### Recap: UIP, PPP, and Exchange Rates

```Review: Exchange Rates
Roberto Chang
March 2014
Material for Midterm
• Basic: chapters 1-4 of FT
• Plus: what we have discussed in class
(applying the theory in real world situations)
Some Basic Concepts
• Exchange rate definitions (spot versus
forward, cross country rates, derivatives, real
exchange rates, appreciation and
depreciation, etc.)
• PPP
• Covered interest parity and UIP
Covered Interest Parity
• A consequence of arbitrage
• It provides a link between interest rates, the
spot exchange rate, and the forward exchange
rate:
1 + i\$ = (1+i€)*(F\$/€ /E\$/€)
Uncovered Interest Parity
• Based on the assumption that investors care
• Gives a link between interest rates, the spot
exchange rate, and the expected future
exchange rate:
1 + i\$ = (1+i€)*(Ee\$/€ /E\$/€)
From UIP to a Theory of Exchange
Rates
• From UIP,
1 + i\$ = (1+i€)*(Ee\$/€ /E\$/€)
we get
E\$/€ = Ee\$/€ *(1 + i\$ )/ (1+i€)
• This says that we understand the current (spot)
exchange rate if we understand interest rates and
the expected future exchange rate.
Exchange Rates in the Long Run
The Monetary Approach
Long Run Exchange Rates
• We focus on the monetary approach
• Key building block: purchasing power parity
(PPP), which will say that the long run
exchange rate is the ratio of price levels at
Law of One Price
• The LOOP says that a particular good must sell
at the same price in different locations, when
the price is quoted in a common currency:
Pjeans,\$ = Pjeans,€*E\$/€
• PPP is like LOOP but applied to baskets of
goods and services (i.e. the CPI):
P\$ = P€*E\$/€
• The price of the said baskets is usually what
we mean by the price level.
• PPP is a reasonable assumption about the
long run
Absolute versus Relative PPP
• Absolute PPP:
PUS = E\$/€ *PEUR
• In changes  Relative PPP:
πUS = (∆ E\$/€ / E\$/€ ) + πEUR
So…
• Absolute PPP implies
E\$/€ = PUS /PEUR
while relative PPP gives
∆ E\$/€ / E\$/€ = πUS – πEUR
==> To derive predictions for the exchange rate,
we need to understand the determinants of
price levels and inflation
From PPP to Long Run Exchange Rates
• From PPP,
P\$ = P€*E\$/€
one gets
E\$/€ = P\$/ P€
• Hence the (long run) exchange rate is given by
the (long run) ratio of price levels.
• Attention then shifts to the determination of
price levels
A Simple Theory of the Price Level
• Supply and Demand for Money:
MUS = MdUS = LPUSYUS
So
PUS = MUS /LYUS
And
πUS = µUS – gUS
Long Run Exchange Rates
• From absolute PPP, now,
E\$/€ = PUS /PEUR = (MUS /LYUS)/(MEU /L* YEU ), or
E\$/€ = (L*/L) (MUS/ MEU)/(YUS/ YEU)
• In changes,
∆ E\$/€ / E\$/€ = πUS – πEUR = (µUS - µEU ) – (gUS - gEU )
Long Run: A More General View
M
P

Real money supply

L(i)Y

Real money demand
 M US 



LUS (i\$ )YUS 

PUS
M US / M EUR 

E\$ / € 



PEUR

 LUS (i\$ )YUS / LEUR (i )YEUR 
M EUR
Exchange rate


 
Ratio of price levels
Relativenominal money supplies
 LEUR (i )YEUR 
divided by
Relativereal money demands
Interest Rates in the Long Run
• Since both UIP and PPP hold in the long run,
E\$e/ €
E\$ / €



e
US
 eEUR

Expectedinflationdifferential
Expectedrate of dollar
depreciation
E\$e/ €
E\$ / €


Expected rate of dollar
depreciation



i\$

Net dollar
interest rate
i\$  i€

Nominal interest rate differential

i€

Net euro
interest rate
e
e
 US
  EUR

Nominal inflation rate differential
(expected)
Real Interest Rate Parity
Or:
i\$  
e
US
 i€  
e
EUR
rUSe  rEeUR  r*
Which says:

Real Interest Rates in LR
• Hence we have found that PPP and UIP imply that
the real interest rate is equalized across countries
in the long run
• We assume that r* is exogenous.
• Then the long run nominal interest rate in each
country is determined by long run inflation, given
in turn by the rate of money growth:
e
e
i\$  rUSe  US
 r*  US
,
e
i€  rEUR
 eEUR  r*  eEUR .
Exchange Rates in the Short Run
The Asset Approach
UIP holds all the time…
• …also in the short run
Changes in Domestic and Foreign Returns and FX Market Equilibrium
FIGURE 4-3 (1 of 3)
(a) A Change in the Home
Interest Rate
A rise in the dollar interest
rate from 5% to 7% increases
domestic returns, shifting the
DR curve up from DR1 to DR2.
