Topic 4: International Monetary Systems
Monetary Economics ECOS3010
Monetary Economics (ECOS3010) Topic 4: International Monetary Systems 1 / 48
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Introduction: International Monetary System
In the Örst three topics, we have examined closed economies ñ economies that operate entirely in isolation with a single Öat money.
In modern world, trade and Önancial links between countries are increasingly important.
We turn our focus to the role of money in economies that encompass more than one country and currency. In this chapter, we will examine
how exchange rates are determined;
di§erent types of international monetary system: Öxed exchange rate, áexible exchange rate and etc.;
the rationales for the European countries to adopt a single currency ñ Euro;
when a countryís currency is more likely to be subject to speculative attack: the Asian Financial Crisis.
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A Model of International Exchange
Based on our standard OLG model with money: suppose there are two countries, country a and country b, each with its own money/currency.
Assume that endowments in each country consist of the same goods (a good in country a is indistinguishable from a good in country b). Individuals are indi§erent to the origin of the goods they purchase. There is free international trade.
We use superscripts a and b to identify the parameters and variables of each country. For example,
growth rates of population: na and nb; growth rates of money supply: za and zb.
For simplicity, assume that any new money created by the government is used to Önance the governmentís own purchases.
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A Model of International Exchange
Let et denote the exchange rate: the units of country b money that
can be purchased with one unit of country a money, et = country b money .
1 unit of country a money
For example, country a is Australia and country b is the U.S.:
et = U.S. dollar . 1 Australian dollar
The inverse of et indicates the number of Australian dollar per U.S. dollar.
For each pair of currencies, there are always two exchange rates, depending on which currency serves as the base currency.
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A Model of International Exchange
Consider an old individual in period t who was born in period t 1. If the old individual owns 1 unit of country a money, he can
use country a money to buy vta units of goods;
or exchange 1 unit of country a money for et units of country b money and buy etvtb units of country b goods.
If the old individual owns 1 unit of country b money, he can
use country b money to buy vtb units of goods;
or exchange 1 unit of country b money for 1/et units of country a money and buy vta/et units of country a goods.
What shall the old individual do?
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A Model of International Exchange
No matter which money the old individual holds, he always compares vta with et vtb when deciding which money to use to purchase the goods.
If vta > et vtb , everyone prefers to use country a money. Country b money is not valued by anyone.
If vta < et vtb , everyone prefers to use country b money. Country a money is not valued by anyone.
Only if vta = et vtb , all individuals are indi§erent between the two monies. For both monies to be valued in equilibrium, the exchange rate
a b vta vt =etvt oret=vtb.
We will examine the behavior of this exchange rate under alternative international monetary arrangements.
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Foreign Currency Controls
The Örst international monetary system that we consider is called "foreign currency controls"ña policy that completely separates the monetary sectors of the two countries:
the citizens of each country are permitted to hold over time only the money of their own country;
free international trade.
In our model, the policy of foreign currency controls implies that
the young of each country can hold only their countryís money from one period to the next;
the old can buy goods from any country, but if he wishes to buy goods from foreign country he needs to exchange his money for the foreign currency and then make the purchase.
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Foreign Currency Controls
With foreign currency controls, demand for country a money comes from country a young individuals and demand for country b money comes from country b young individuals. The money market clearing conditions for country a and country b are
vtaMta = Nta ya c1a,t; vtbMtb = Ntbyb c1b,t.
