Download Lectures on International Money

Lectures on
International Money
Haakon O. Aa Solheim
Norwegian School of Management, 2002
February 28, 2003
“There is no sphere of human thought in which it is
easier to show superficial cleverness and the appearance
of superior wisdom than in discussing questions of
currency and exchange.”
Winston Churchill,
House of Commons, September 29, 1949
Preface
These lectures where prepared for for a course the course “International
money”, held at the Norwegian School of Management during the spring
of 2002.
The notes are incomplete, as far as they include no citations.
Sandvika, March 2003
Haakon O. Aa. Solheim
Contents
1 Money
6
1.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
1.2
Money and currency . . . . . . . . . . . . . . . . . . . . . . .
6
1.2.1
Examples of money . . . . . . . . . . . . . . . . . . . .
8
1.2.2
The creation of a national currency . . . . . . . . . . . 13
1.3 Money versus currency . . . . . . . . . . . . . . . . . . . . . . 15
1.4 Money and prices—the Cagan model . . . . . . . . . . . . . . 17
1.4.1
Solving the Cagan model . . . . . . . . . . . . . . . . . 19
1.4.2
Seignorage . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.5 The balance sheet of the central bank . . . . . . . . . . . . . . 32
1.5.1
Models without money . . . . . . . . . . . . . . . . . . 34
1.6 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2 International money
37
2.1 Some final remarks on the importance of money . . . . . . . . 37
2.2 Introduction to a discussion on international money . . . . . . 39
2.3 The relationship between the national currency and the international currency . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.3.1
A model of the exchange rate . . . . . . . . . . . . . . 41
2.3.2
Choice of exchange rate regime . . . . . . . . . . . . . 48
1
2.4
2.5
The central bank and the supply of money . . . . . . . . . . . 49
2.4.1
The balance sheet of the central bank . . . . . . . . . . 49
2.4.2
Central bank interventions . . . . . . . . . . . . . . . . 52
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3 Exchange rate regimes
3.1
59
Relating the national currency to the international currency
market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.2
3.1.1
A short history of exchange rate regimes . . . . . . . . 61
3.1.2
Types of exchange rate regimes . . . . . . . . . . . . . 65
3.1.3
Optimal currency areas . . . . . . . . . . . . . . . . . . 68
3.1.4
The death of fixed exchange rates? . . . . . . . . . . . 70
Why a fixed exchange rate system might be unstable . . . . . 82
3.2.1
The n-1 problem . . . . . . . . . . . . . . . . . . . . . 82
3.2.2
The adjustment problem . . . . . . . . . . . . . . . . . 87
3.2.3
The problem of a credible policy—the Barro Gordon
model . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
3.2.4
Appendix: The real exchange rate . . . . . . . . . . . . 93
4 Currency crises
96
4.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.2
Speculative attacks . . . . . . . . . . . . . . . . . . . . . . . . 98
4.3
The Krugman model . . . . . . . . . . . . . . . . . . . . . . . 103
4.4
Crises with no trend? . . . . . . . . . . . . . . . . . . . . . . . 106
4.5
4.4.1
The strategy of speculators
. . . . . . . . . . . . . . . 109
4.4.2
The role of large speculators . . . . . . . . . . . . . . . 113
4.4.3
A short note on the Tobin tax . . . . . . . . . . . . . . 120
Contagion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
2
4.5.1
Transmission of currency crisis via trade channels . . . 124
4.5.2
Transmission via a credit crunch . . . . . . . . . . . . . 127
5 The FX-market
5.1
5.2
130
Some definitions . . . . . . . . . . . . . . . . . . . . . . . . . . 130
5.1.1
Instruments . . . . . . . . . . . . . . . . . . . . . . . . 130
5.1.2
Bid-ask . . . . . . . . . . . . . . . . . . . . . . . . . . 131
What we know for certain about the FX-market . . . . . . . . 132
5.2.1
Triangular arbitrage . . . . . . . . . . . . . . . . . . . 132
5.2.2
Covered interest rate parity—CIP . . . . . . . . . . . . 133
5.3
How the FX-market is organised . . . . . . . . . . . . . . . . . 134
5.4
Data from the FX-market . . . . . . . . . . . . . . . . . . . . 140
5.4.1
International currency . . . . . . . . . . . . . . . . . . 141
5.4.2
The roles of international money . . . . . . . . . . . . 143