At the initial equilibrium
exchange rate of 1.20 \$/€ on
DR2, domestic returns are
above foreign returns at point
4.
Dollar deposits are more
attractive and the dollar
appreciates from 1.20 \$/€ to
1.177 \$/€. The new
equilibrium is at point 5.
…but PPP does not hold in the short
run
• Instead, the price level is taken to be fixed in
the short run.
• Changes in the quantity of money then affect
the short run interest rate!
M US
PUS
 L(i\$ ) YUS
U.S. supply of
real money balances
U.S. demand for
real money balances
Changes in Money Supply and the Nominal Interest Rate
FIGURE 4-6 (2 of 2)
Home Money Market with Changes in Money Supply and Money Demand (continued)
In panel (b), with a fixed price level P1US, an increase in real income from Y1US to Y2US causes real
— .
money demand to increase from MD1 to MD
2
To restore equilibrium at point 2, the interest rate rises from i1\$ to i2\$.
Short Run Exchange Rates
• In the short run, the money market
equilibrium condition:
MUS/PUS = L(iUS) YUS
determines iUS
• FX Market: Then you can get the exchange
rate from UIP:
DR = i\$ = i€ + (Ee\$/€ - E\$/€)/E \$/€ = FR
The Asset Approach to Exchange Rates: Graphical Solution
FIGURE 4-7 (2 of 2)
Home Money Market with Changes in Money Supply and Money Demand
In panel (b), in the dollar-euro FX market, the spot exchange rate E1\$/€ is determined by foreign and
domestic expected returns, with equilibrium at point 1′. Arbitrage forces the domestic and foreign
returns in the FX market to be equal, a result that depends on capital mobility.
Short-Run Policy Analysis
FIGURE 4-8 (1 of 2)
Temporary Expansion of the Home Money Supply
In panel (a), in the Home money market, an increase in Home money supply from M1US to M2US
—
—
causes an increase in real money supply from M1US/P1US to M2US/P1US.
To keep real money demand equal to real money supply, the interest rate falls from to i1\$ to i2\$,
and the new money market equilibrium is at point 2.
Short-Run Policy Analysis
FIGURE 4-8 (2 of 2)
Temporary Expansion of the Home Money Supply
In panel (b), in the FX market, to maintain the equality of domestic and foreign expected
returns, the exchange rate rises (the dollar depreciates) from E1\$/€ to E2\$/€, and the new FX
market equilibrium is at point 2′.
Temporary versus Permanent
• In the previous analysis, we assumed that the
expected long run exchange rate did not
move.
• This is justified only if the policy change is
temporary.
The Impact of Permanent Changes
• For permanent changes in policy, we need to
trace the effect on the long run expected
exchange rate.
• Easier to work out the long run first, then the
short run.
• Example: A permanent increase in MUS
Figure 4.12 (a) (b) Permanent Expansion of the Home Money Supply Short-Run Impact
Feenstra and Taylor: International Macroeconomics, Second Edition
Figure 4.12 (c) (d) Long-Run Adjustment
Feenstra and Taylor: International Macroeconomics, Second Edition
Figure 4.13 Responses to a Permanent Expansion of the Home Money Supply
Feenstra and Taylor: International Macroeconomics, Second Edition
Remarks
• Overshooting: In the short run, the exchange
rate depreciates more that in the long run
• In the short run, iUS falls, but in the long run it
does not change. Why?
Fixed Exchange Rates and the
Trilemma
Simultaneous Equilibrium
• In the short run, the money market
equilibrium condition:
MUS/PUS = L(iUS) YUS
determines iUS
• FX Market: Then you can get the exchange
rate from UIP:
DR = i\$ = i€ + (Ee\$/€ - E\$/€)/E \$/€ = FR
• Suppose that Denmark decides to fix its
exchange rate against the Euro at some level
EDkr/€
• How can it accomplish that goal?
Fixing in the Long Run
• The Euro area price level in the long run is
determined by ECB monetary policy
(monetary approach).
• In the long run, also, we must have PPP and
money market equilibrium:
PDEN = EDkr/€ PEUR
MDEN/PDEN = LDENYDEN
==> This can only happen if MDEN adjusts to
ensure the equalities
Fixing in the Short Run
• In the short run, UIP ( iDEN = i€ + (EeDKr/€ EDKr/€)/E DKr/€) becomes simply
iDEN = i€
• Then money market equilibrium
MDEN/PDEN = LDEN (i€) YDEN
again requires MDEN to adjust accordingly
Figure 4.15 A Complete Theory of Fixed Exchange Rates: Same Building Blocks, Different Known and Unknown Variables
Feenstra and Taylor: International Macroeconomics, Second Edition
Can Exchange Rates Be Fixed?
• The conclusion is that a country that wants to
fix its exchange rate must give up its ability to
control its money supply
• Importantly: we have maintained the UIP
assumption, which requires that capital be
mobile across countries
• So, an alternative for a country that fixes its
exchange rate is to impose barriers to capital
mobility (capital controls)
Figure 4.16 The Trilemma
Feenstra and Taylor: International Macroeconomics, Second Edition