It follows that
Nta(ya c1a,t) a a a b M ta = N t y c 1 , t M t
Ntb yb c1b,t Mta
The exchange rate et depends on the relative values of the demand
for money and the supply of money in the two countries.
e t = v t = vtb
Ntb(yb c1b,t) Mtb
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Foreign Currency Controls
Recall: growth rates of population: na,nb; and growth rates of money supply: za,zb ñwe consider constant growth rates of money supply in this chapter. Suppose that we focus on stationary allocations. We have
a N t a + 1 ( y a c 1a ) a a a
vt+1=Mta+1 =Nt+1Mt=n,
N t a ( y a c 1a ) Mta
N tb+ 1 ( y b c 1b ) Mtb+1
N t a M t a + 1 z a b b b
Ntb(yb c1b) Mtb
=Nt+1Mt =n. Nb Mb zb
t t+1 The path of the exchange rate can be expressed as
vta+1 a b ab ab e vb v v nz nz
t+1=t+1=t+1t= = . et vta vta vb zanb nbza
v tb t + 1
Monetary Economics (ECOS3010) Topic 4: International Monetary Systems
Foreign Currency Controls
What are the factors that determine how the exchange rate changes
over time? From
et+1 na zb e =nbza,
growth rates of population and growth rates of money supply a§ect the path of the exchange rate.
Population growth: the greater the growth rate of country aís population relative to country bís, the greater the growth rate of the exchange rate.
Greater growth of population in one country ! higher demand for the countryís money ! the value of the countryís money increases ! the countryís money appreciates over time.
In general, any factor that contributes to increase in the demand for a countryís money will drive up the value of the countryís money.
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Foreign Currency Controls
Money growth: the greater the growth rate of country aís money supply relative to country bís, the lower the growth rate of the exchange rate.
Greater growth of money supply in one country ! higher supply for the countryís money ! the value of the countryís money decreases ! the countryís money depreciates over time.
In general, any factor that contributes to increase in the supply of a countryís money will lower the value of the countryís money.
A special case is et+1 = et ñÖxed exchange rate.
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Foreign Currency Controls Fixed Exchange Rates
A special case: et = et+1, it requires that a nab
z = nb z . (1)
If country a choose to keep a Öxed exchange rate with country b, it needs to set its growth rate of money supply according to (1). Country a loses its independence in monetary policy.
Country a money and country b money have the same rate of return. If country b increases its growth rate of money supply zb, country a will be forced to increase za to keep the Öxed exchange rate.
Country a government cannot acquire its preferred level of seigniorage revenue.
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Foreign Currency Controls Fixed Exchange Rates
With foreign currency controls, a country can choose the growth rate of money supply either to Öx the exchange rate or to acquire its preferred level of seigniorage, it cannot meet both objectives.
Example: Tutorial 3 Q6 ñoptimal z that maximizes G?
Now, suppose that the (gross) rate of return on money in Australia (country a) is 1.0 and that of the U.S. is 2.0. The (gross) growth rate of the Australia population (na) is 1. Foreign currency controls are in e§ect.
What is the time path of the exchange rate (et+1/et)?
Suppose Australia wishes to maintain a Öxed exchange rate with the U.S.. To accomplish this goal, Australia must set its gross rate of money supply za to what value? Is za = z?
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The Indeterminacy of the Exchange Rate
Suppose now that people are free to hold and use the money of any country. We can no longer have two separate money market clearing conditions. Instead,
the worldís supply of money
v ta M ta + v tb M tb ; the worldís demand for money
N ta y a c 1a , t + N tb y b c 1b , t ; the worldís money market clearing condition
vtaMta+vtbMtb =Nta ya c1a,t+Ntbyb c1b,t. How can we determine the exchange rate?
et = vta vtb
Monetary Economics (ECOS3010) Topic 4: International Monetary Systems
The Indeterminacy of the Exchange Rate
To Önd et , we need to know vta and vtb. However, with one money market clearing condition, how can we solve for two unknowns vta,vtb?
One cannot solve for two unknowns with one equation.
There exists an inÖnite combinations of vta,vtb that satisfy (2).
In other words, for any positive exchange rate et , we can Önd an equilibrium in which (2) is satisÖed.
The exchange rate is indeterminate!
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The Indeterminacy of the Exchange Rate Exchange Rate Fluctuations
In the absence of the government determination of the exchange rate, the exchange rate in a uniÖed world economy can be whatever people believe it to be. The exchange rate could áuctuate because these beliefs áuctuate.
