Lecture 5
Short-run exchange rate model:
Asset approach to exchange rate
Short run asset approach to exchange rate
 Output (real income) Y is fixed and price level P is sticky.
 𝐸 = %𝑞
 Nominal interest rate (𝑖) = Real interest rate (𝑟)
 In the short run, nominal interest rate bears the burden of
clearing the money market and can deviate from its long
run level.
 Short run asset approach to exchange rate has two building
blocks: money market equilibrium and FX market
equilibrium (i.e. bond market equilibrium)
𝑀
 Short run money market equilibrium:
=𝐿 𝑖
𝑃
 FX market equilibrium:
𝑌
𝑒
𝐸 −𝐸
∗
𝑖= 𝑖 +
𝐸
Short run money market equilibrium
 MM equilibrium is achieved as people switch between
money and bond to achieve their desired money holdings.
𝑒 −𝐸
𝐸
FX market equilibrium (UIP): 𝑖 = 𝑖 ∗ +
𝐸
Short run asset approach to exchange rate
 Exogenous variables: 𝑀, 𝑀 ∗ , 𝑃, 𝑃∗ , 𝑌, 𝑌 ∗ , 𝐸𝑒
 𝐸𝑒 is based on a long-run exchange rate according to some long
run theory – we use the “monetary approach” (FPMM) from the
previous lecture.
 Endogenous variables: 𝑖, 𝑖 ∗ , 𝐸
𝑀
 (1)
= 𝐿(𝑖) 𝑌
𝑃
𝑀∗
 (2) ∗ = 𝐿(𝑖 ∗ )𝑌 ∗
𝑃
𝑒 −𝐸
𝐸
 (3) 𝑖 = 𝑖 ∗ +
𝐸
 𝑖 = 𝑓 (𝑀, 𝑃, 𝑌)
 𝑖 ∗ = 𝑓 (𝑀∗ , 𝑃∗ , 𝑌 ∗ )
 𝐸 = 𝑓 (𝐸 𝑒 , 𝑖, 𝑖 ∗ )
The Asset Approach to Exchange Rates:
Graphical Solution
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Applying the model
 Consider how the exchange rate adjusts to different
shocks to the fundamentals
 Temporary shocks: No effect on long run 𝐸 and  𝐸𝑒
 Permanent shocks: Long run 𝐸 and  𝐸𝑒 is affected
 Let the economy be in long run stationary
𝑃 ∆𝐸
equilibrium initially, i.e. 𝐸 = ∗, = 0 (i.e.
𝑃 𝐸
fundamentals M, M*, Y, Y* have no growth rate)
 UIP  𝑖 = 𝑖 ∗
A temporary positive shock to the level of M (Fig 4.8)
A permanent positive shock to the level of M (Fig 4.12)
 Short run effects Figure 4.12 (a), (b)
 i  (DR shifts down)
 Ee  (FR shifts up); E  (via UIP)
A permanent positive shock to the level of M (Fig 4.12)
 Long run effects Fig 4-12 (c), (d)
 P  to clear the MM ( E  via PPP)
 i returns to its initial level (DR curve shifts up to DR1)
 E appreciates from to its short-run equil level but still depreciates
overall  Overshooting!
A permanent positive shock to the level of M (Fig 4.13)
2
𝐸$/
€
Exchange Rate Overshooting (ERO)
 ERO is the phenomenon that the exchange rate response
to a permanent shock is stronger in the short run than in
the long run.
 %E in the short-run > %E in the long-run
 ERO is a direct consequence of price rigidity in the short
run.
 Overshooting can explain the wide swings of exchange
rates of major currencies after 1973.
Overshooting in Practice
Fixed exchange rate under asset approach
Central Bank Balance Sheet
Assets
Liabilities
Foreign exchange reserves (FXR) R
Currency in circulation CC
(R is the book’s notation.
(currency held by the nonbank public)
We will use FXR and R interchangeably.)
Domestic assets (or domestic credits) B
Member banks’ reserves RD
(Mainly domestic government bonds, hence the
notation B)
(Vault cash + reserve deposit of
commercial banks at the central
bank)
𝑀0 = 𝑪𝑪 + 𝑹𝑫 = 𝑩 + 𝐸 ∗ 𝑹 (the book assumes 𝐸=1)
𝑀1 = 𝑪𝑪 + 𝑫𝑫
= 𝑪𝑪 + 𝑚 𝑹𝑫
𝑤ℎ𝑒𝑟𝑒 𝑚 = 𝑚𝑜𝑛𝑒𝑦 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒𝑟
Monetary consequence of FX Intervention
 Base money M0 = CC + RD = 𝐸 (R) + B
 FX intervention  R  has consequence on M0.
 If CB sells DC (buys FC)  R and M0 ↑
 If CB buys DC (sells FC)  R and M0 ↓
 We ignore the banking sector from now on, M1 = M0 = M.
Fixing the exchange rate
under asset approach to exchange rate
 FX equilibrium (UIP):
𝑖= 𝑖
∗
𝐸𝑒 − 𝐸
+
𝐸
 Money market equilibrium: 𝑀 = 𝐿 𝑖 𝑃𝑌 (or
𝑀
=𝐿 𝑖 𝑌)
𝑃
 Under a credible fixed rate system, 𝐸 𝑒 = 𝐸

