Exchange Rate Determination

Exchange Rate Exchange Rate DeterminationDetermination 4

Chapter Objective:•Reviews PPP and understands•Examines MABP and exchange rate determination.•Understands portfolio balance approach•Knows exchange rate dynamics and overshooting

Exchange Rate Exchange Rate DeterminationDetermination

PPP

IRP

Monetaryapproach

Ms , Md

Exchange rate and BP

portfolio balance approach

asset

DifferentExchange rate system

ElasticitySticky

Chapter ThreeChapter Three Outline Outline 1.Purchasing Power Parity 2.Monetary Approach to the Balance of payments

and Exchange Rate Determination 3. Exchange Rate Dynamics 4. Asset Market model and Exchange

Rates.Portfolio-Balance Approach 5.Empirical tests and Exchange Rates Forecasting

1. 1. Purchasing Power ParityPurchasing Power Parity

(1)A law of one price(2)Absolute and relative PPP(3) PPP Deviations and Evidence on it(4) Empirical tests of Purchasing Power

Parity

(1) (1) a law of one pricea law of one price1)In one countryP=P’+cP=P’+c(cost)+L(law)+A(arrest)Non traded goods: Real estate haircuts2)In an open economyP=RP’+c

(2) (2) Absolute and relative PPPAbsolute and relative PPP The exchange rate between two currencies should equal the

ratio of the countries’ price levels.

Relative PPP states that the rate of change in an exchange rate is equal to the differences in the rates of inflation.

If U.S. inflation is 5% and U.K. inflation is 8%, the pound should depreciate by 3%.

0

011

*

0

*

1/

/R

PP

PPR

*/ PPR

(4)Evidence on PPP(4)Evidence on PPP PPP probably doesn’t hold precisely in the real

world for a variety of reasons.– Haircuts cost 10 times as much in the developed

world as in the developing world.– Film, on the other hand, is a highly standardized

commodity that is actively traded across borders.– Shipping costs, as well as tariffs and quotas can

lead to deviations from PPP. PPP-determined exchange rates still provide a

valuable benchmark.

PPP GDP 2006 (millions of dollars) 1 United States 13,201,819 2 China 10,048,026 a 3 India 4,247,361 b 4 Japan 4,131,195 5 Germany 2,616,044 6 United Kingdom 2,111,581 7 France 2,039,171 8 Italy 1,795,437 9 Brazil 1,708,434 10 Russian Federation 1,704,756 11 Spain 1,243,440 12 Mexico 1,201,838 13 Korea, Rep. 1,152,356

Total GDP 2006(millions ofRanking Economy US dollars)1 United States 13,201,8192 Japan 4,340,1333 Germany 2,906,6814 China 2,668,0715 United Kingdom 2,345,0156 France 2,230,721 a7 Italy 1,844,7498 Canada 1,251,4639 Spain 1,223,98810 Brazil 1,067,96211 Russian Federation 986,94012 India 906,26813 Korea, Rep. 888,024

(4) (4) Empirical tests of Empirical tests of Purchasing Power ParityPurchasing Power Parity

See p.508 three points

2.2.Monetary Approach to the Balance Monetary Approach to the Balance of Payments and Exchange Rate of Payments and Exchange Rate

DeterminationDetermination

(1)Monetary Approach to the balance of payments under Fixed Exchange Rates

(2) Monetary Approach to Exchange Rate

Determination (flexible price)


DeterminationDetermination• In the 1970s, the monetary approach to the

balance of payments came to popularity, that emphasizes the monetary aspects of the balance of payments.

Money plays the crucial role in the long run both as a disturbance and as an adjustment in the nation’s BP.


DeterminationDeterminationMABP emphasizes the determinants of

money demand and supply that will determine the balance of payments.

Those items that directly affect the money supply are below the line which MABP concentrate on.

(1)(1)MABPMABP

Fixed Money flowing

between countries to adjust the disequilibrium.