6 The floating exchange rate
152
6.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
6.2
High expectations . . . . . . . . . . . . . . . . . . . . . . . . . 153
6.3
“Excess volatility” and some ‘puzzles’ of exchange rate economics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
6.3.1
The FX market vs. the stock market . . . . . . . . . . 157
6.4
Random walk?—the Meese and Rogoff results . . . . . . . . . 164
6.5
Equilibrium models . . . . . . . . . . . . . . . . . . . . . . . . 167
6.6
Disequilibrium models . . . . . . . . . . . . . . . . . . . . . . 169
6.6.1
The Dornbusch model . . . . . . . . . . . . . . . . . . 171
6.7
Chartists and noise traders . . . . . . . . . . . . . . . . . . . . 179
6.8
Microstructure theories . . . . . . . . . . . . . . . . . . . . . . 182
6.9
The uncovered interest rate parity (UIP) . . . . . . . . . . . . 185
3
6.9.1
Testing the UIP . . . . . . . . . . . . . . . . . . . . . . 188
7 Portfolio choice, risk premia and capital mobility
7.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
7.1.1
7.2
7.3
193
Some notes on methodology . . . . . . . . . . . . . . . 194
Demand for foreign currency . . . . . . . . . . . . . . . . . . . 195
7.2.1
The minimum-variance portfolio . . . . . . . . . . . . . 198
7.2.2
The speculative portfolio . . . . . . . . . . . . . . . . . 199
7.2.3
Empirical calculations . . . . . . . . . . . . . . . . . . 200
7.2.4
Heterogenous agents . . . . . . . . . . . . . . . . . . . 202
7.2.5
Aggregate behaviour . . . . . . . . . . . . . . . . . . . 203
The collapse of a currency board . . . . . . . . . . . . . . . . 214
7.3.1
Risk premium and the need for capital . . . . . . . . . 214
7.3.2
Risk premium and expected depreciation . . . . . . . . 214
7.3.3
Effects of a fall in risk premiums
. . . . . . . . . . . . 216
7.4
Empirical applications of the portfolio choice model . . . . . . 219
7.5
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
7.5.1
Mean-variance vs. state-preference . . . . . . . . . . . 220
7.5.2
The exchange rate . . . . . . . . . . . . . . . . . . . . 221
8 The real exchange rate and capital flows
223
8.1
Some notes on research strategy . . . . . . . . . . . . . . . . . 223
8.2
Some empirical observations . . . . . . . . . . . . . . . . . . . 223
8.2.1
8.3
8.4
Differences in the price level . . . . . . . . . . . . . . . 225
Accounting for what we do not know about the real exchange
rate
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
8.3.1
External balance . . . . . . . . . . . . . . . . . . . . . 230
Explaining long term shifts in the real exchange rate . . . . . 232
4
8.4.1
8.5
Fluctuations in the real exchange rate and capital flows . . . . 242
8.5.1
8.6
The Balassa-Samuelson effect . . . . . . . . . . . . . . 233
Model of two countries and terms of trade shocks . . . 243
The importance of capital flows for consumption smoothing . . 255
8.6.1
Explaining the Feldstein-Horioka puzzle
. . . . . . . . 256
9 International capital flows, the IMF and monetary reform 259
9.1
Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
9.2
Capital flows . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
9.3
The international debt market . . . . . . . . . . . . . . . . . . 265
9.4
Can a country default? . . . . . . . . . . . . . . . . . . . . . . 273
9.5
The role of the International Monetary Fund (IMF) . . . . . . 274
9.6
Capital controls in Chile . . . . . . . . . . . . . . . . . . . . . 280
10 Exercises
284
11 Solutions
319
5
Chapter 1
Money
1.1
Introduction
This lecture will discuss the topic of money. Why do we use money? I then
present the “Cagan model”—a framework that provides a useful view on the
relationship between money and prices. In the next lecture we will use this
model as a basis for a first discussion of foreign exchange rates.
1.2
Money and currency
If you ask a non-economist what he thinks of when he hears the word economics he will probably say money. But as you are approaching the last
months of a four year study in economics, how much have you actually learned
about money?
Economics is not about money. Economics is about maximising utility
under constraints. To achieve this prices must adjust to clear markets. Prices
are only ratios—the price of good 1 is the number of good 2 you need to obtain
one unit of good 1. You don’t need “money”—that is currency—for that.