Exchange rate áuctuations need not be tied to changes in real economic conditions.
Before 1971, the U.S. dollar is pegged to gold at 35 dollars per ounce of gold (the Bretton Woods System). In 1971, the U.S. abandoned the e§ort to control exchange rates. Afterwards, the world has seen tremendous volatility in exchange rates.
See following Ögures for an example of the U.S. dollar against four major currencies.
See Table 1 for an illustration of the extreme movements in exchange rates.
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The Indeterminacy of the Exchange Rate Exchange Rate Fluctuations
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The Indeterminacy of the Exchange Rate Exchange Rate Fluctuations
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The Indeterminacy of the Exchange Rate Exchange Rate Fluctuations
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The Indeterminacy of the Exchange Rate Exchange Rate Fluctuations
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The Indeterminacy of the Exchange Rate Exchange Rate Fluctuations
Country France Germany Italy Japan U.K.
Dec 1973 - Jan 1974 Jun 1973 - Jul 1973 Sep 1992 - Oct 1992 Sep 1998 - Oct 1998 Sep 1992 - Oct 1992
Exchange Rate Movements 9.4% depreciation of the franc 9.4% appreciation of the mark 11.3% depreciation of the lira 10.0% appreciation of the yen 11.7% depreciation of the pound
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The Indeterminacy of the Exchange Rate Exchange Rate Fluctuations
Exchange rate between U.S. dollar and Australian dollar.
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The Indeterminacy of the Exchange Rate International Currency Traders
Even with foreign currency controls sometimes the exchange rate can be indeterminate.
A model by King, Wallace and Weber (1992) about international currency traders. Three types of individuals:
citizens of country a, forced by law to hold only country aís money; citizens of country b, forced by law to hold only country bís money; multinational people, free to hold either currency.
The numbers of each type individuals born in period t are denoted as Nta, Ntb and Ntc.
Each countryís money is held by its own citizens and perhaps by multinational people as well. Let λt be the fraction of country a money in the multinational peopleís real money balances.
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The Indeterminacy of the Exchange Rate International Currency Traders
Money market clearing conditions for country a money and country b money:
vtaMta = Nta ya c1a,t+λtNtc yc c1c,t,
vtbMtb = Ntb yb c1b,t+(1 λt)Ntc yc c1c,t.
The value of country a money is
va = Nta ya c1a,t+λtNtc yc c1c,t.
t Mta The value of country b money is
vtb = Ntb yb c1b,t+(1 λt)Ntc yc c1c,t. Mtb
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The Indeterminacy of the Exchange Rate International Currency Traders
The exchange rate in the world economy is
a Nta (y a c1a,t )+λt Ntc (y c c1c,t )
et=vt = Mta . vtb Ntb (y b c1b,t )+(1 λt )Ntc (y c c1c,t )
A simple case: suppose that preferences are such that the total real demand for money is identical across the di§erent types of people. That is, Nta ya c1a,t = Ntb yb c1b,t = Ntc yc c1c,t. The exchange rate can be simpliÖed to
1+λt 1+λt et=Mta =Mta.
1+(1 λt ) 2 λt
When λt increases, et increases. When λt decreases, et decreases. The change in λt will cause change in et .
Example: if Mta = Mtb, et = (1+λt)/(2 λt). What is the range of
values for et ?
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The Indeterminacy of the Exchange Rate International Currency Traders
With international currency traders, the exchange rate is still indeterminate. There exist multiple exchange rates that satisfy the money market clearing conditions. Exchange rates may áuctuate dramatically as multinationals change the composition of their money balances.
The áuctuations in exchange rates make each countryís money a risky asset.
Multinationals may be able to free themselves from this risk if they hold a balanced portfolio of both monies.
Citizens of each country su§er the risk associated with exchange rate áuctuations.
Maybe monetary authorities would like to stabilize the exchange rate to reduce the risk associated with exchange rate áuctuations. How?