Adjustment to changes through international money flows

Flexible

•At a point where the flow of exports just equals the flow of imports, no net international money flows required.

•Adjustment through exchange rates.

(1)MABP(1)MABP

1)basic concepts and assumptionsCentral bank controls the money supply by

altering base moneyBase money changes, the lending ability of

commercial banks changes.Divide base money into domestic and

international components.

(1)MABP(1)MABP

2)framework for the analysis under MABPMinimum money modelMd=kPY

A stable demand for moneyMs =m(D+F)

Md =Ms

(1)MABP(1)MABP

Md=kPYP=RP* here P* the foreign price levelR the domestic currency price of foreign

currencyk RP* Y=m(D+F) To discuss the money demand and supply,

in terms of percentage changes, since k, m is constant, the changes are zero.

(1)MABP(1)MABP

So

•Rearrange

FDYPR ˆˆˆˆˆ *

DYPRF ˆˆˆˆˆ *

(2) Monetary Approach under (2) Monetary Approach under Flexible Exchange RatesFlexible Exchange Rates

DYPR

F

ˆˆˆˆ

0̂ˆ

*

Under flexible

DYPF

R

ˆˆˆˆ

0*

^

•Fixed

(1) MABP(1) MABP

Managed float

Given money demand or money supply changes, the central bank can choose to let

adjust to the free-market level; or by holding R at some disequilibrium,it will allow to adjust.

FDYPR ˆˆˆˆˆ *

R̂

F̂

(1)(1)MABPMABP

Fixed Money supply adjusts to demand through international money flows

Flexible Set by the central bank via exchange rate changes

Managed floatBoth international money flows and exchange rate changes

(2)Monetary Approach and (2)Monetary Approach and Exchange Rate DeterminedExchange Rate Determined

1)money plays the crucial role in the long run: both as a disturbance and as an adjustment in a

nation’s BP 2)The exchange rate is determined by flow of funds, in

the process of balancing the total demand and supply of the national currency in each country.

3)money supply and demand: The supply of monetary determined by the monetary

authorities, the demand for monetary depending on the level of real income, general price level and the interest rate.

The higher are the real income and prices ,the greater is the demand for monetary balances that individuals and businesses demand for their day to day transactions.

The higher of interest, the greater is the opportunity cost of holding money.the higher the rate of interest ,the smaller is the quantity of money demanded.

For a given level of real income and prices, the equilibrium interest rate determined at the intersection of demand and supply curves of money.

(2)Monetary Approach and (2)Monetary Approach and Exchange Rate Determined(MAER)Exchange Rate Determined(MAER)

Suppose the FX market being equilibrium or at IRP, suppose that monetary authorities increase the money supply, in the long run, leads to a proportionate increase in the price level in the home country and depreciation of its currency, as PPP discussed.

But it leads to decline of interest and affect financial markets and exchange rates immediately, resulting in increased financial investment flows to the foreign countries.

(2)Monetary Approach and (2)Monetary Approach and Exchange Rate DeterminedExchange Rate Determined

(2)MAER(2)MAER

Under flexible exchange rate Backgrounds : elasticity supply ; stable

demand; markets are competitive and no tariffs, no obstructions to trade; PPP

Income and interest are not relative to money supply. Supply only leads to the changes of the price.

(2)MAER(2)MAER

Elasticity supply:

kPyM d

kPyMM ds

PyY

(2)(2)MAERMAER

Equilibrium :

kPyM s **** YPkM s

(2)(2)MAERMAER

Since

*P

PR

•so

kYM

YkMR

s

s*

**

(2)(2)MAERMAER

ConclusionChanges in R are proportional to changes in

inversely.

