Review: Exchange Rates

Roberto ChangMarch 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 only about expected returns

• 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 getE$/€ = 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 home and abroad

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$/€

Purchasing Power Parity

• 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 impliesE$/€ = 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 getsE$/€ = P$/ 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 = Md

US = LPUSYUS

SoPUS = MUS /LYUS

AndπUS = 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

demandmoney Real

supplymoney Real

)( YiLP

M

demandsmoney real Relativeby divided

suppliesmoney nominal Relative

$

$

levels price of Ratiorate Exchange

€/$ )(/)(

/

)(

)(

EUREURUSUS

EURUS

EUREUR

EUR

USUS

US

EUR

US

YiLYiL

MM

YiLM

YiLM

P

PE

Interest Rates in the Long Run

• Since both UIP and PPP hold in the long run,

aldifferentiinflation Expected

ondepreciati dollar of rate Expected

€/$

€/$ eEUR

eUS

e

E

E

rateinterest

euroNet

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€/$

€/$ iiE

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(expected)

aldifferenti rateinflation Nominalaldifferenti rateinterest Nominal

€$eEUR

eUSii

Real Interest Rate Parity

eEUR

eUS ii €$Or:

rUSe rEUR

e 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:

., *€

*$

eEUR

eEUR

eEUR

eUS

eUS

eUS rrirri

Exchange Rates in the Short Run

The Asset Approach

UIP holds all the time…

• …also in the short run

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.

Changes in Domestic and Foreign Returns and FX Market Equilibrium

…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!

MUS

P US

U.S. supply ofreal money balances

L(i$ )YUS

U.S. demand forreal money balances

FIGURE 4-6 (2 of 2)

Changes in Money Supply and the Nominal Interest Rate

Home Money Market with Changes in Money Supply and Money Demand (continued)In panel (b), with a fixed price level P1

US, an increase in real income from Y1US to Y2

US causes real money demand to increase from MD1 to MD2.

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

FIGURE 4-7 (2 of 2)

Home Money Market with Changes in Money Supply and Money DemandIn 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.

The Asset Approach to Exchange Rates: Graphical Solution

FIGURE 4-8 (1 of 2)

Temporary Expansion of the Home Money SupplyIn panel (a), in the Home money market, an increase in Home money supply from M1

US to M2US

causes an increase in real money supply from M1US/P1

US to M2US/P1

US.

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 SupplyIn 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 .′

Short-Run Policy Analysis

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 ImpactFeenstra and Taylor: International Macroeconomics, Second EditionCopyright © 2012 by Worth Publishers

Figure 4.12 (c) (d) Long-Run AdjustmentFeenstra and Taylor: International Macroeconomics, Second EditionCopyright © 2012 by Worth Publishers

Figure 4.13 Responses to a Permanent Expansion of the Home Money SupplyFeenstra and Taylor: International Macroeconomics, Second EditionCopyright © 2012 by Worth Publishers

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

Fixing Your Exchange Rate

• 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 VariablesFeenstra and Taylor: International Macroeconomics, Second EditionCopyright © 2012 by Worth Publishers

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 TrilemmaFeenstra and Taylor: International Macroeconomics, Second EditionCopyright © 2012 by Worth Publishers