Chapter 4: Exchange rates II: the asset approach in the
short run
Goals: Understanding how the exchange rates are
determined in the short run.
4-1
The long run monetary-approach model assumes that price is
flexible, and uses the purchasing power parity to determine the
exchange rate.
Empirical researches support PPP in long run, but find
significant deviation from PPP in short run.
One of the reasons for the failure of PPP in short run is due to
sticky price. This chapter considers a different model to explain
the behavior of exchange rate in short run.
Basic idea:
The short run asset-approach model treats the exchange rate as
the price of an asset, the foreign exchange.
In asset market the price is determined by the no-arbitrage
condition. That is, the price is determined in such a way that
expected returns of two assets in different currencies are equal.
Recall that the no-arbitrage condition in the foreign exchange
market implies the uncovered interest parity (UIP).
1
The annual return of a US deposit is 1 + 𝑖$ , where 𝑖$ is the
annual nominal interest.
One can alternatively convert US dollars into euros, invest in a
euro deposit that pays annual interest rate of 𝑖€ , and at the end of
one year convert euro returns back to US dollars. The annual
return is__________________.
No-arbitrage requires that the two returns are equal, i.e., UIP
holds:
𝑒
𝐸$/€
1 + 𝑖$ = (1 + 𝑖€ ) 𝐸
$/€
(2-2) Uncovered Interest Parity (UIP)
Please see figure 2-10 for a quick review of UIP.
Exercise: rewrite (2-2) using the exchange rate expressed as
𝐸€/$
Algebra rearrangement of (2-2) leads to
𝑖$ ≈ 𝑖€ +
𝑒
𝐸$/€
−𝐸$/€
𝐸$/€
(4-1) an approximation of UIP
(4-1) is an approximation of (2-2).
(4-1) implies that if the US interest rate 𝑖$ is greater than the
𝑒
euro rate 𝑖€ , then 𝐸$/€
should be (greater or less) than 𝐸$/€ , or
US dollar is expected to (appreciate or depreciate).
2
This result is intuitive. If a US deposit pays a higher rate than a
euro deposit, then investors will not consider euro deposits
unless they expect that euro will (appreciate or depreciate),
or conversely, dollar will (appreciate or depreciate), in the
future.
Exercise: if a US deposit pays a lower rate than a euro deposit,
then dollar is expected to (appreciate or depreciate) in the
future.
(Optional) Derivation of (4-1)
Chapter 4 is based on (4-1).
We can rearrange (4-1) and get
𝑒
𝐸$/€
𝐸$/€ = (1+𝑖
$ −𝑖€ )
(4-1b)
which clearly shows that we can solve for 𝐸$/€ if we know all
the three variables on the right hand side of (4-1b). (4-1b) is the
basis for the short run asset-approach model for exchange rate.
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According to (4-1b), everything else equal, 𝐸$/€ will rise (so
dollar will depreciate) if
(1) 𝑖€ goes (up or down)
𝑒
(2) 𝐸$/€
goes (up or down)
(3) 𝑖$ goes (up or down)
The intuition is, if euro deposit is expected to pay a higher rate
or euro is expected to appreciate, either one makes the euro
deposit more attractive. People will convert dollars to euros and
move to euro deposit now. Selling dollars causes the
depreciation of dollars.
A dollar deposit with a lower interest rate also makes the euro
deposit more attractive.
The equilibrium condition for foreign market, equation (4-1), is
graphically illustrated in figure 4-2. That figure shows the
foreign exchange market reaches equilibrium (no-arbitrary
condition is satisfied) when the domestic return line (DR) and
the foreign return (FR) line cross at point 1.
The variable on the horizontal line (X-variable) is
____________________
The variable on the vertical line (Y-variable) is
_______________________
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DR line is horizontal because ________________________
FR line is (upward or downward) sloping because
__________________
Intuitively FR line is downward sloping because when 𝐸$/€ rises
one can convert one dollar to (more or less) euros, and so
have (lower or higher) return from holding a euro deposit.
(1) To the left of point 1 such as at point 2, (dollar or euro)
deposit is more attractive. People will convert ________
to __________, and dollar will ____________ and 𝐸$/€
will go (up or down).
(2) To the right of point 1 such as at point 3, (dollar or
euro) deposit is more attractive. People will convert
________ to __________, and dollar will ____________
and 𝐸$/€ will go (up or down).
So when the market is out of equilibrium at the beginning, the
market force will push the market back to equilibrium.
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Exercise:
Rising US interest rate will shift __________ line
____________
Rising Euro interest rate will shift _______________ line
________________
𝑒
Rising 𝐸$/€
will shift _______________ line
________________
We move along the FR line
when____________________________
4-2
In order to use (4-1b) to determine the interest rate 𝐸$/€ we need
to know
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𝑒
(1) 𝐸$/€
, which is determined by PPP over long run
(2) 𝑖$
(3) 𝑖€
In the long-run monetary-approach model, the nominal interest
equals the sum of real interest rate and expect inflation rate. See
the two equations on page 95. However, the real interest parity
is derived from PPP, which is invalid in short run because of
sticky prices.
Instead, the short run asset-approach model uses the equilibrium
in money market to determine the nominal interest rate.