It depends on PPP and the law of one priceNot include interest rate (UIRP)Exchange rate to adjustment

*s

s

M

M

EAii *

•EA is the expected percentage appreciation per year of the foreign currency to the home currency.•UIA formulation

3.Asset Market model and 3.Asset Market model and Exchange RatesExchange Rates

(1)Asset market model(2)Extended asset market model (3) Portfolio Balance Approach

(1)(1)Asset market modelAsset market model

Asset market model(PB) differs from the monetary approach(MA)

• Perfect capital flow(MA, PB)• Perfect substitutes(uncovered interest arbitrage

and no foreign exchange risk premium(MA)


W=M+D+FM:domestic currency (transactions)D:domestic bonds (return it yields)F:foreign bonds (return and spreading risks)A change in any of underlying factors will

achieves a new portfolio; An increase in wealth increases the demand

for these three assets.


According to asset market approach ,equilibrium in each financial market occurs when the quantity demanded of each financial asset equals its supply.

The exchange rate is determined in the process of reaching equilibrium in each financial market.

(2) (2) Extended asset market modelExtended asset market model

Book , p.522 models

RPEAii

EAii

*

*

(2) (2) Extended asset market model Extended asset market model

Domestic currency equilibrium

i

RM

increaseD

FM

R

i

(2) (2) Extended asset market modelExtended asset market model

foreign bondsDomestic bonds

R

i

D increase

increase

FR

i

(3) (3) Portfolio Balance ApproachPortfolio Balance Approach

open market purchase

E

E’

R

i

M increases,E’new equilibriumDomestic currency depreciatesInterest decreases

M’

F’

MD

F

(3) (3) Portfolio Balance ApproachPortfolio Balance Approach

(BCA surplus)

MD

F

F’

D’

M’

E

R

iE’

Domestic currency appreciates Save foreign currency to change MMore foreign currency supplyF depreciates i* increasesIf i unchanged, wealth unchanged

4.Exchange Rate Dynamics4.Exchange Rate Dynamics

Exchange Rate Overshooting (sticky price)

4.Exchange Rate Overshooting4.Exchange Rate Overshooting

1)concept Stock adjustments in financial assets are much

larger and quicker to occur than in trade flows.in the short run ,changes in R are likely to reflect the effect of stock adjustments in financial assets and expectations.but in the long run ,adjustments in trade flows occurs.

The immediate flows of financial investment leads to an immediate depreciation of home currency which exceeds or overshoots the expected in the long run according to PPP.

2)Sequence : the money supply increases,the interest rate

falls,capital flows out, leads to an immediate depreciation of the home currency. In the long run the home currency’s prices rice and it appreciates to eliminate the overshooting.


3)model Regarding a higher trade deficit for the domestic country, the spot

exchange rate will jump immediately above E0

R1

R0

until the new long run equilibrium E1 is reached. After a disturbance, the exchange rate may not move in such an orderly fashion.


t

R

PPP doesn’t hold well under flexible exchange rate. Exchange rates exhibit much more volatile behavior than prices do. In the short run, following some disturbance to equilibrium, prices will adjust slowly to the new equilibrium level, but the exchange rates and interest rates will adjust quickly. This different speed of adjustment to equilibrium allows for behavior regarding rates and prices.


At times,spot exchange rates move too much given some economic disturbance.Also, we have observed instances when country A has a higher inflation rate than country B, yet A’s currency appreciates relative to B’s. such anomalies can be explained in the context of an “overshooting” exchange rate model. We assume that financial markets adjust instantaneously to an exogenous shock, whereas goods markets adjust slowly over time. With this setting, we analyze what happens when country A increases its money supply.


For equilibrium, money demand must equal supply. If the money supply increases, something must happen to increase demand. Assuming that people hold money for transactions purposes, and holding bonds to pay an interest rate i. A money demand equation: Md=aY+bi

Md,the real stock of money demanded Y, income I, interest rate and i, or b is negative.


As y increases, tend to demand more things including money. Interest rate is the opportunity cost of holding money, there is an inverse relation between money demand.

In the short run, both income and the price level are relatively constant.

Result :interest rate must drop to equate money demand to supply.