UIP: 𝑖 = 𝑖
∗
𝐸− 𝐸
+
𝐸
 To target 𝐸 = 𝐸, the CB must set 𝑖 = 𝑖 ∗ for FXM equil.
 Required 𝑀 = 𝑀𝑑 when 𝑖 is at 𝑖 ∗


= 𝐿 𝑖∗ 𝑃 𝑌
= 𝑀(𝑃 , 𝑌 , 𝑖 ∗ ⊖)
Pegging sacrifices monetary policy autonomy
in the short run
 In the short run, price and output are fixed and there is
only one feasible of money supply consistent with the peg:
Required 𝑀 = 𝐿 𝑖 ∗ 𝑃 𝑌
 e.g. Let Denmark be the home country, 𝐸 = 𝐷𝐾𝑟 €
To peg the Danish krone to the euro, the Danish CB
must set
𝑀𝐷𝐸𝑁 = 𝐿 𝑖€ 𝑃𝐷𝐸𝑁 𝑌𝐷𝐸𝑁
Short run asset approach model under fixed
exchange rate (upper part of Fig 4-15)
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Any attempt by the CB to deviate from the required 𝑀 is
doomed to fail
 Assume the peg is credible. At Point A 𝑖1 = 𝑖 ∗ and 𝐸 = 𝐸 and 𝑀 =
required 𝑀. If the CB tightens 𝑀 and raises 𝑖 to 𝑖2 → 𝑈𝐼𝑃 arb and 𝐸 ↓
to 𝐸2 (Point B) → FXI → 𝐹𝑋𝑅 ↑, 𝑀 ↑ → 𝑖 ↓ to 𝑖3 → 𝑈𝐼𝑃 𝑎𝑟𝑏 and
 𝐸 ↑ 𝑡𝑜 𝐸3 (Point C). FXI continues until 𝑖 ↓ back to 𝑖1 and 𝐸 ↑ to 𝐸.
Pegging also sacrifices monetary policy autonomy
in the long run
 To peg the Danish krone to the euro, the Danish CB must
𝑑
set 𝑀𝐷𝐸𝑁 = 𝑀𝐷𝐸𝑁
at 𝑖𝐷𝐾𝑟 = 𝑖€ (ECB’s long run target
interest rate).
 Under PPP, 𝑃𝐷𝐸𝑁 = (𝐸𝐷𝐾𝑟 € )(𝑃𝐸𝑈𝑅 )
 Required 𝑀𝐷𝐸𝑁 = 𝐿 𝑖𝐷𝐾𝑟 𝑃𝐷𝐸𝑁 𝑌𝐷𝐸𝑁 becomes:

𝑀𝐷𝐸𝑁 = 𝐿 𝑖€ (𝐸𝐷𝐾𝑟 € )(𝑃𝐸𝑈𝑅 ) 𝑌𝐷𝐸𝑁
Monetary model under fixed exchange rate
(lower part of Fig 4-15)
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Fixing the exchange rate when the peg is not credible
 Starting from a credible fixed exchange rate regime
(𝐸 𝑒 = 𝐸), 𝑀 is at the required level to bring 𝑖 = 𝑖 ∗ .
 If the peg is not credible and the market expects a
devaluation or depreciation if the peg is abandoned.
𝐸 𝑒 = 𝐸 + 𝛿, 𝛿 > 0
 How would this affect the required money supply and the
interest rate?
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Fixing the exchange rate when the peg is not credible
𝑒− 𝐸
𝐸
 UIP: 𝑖 = 𝑖 ∗ +
𝐸
𝐸+𝛿 −𝐸
∗

=𝑖 +
𝐸
𝐸−𝐸
𝛿
∗

=𝑖 +
+
𝐸
𝐸
𝛿
 To keep 𝐸 = 𝐸 , the CB must set 𝑖 = 𝑖 +
𝐸
𝛿
𝑑
∗
 ∴ Required 𝑀 = 𝑀 when 𝑖 is set at 𝑖 +
𝐸
𝛿
∗

=𝐿 𝑖 +
𝑃𝑌
𝐸
∗
∗
= 𝑀(𝑃 , 𝑌 , 𝑖 ⊖, 𝛿 ⊖)
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The Impossible Trinity ( “Trilemma”)
 Choose any 2 goals, the 3rd goal must be forgone!
 (1) Fixed exchange rate (credible):
 (2) Perfect capital mobility:
 (3) Monetary policy autonomy:
𝐸𝑒 − 𝐸
𝐸−𝐸
=
=0
𝐸
𝐸
𝐸𝑒 − 𝐸
∗
𝑖=𝑖 +
𝐸
𝑖 can be set at any level