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Fixing the Exchange Rate
Monetary authorities may want to stabilize the exchange rate to reduce exchange rate áuctuations.
How shall we organize the world to maintain a stable exchange rate?
Cooperative stabilization: countries coordinate to Öx the exchange rate. Unilateral defense: unilateral commitment to a Öxed exchange rate.
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Fixing the Exchange Rate Cooperative Stabilization
If we take a cue from the monetary organization of national economies, what determines the exchange rate between two di§erent bills in a single national economy?
The government tells us the exchange rate by printing the denomination on each bill.
The government also stands ready to exchange the bills at that rate.
For the world economy, if the two governments stand ready to exchange their currencies at some given rate, can they determine the exchange rate?
A recent example: during reuniÖcation of Germany, the German central bank announced that it would accept East German marks at a one-for-one rate of exchange with West German marks.
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Fixing the Exchange Rate Cooperative Stabilization
We rarely see countries cooperatively Öx the exchange rate.
European Economic Community (now the European Union) had tremendous di¢ culties in maintaining Öxed exchange rates.
One major impediment:
the strong incentive to ináate when exchange rate is Öxed.
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Fixing the Exchange Rate Unilateral Defense
For the world economy, Öxing the exchange rates requires cooperation of foreign central banks. In the absence of such cooperation, the government can keep a Öxed exchange rate through unilateral defense of the exchange rate.
When a government commits to a Öxed exchange rate unilaterally, the government needs to tax its citizens to acquire enough resources to defend the exchange rate.
If such a commitment is believed, there will be little incentive for anyone to turn in one form of money for the other.
Is it believable that the government can defend the Öxed exchange rate by taxing its citizens?
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Fixing the Exchange Rate Unilateral Defense of the Exchange Rate
Consider an OLG model with two countries. No foreign currency controls is in e§ect. The government of country a pledges to tax the old in order to defend a Öxed exchange rate. The world money market clearing condition is
v t a M t a + v t b M t b = N t a y a c 1a , t + N t b y b c 1b , t . Or with a Öxed exchange rate e ̄,
e ̄vtbMta+vtbMtb =Nta ya c1a,t+Ntbyb c1b,t.
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Fixing the Exchange Rate Unilateral Defense of the Exchange Rate
We consider a speciÖc example to have a better understanding of the di§erences between cooperative stabilization versus unilateral defense of the exchange rate.
Suppose country a (Australia) and country b (the U.K.) are identical. In each country, the population of every generation is 100,
Na =Nb =100.
Each young wants to hold real money balances worth 10 goods. It follows that the aggregate demand for money in real terms in each country is
Na (ya c1a) = Ntb yb c1b = 10010 = 1,000.
Assume that the total money supply in country a is $800 and in country b is £ 600.
In the Örst period, each initial old holds $4 and £ 3, regardless of citizenship.
The exchange rate is Öxed at e ̄ = 1/2 ñ $1 trades for £ 0.5.
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Fixing the Exchange Rate Unilateral Defense of the Exchange Rate
We can derive the value of country b money vb vb = ? ,
and the value of country a money vta va=? .
We can also derive the consumption by each old in both countries c2a = ? and c2b = ? .
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Fixing the Exchange Rate Cooperative Stabilization
Now suppose that every member of the initial old of both countries decides to cut their balances of country a money in half. Each member of the initial old turns in $2 to the monetary authority of country a to acquire £ 1.
Cooperative stabilization: if monetary authority of country b agrees to cooperate by printing the amount of its currency demanded. At the end of currency exchange, the stock of dollars is $400 and the stock of pounds is £ 800.
The value of country b money is vb=? ,
The value of country a money is va=? .
Consumption of each old is
c2a = ? and c2b = ? .
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Fixing the Exchange Rate Cooperative Stabilization: Ináationary Incentives
With a Öxed exchange rate, the world money market clearing condition suggests that
vtb=Nta ya c1a,t +Ntb yb c1b,t . e ̄ M ta + M tb
An increase
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