Bring into analysis a second country: IRP: i=i*+EA i falls, i* EA(forward premium on foreign

currency ) fall. The money supply in one nation increases ,expect prices in one nation will rise. And spot rate expected depreciation. Imply a higher future exchange rate to achieve PPP, a long run value of exchange rate

RLR=P/P*

P expected to rise over time, given P*, R will rise.


overshooting R

R0

t0

i0

t0 t0

RLR

P0

5.Forecasting Exchange Rates5.Forecasting Exchange Rates

Forecasting is difficult, especially with regard to the future. Two reasons , p.530

As a whole, forecasters cannot do a better job of forecasting future exchange rates than the forward rate.

The founder of Forbes Magazine once said: “You can make more money selling advice than following it.”

MA Money supply and P

Perfect institutesPPP alwaysUIAP, EAMs elastic, Md

stableCurrency depreciates

PB Financial assets

Imperfect institutesPPP longCIAP, EA-RPW=M+D+F

In short, depreciatesIn long, BCA and rate affects each other till BCA=0

OvershootingDifferent adjustment speed and iPerfect PPP longUIAP, EAP sticky Md

stableIn short, depreciates over RLR

In long, RLR(same as MA)

Rate determined

Ms increasessequence

suppose

Key WordsKey Words

Arbitrage Covered and uncovered interest arbitrage

parity Purchasing power parity Nominal and real income Money supply and demand Base money MABP MA PB Overshooting Stock and flow

1.While you were visiting London, you purchased a Jaguar for £35,00, payable in three months.you have enough cash at your bank in New York City, which pays 0.35% interest per month, compounding monthly, to pay for the car.Currently, the spot exchange rate is $1.45/£ and the three-month forward exchange rate is $1.45/£. In London the money market interest rate is 2.0% for a three-month investment. Two alternative ways of paying for your Jaguar.

1)Keep the funds at your bank in the U.S and buy £35,000 forward.

2)Buy a certain pound amount spot today and invest the amount in the U.K. for three months so that the maturity value becomes equal to £35,000.

Which Which method method would you would you prefer? prefer? Why?Why?

2.Currently ,the spot exchange rate is $1.50/£ and the three-month forward exchange rate is $1.50/£. The three-month interest rate is 8.0% per annum in the U.S. and 5.8% in the U.K. Assume that you can borrow as much as $1,500,000 or £1,000,000.

1)Determine whether IRP is holding? 2)If IRP holding ,how would you carry

out covered interest arbitrage? Show all the steps and

determine the arbitrage profit.

Explain how Explain how IRP will be IRP will be restore as a restore as a result of result of covered covered arbitrage arbitrage activities.activities.

True, false, uncertain, explain 1 PPP holds better in the long

run than in the short run. 2 PPP is no theory of exchange

rate determination. 3 If nontradable goods prices rise

faster in country A than B, and if nontradable goods prices rise faster than prices in general, the currency of A will appreciate by more than is called for by PPP, as measured by price indexes.

1 For what type of goods does the law of one price hold quite well?

2 Why IRP hold better than PPP over time?

3 true or false,explain: “lenders benefit from unexpected inflation, but borrowers are hurt by it”.

4 Should we believe that interest differentials cause exchange rate changes, or that exchange rate changes cause interest differentials?

5.What is the difference between the MA and PB.and what are the similarities between them?

6.Using MABP or MA model explain how the following events will affect the foreign-exchange value of domestic currency (assume flexible rates)

1)The foreign inflation rate decreases. 2)A natural disaster destroys a significant fraction of

domestic industry and therefore destroys productive capacity. 3)The domestic central bank decreases the growth rate of the

domestic credit component of base money to try to reduce the domestic inflation rate.

7.Discuss the value of domestic currency under flexible rates: A foreign oil cartel succeeds in doubling the market price of oil, and the domestic economy(such as China) is heavily dependent on imported oil.

Exchange Rate Determination

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