency f in the numerator is replaced by a basket of foreign currencies, then xtf/d provides a measure of the purchasing power of the domestic currency relative to other currencies in the currencies basket.
Figure 4.11 plots the real value of the euro, yen, pound, and dollar in this way since the early 1970s. Most exchange rates began to float in early 1973, so only the period since early 1973 is relevant to the modern era. The dollar and the yen were grossly out of balance in the fixed exchange rate regime that preceded the 1973 float.
The floating rate era brought currency values closer to equilibrium, but was unable to achieve true parity. For example, at times the yen has been 50 percent higher and at other times 20 percent lower than its average value. Figure 4.11 illustrates that there are large and persistent deviations from real PPP.
Academic studies confirm our casual interpretation of Figure 4.11.
■ Deviations from real exchange rate parity can be substantial in the short run.
■ Deviations from real exchange rate parity can last several years.
APPLICATION Keeping Track of Your Currency Units
In the international parity conditions, the currency in the numerator (denomi- nator) stays in the numerator (denominator) of the interest rates and exchange rates. For example, in RPPP,
E[Std/f]/S0d/f=[(1+E[pd])/(1+E[pf])]t (4.5) the currency in the numerator of each spot rate also is in the numerator of the inflation ratio. Conversely, the currency in the denominator of the left-hand side stays in the denominator on the right-hand side.
Real exchange rates are the only exception to this rule. With a real exchange rate, we want toreversethe effects of inflation on nominal exchange rates.
1+xtd/f=(Xtd/f/Xt
−1
d/f)=(Std/f/St
−1
d/f)[(1+ptf)/(1+ptd)] (4.13) The currency in the numerator of the real and nominal spot exchange rates moves to the denominator in the inflation ratio, and vice versa. The equation for change in the real exchange rate provides the only exception to the ‘‘numerator to numerator and denominator to denominator’’ rule.
0%
50%
100%
150%
200%
1970 1980 1990 2000 2010
Euro area Japan
United Kingdom United States Floating
rate era begins
FIGURE 4.11 Real Value of the Dollar.
Source:Based on Bank for International Settlements indices (www.bis.org/statistics/eer/).
Although real exchange rates tend to revert to their long-run average, in the short run there can be substantial deviations from the long-run average. In a study of real exchange rates over a 200-year sample period, Lothian and Taylor estimate that it takes between 3 and 6 years for a real disequilibrium in the exchange rate to be reduced by half.8
Deviations from parity in real exchange rates appear to be a consequence of differential frictions in the markets for real and financial assets, with goods prices adjusting more slowly than financial prices. PPP holds for actively traded financial assets, but seldom holds for inactively traded goods such as land or human labor.
Consequently, PPP typically does not hold for general price levels, either. It can take the markets for real (nonfinancial) assets a long time to bring price levels back into equilibrium.
The Effect of a Change in the Real Exchange Rate
If RPPP holds, then changes in nominal exchange rates should reflect the influence of foreign and domestic inflation. Moreover, nominal exchange rate changes that reflect merely the influence of inflation should have little economic significance of their own. Real changes in exchange rates, on the other hand, have a profound impact on the operations of multinational corporations (MNCs), as well as on a country’s balance of trade. In particular,
■ Areal appreciationof the domestic currency raises the price of domestic goods relative to foreign goods.
■ Areal depreciationof the domestic currency lowers the price of domestic goods relative to foreign goods.
A real appreciation of the domestic currency is both good and bad news for the domestic economy. A real appreciation helps domestic importers and consumers because raw materials and imported goods cost less. This helps to hold down inflation. On the other hand, it hurts domestic exporters and their employees as the goods and services produced by domestic companies are relatively expensive in international markets. The effect on domestic producers is asymmetric, in that goods and services competing on the world market are hurt more than those competing solely on the domestic market. This shifts resources within the domestic economy from export-oriented firms toward firms that import goods or services from other countries or that compete primarily in the domestic market.
A real appreciation of a currency reflects an increase in purchasing power.
Consider the labor expense of a Japanese exporter that sells its goods in international markets. A real yen appreciation increases the Japanese exporter’s
labor costs relative to foreign competitors because its local wages are paid in yen.
Conversely, the labor costs of non-Japanese competitors remain constant in their local currencies but decrease in terms of yen. Under these conditions, Japanese exporters face a real cost disadvantage.
Consider instead a Japanese investor such as an MNC that is seeking investment opportunities overseas. A real appreciation of the yen means that foreign assets become less expensive for the Japanese investor. If the investor is in the market to purchase real estate, a real appreciation of the yen makes California real estate relatively less expensive than it used to be. The value of the yen will fall as capital flows out of costly Japanese assets and into relatively less expensive foreign (non-Japanese) assets. Market equilibrium eventually will be restored, if only in passing.
A real depreciation of the domestic currency is the flip side of a real appreciation.
A real depreciation of the domestic currency results in lower prices for domestic goods in foreign and domestic markets. This promotes domestic employment. On the downside, a real depreciation results in higher prices for imported goods and an increase in domestic inflation. Whether a real depreciation is good or bad for the domestic economy depends on which of these countervailing forces triumphs.