𝑀𝑈𝑆
𝑃̅𝑈𝑆
𝑀𝐸𝑈𝑅
𝑃̅𝐸𝑈𝑅
= 𝐿(𝑖$ )𝑌𝑈𝑆
= 𝐿(𝑖€ )𝑌𝐸𝑈𝑅
(4-2)
(4-3)
Note in short run we assume sticky prices, so 𝑃̅ is a constant.
This implies that the short run money-market equilibrium is
achieved via the adjustment of nominal interest rate, instead of
the price.
𝐿(𝑖) is a decreasing function of nominal interest: the opportunity
cost of holding cash rises when nominal interest rate rises, so
people will convert cash to interest-bearing assets and the
demand for money falls.
According to (4-2), everything else equal, 𝑖$ will go down if
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(1) 𝑀𝑈𝑆 goes (up or down)
(2) 𝑌𝑈𝑆 goes (up or down)
Graphically, we can use the real money balance as the Xvariable, and the nominal interest rate as the Y-variable. Then
the money supply curve is a vertical line (why?), and the money
demand curve is downward sloping (why?). The money market
is on equilibrium when the two lines cross.
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Exercise
Use the graph to show the effect on 𝑖$ when
(1) 𝑀𝑈𝑆 goes up
(2) 𝑌𝑈𝑆 goes up
Please compare your graphs to Figure 4-6.
4-3
Now we can complete the short run asset-approach model by
considering the equilibriums in both foreign exchange market
and money market.
Short run policy analysis can be done using the short run assetapproach model.
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Short run policy analysis
(1) Temporary increase in 𝑀𝑈𝑆
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In words, rising US money supply lowers the dollar interest rate,
makes euro deposit more attractive, and causes dollar to
𝑒
depreciate. Note FR line is fixed because both 𝐸$/€
and 𝑖€ are
unchanged.
(2) Temporary increase in 𝑀𝐸𝑈𝑅
In words, rising EUR money supply lowers the euro interest rate,
makes euro deposit less attractive, and causes dollar to
appreciate.
Exercise: please show graphically how a temporary decrease in
𝑀𝐸𝑈𝑅 affects 𝐸$/€ .
A real-data check of the short run asset-approach model
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4-4
Long-run policy analysis
Price
Nominal Interest
Rate
Money Market
Foreign Exchange
Long Run
flexible
Fixed (due to
𝜋 𝑡𝑎𝑟𝑔𝑒𝑡𝑒𝑑 )
Price adjusts
PPP applies
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Short Run
fixed
flexible
Nominal interest rate adjusts
UIP applies
Market
Spot Exchange
Rate
Expected
Exchange Rate
Moves by same Overshoots its long-run level
proportion as
price level
Moves by same Moves by same proportion as pr
proportion as
price level
In order to analyze the effect of permanent policy shocks,
we must solve backward from the future to the present:
Step 1: use the long run monetary-approach model to
determine the expected exchange rate.
Step 2: use the short run asset-approach model, along
with the expected exchange rate obtained in step 1, to
determine the exchange rate in short run.
Example
Consider the effect on exchange rate when US money
supply increases by 3% permanently. We will show that
the short-run effect differs from the long-run effect.
In long run:
In the money market
Nominal interest rate remains unchanged at level of
𝑖 𝑡𝑎𝑟𝑔𝑒𝑡𝑒𝑑 = 𝑟 ∗ + 𝜋 𝑡𝑎𝑟𝑔𝑒𝑡𝑒𝑑 .
Real income remains unchanged (no growth)
13
Price is flexible, and price rises by the same proportion
as money supply to clear the money market:
𝑀𝑈𝑆
= 𝐿̅(𝑖 𝑡𝑎𝑟𝑔𝑒𝑡𝑒𝑑 )𝑌̅𝑈𝑆 → ∆𝑃𝑈𝑆 % = ∆𝑀𝑈𝑆 %
𝑃𝑈𝑆
PPP implies that exchange rate will rise by the same
proportion as price:
𝑃𝑈𝑆
𝐸$/€ =
→ ∆𝐸$/€ % = ∆𝑃𝑈𝑆 %
𝑃̅𝐸𝑈𝑅
So in long run, dollar will depreciate by 3%.
In short run
In the money market
Price is fixed; while nominal interest rate adjusts to clear
the money market.
𝑀𝑈𝑆
= 𝐿(𝑖𝑈𝑆 )𝑌̅𝑈𝑆
̅
𝑃𝑈𝑆
So 𝑀𝑈𝑆 ↑→ 𝑖𝑈𝑆 ↓
In the foreign exchange market falling 𝑖𝑈𝑆 shifts the DR
𝑒
line down, while rising 𝐸$/€
shifts the FR line up.
In the long run, DR line moves back to its original place
(why?) while FR line remains at its higher position
(why?).
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The short-run equilibrium exchange rate is higher than
the long-run equilibrium exchange rate. This
phenomenon is called overshooting. To see this recall
UIP:
𝑖$ = 𝑖€ +
𝑒
𝐸$/€
− 𝐸$/€
𝐸$/€
𝑒
In long run 𝑖$ remains unchanged, so 𝐸$/€
and 𝐸$/€ must
rise by the same proportion of 3%.
𝑒
In short run 𝑖$ falls and 𝐸$/€
rises by 3%. Then 𝐸$/€
must rise by more than 3% to ensure UIP.
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Short-run equilibrium is located at point 2’ in panel (b)
Long-run equilibrium is located at point 4’ in panel (d)
Did you see a typo in (d)?
Exercise: please draw the time path for the real exchange
rate
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