The Fisher Effect, the Interest Rate, and the Exchange

The Fisher Effect, the Interest Rate, and the Exchange
Rate Under the Flexible-Price Monetary Approach
The monetary approach to exchange rates, which assumes that the prices of goods are perfectly
flexible, implies that a country’s currency depreciates when its nominal interest
rates rise because of higher expected future inflation. This appendix supplies a detailed
analysis of that important result.
Consider again the dollar/euro exchange rate, and imagine that the Federal Reserve raises
the future rate of U.S. money supply growth by the amount . Figure 16A-1 provides a
diagram that will help us keep track of how various markets respond to that change.
The lower right quadrant in the figure is our usual depiction of equilibrium in the U.S.
money market. It shows that before the increase in U.S. money supply growth, the nominal
interest rate on dollars equals (point 1). The Fisher effect tells us that a rise in the
future rate of U.S. money supply growth, all else equal, will raise the nominal interest rate
on dollars to (point 2).
As the diagram shows, the rise in the nominal dollar interest rate reduces money
demand and therefore requires an equilibrating fall in the real money supply. But the nominal
money stock is unchanged in the short run because it is only the future rate of U.S.
money supply growth that has risen. What happens? Given the unchanged nominal money
supply , an upward jump in the U.S. price level from to brings about the
needed reduction in American real money holdings. The assumed flexibility of prices
allows this jump to occur even in the short run.
To see the exchange rate response, we turn to the lower left quadrant. The monetary
approach assumes purchasing power parity, implying that as rises (while the European
price level remains constant, which we assume), the dollar/euro exchange rate must
rise (a depreciation of the dollar). The lower left quadrant of Figure 16A-1 graphs the
implied relationship between U.S. real money holdings, and the nominal
exchange rate, , given an unchanged nominal money supply in the United States and
an unchanged European price level. Using PPP, we can write the equation graphed there
(which is a downward-sloping hyperbola) as:
This equation shows that the fall in the U.S. real money supply, from to
, is associated with a dollar depreciation in which the dollar/euro nominal
exchange rate rises from to (shown as a movement to the left along the horizontal
axis).
The 45-degree line in the upper left quadrant of Figure 16A-1 allows you to translate
the exchange rate change given in the lower left quadrant to the vertical axis of the upper
right quadrant’s diagram. The upper right quadrant contains our usual portrayal of equilibrium
in the foreign exchange market.
There you can see that the dollar’s depreciation against the euro is associated with a
move in the foreign exchange market’s equilibrium from point to point . The picture
shows why the dollar depreciates, despite the rise in R$. The reason is an outward shift in
1¿ 2¿
E$/€
E 2 $/€
1
MUS
2 /PUS
2
MUS
1 /PUS
1
E$/€ = PUS/PE =
MUS/PE
MUS/PUS
.
E$/€
MUS/PUS,
E$/€
PUS
PUS
P 2 US
M 1 US
1
R$
2 = R$
1 + ¢p
R$ ¢p
1
¢p
CHAPTER 16 Price Levels and the Exchange Rate in the Long Run 419
1
2
1'
2'
Dollar/euro
exchange rate, E$/€
Dollar/euro
exchange
rate, E$/€
PPP relation
U.S. real
money holdings
U.S. real
money supply
Money demand,
L(R$, YUS)
Expected return on euro deposits after
rise in expected future dollar depreciation
45˚ line
Initial expected return
on euro deposits
Rates of return
(in dollar terms)
E$/€
2
E$/€
1
E$/€
1 R$
1 R$
E 2 = R$1 + Δπ $/€
2
MUS
1
PUS
2
MUS
1
PUS
1
Figure 16A-1
How a Rise in U.S. Monetary Growth Affects Dollar Interest Rates and the Dollar/Euro Exchange Rate When Goods
Prices Are Flexible
When goods prices are perfectly flexible, the money market equilibrium diagram (southeast quadrant) shows two
effects of an increase, , in the future rate of U.S. money supply growth. The change (i) raises the dollar interest rate
from to , in line with the Fisher effect, and (ii) causes the U.S. price level to jump upward, from
to . Money market equilibrium therefore moves from point 1 to point 2. (Because doesn’t change immediately,
the real U.S. money supply falls to , bringing the real money supply into line with reduced money demand.)
The PPP relationship in the southwest quadrant shows that the price level jump from to requires a depreciation
of the dollar against the euro (the dollar/euro exchange rate moves up, from to ). In the foreign exchange market
diagram (northeast quadrant), this dollar depreciation is shown as the move from point to point . The dollar
depreciates despite a rise in because heightened expectations of future dollar depreciation against the euro cause an
outward shift of the locus measuring the expected dollar return on euro deposits.
R$
1¿ 2¿
E$/€
E 2 $/€
1
PUS
P 2 US
1
MUS
1 /PUS
2
MUS
P 1 US
2
PUS
R 1 $
2 = R$
R 1 + ¢p $
1
¢p
the downward-sloping schedule, which gives the expected dollar rate of return on euro deposits.
Why does that schedule shift outward? Higher expected future monetary growth
implies faster expected future depreciation of the dollar against the euro, and therefore a
rise in the attractiveness of euro deposits. It is that change in expectations that leads simultaneously
to a rise in the nominal interest rate on dollars and to a depreciation of the dollar
in the foreign exchange market.
To summarize, we cannot predict how a rise in the dollar interest rate will affect the
dollar’s exchange rate without knowing why the nominal interest rate has risen. In a flexible-
price model in which the home nominal interest rate rises because of higher expected
future money supply growth, the home currency will depreciate, not appreciate, thanks to
expectations of more rapid future depreciation.