6
You only need more than one good.
However, without money the economy turns into a barter economy. I will
trade with you only if you have a good that I need, and you will trade with me
only if I have a good you need. For a barter economy to work, there must be
a high coincidence of wants. That might work in an economy where everyone
supplies most of their own needs. In a more advanced economy individuals
become specialised, and coincidence of wants become scarce. The economy
needs an asset used for transactions. That asset is money.
Money is introduced to play three main roles. It is supposed to be
• a unit of account,
• a means of payment, and
• a store of value.
The unit of account is just an accounting measure. We need something
so standardised that everyone has a common understanding of its value. We
can then measure the value of other things in quantities of this unit.
The means of payment is the physical thing we use for transactions. Instead of exchanging one good for another we can exchange the good in the
means of payment, and use this in new transactions. It is important that it
is easy to evaluate the true value of this ‘product’. It must be reasonably
safe from forgery or fraud. And it should be easy to carry around.
The store of value is a more difficult concept. A store of value must be
safe—one must be reassured that it does not lose its value over time. Iron,
that rusts, is dominated by gold. Paper that receives no interest, like a USD
100 bill, is dominated by a bond that receives interest.
The good that is supposed to fill these three criteria in the modern economy is currency. Today a currency is generally understood as a liability on
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the national central bank. The national currency works as a unit of account,
as a means of payment and as a store of value. As a store of value currency,
that receives no interest, it is dominated by a number of other goods. Note
that money is something more than currency. In this course money and
currency will however be the same thing, unless otherwise stated.
1.2.1
Examples of money
Different periods have solved the need for money by different means. Here
is a number of examples of money.
• In World War 2 prison camps the Red Cross supplied prisoners various
goods, like food, clothing and cigarettes. However, the goods were
distributed without attention to the prisoners actual needs; one might
get cigarettes even if one was not a smoker. In these camps there
evolved a system for trading the Red Cross rations. The “money” in
this system was cigarettes.
– A unit of account: all prices were stated in cigarettes. Mankiw
(1992) reports that one shirt costed about 80 cigarettes.
As a unit of account cigarettes is adequate. However, note that it
would not work if the quality of different types of cigarettes differ
to much. If e.g. American cigarettes were much better than e.g.
German cigarettes, the price would have to specify the type of
cigarette as well.
– A means of payment: cigarettes are easily transportable. One
problem is that they lose value if they get wet.
– Store of value: cigarettes can be stored for some time without
losing flavour. And there was a stable underlying real demand, as
8
smokers would demand cigarettes even if they were not used as
money. However, cigarettes could be expected to lose value when
the war ended.
• Gold coins.
Metal became the leading fabric used for currency in the European
economies. Three metals were used: copper for smaller purchases, silver
for medium sized purchases and gold for larger purchases. These were
all commodity money. That means that they had a value independent
from their value as money. One is willing to hold precious metals even
if one can not use them in day-to-day transactions.
– As a unit of account: gold works well if one can agree on a standardised weight. However, often one can not. This is one reason
why currency, even in the time of the gold standard, was national.
Weight measures were national specific to the end of the last century. They still to some degree are—i.e. the difference between
US and European standards.
– As a means of payment: gold as such is not a good means of
payment. First, it is very expensive. For most purchases the
amount need is so small that other metals, like copper, is more
useful. Second, it needs to be meticulously measured each time to
assure that one pay the right amount.
To alleviate the last problem public authorities or banks—like the
banks in Florence, therefore the “Florin”—issued gold coins. Each
coin had a standardised value.
However, even such coins can be problematic. A coin can be
“shaved”—i.e. people take of some gold and hope to sell the coin
9
for its original value. Or the issuing institution can attempt to
make money by issuing coins with less gold content, but sell the
coin for its original value. This is called debasing the currency.
In fact, debasing might lead to currency crises—people will try to
store the coins with high gold content, and sell the coins with low
gold content. Such currency crises were frequent in the later years
of the Roman empire.
– Store of value: over time the value of gold depends on who much
gold is available. If much gold is found, the value of gold will fall.
However, gold is scarce. And as gold has an intrinsic value in its
beauty, it can be considered fairly safe.
• Gold backed currency.
Gold is bulky, heavy and difficult to carry around. So instead of using
gold directly, people started to use claims on gold. A bank issues a “bill
of credit” that states that a given amount of gold can be redeemed from
the bank with this bill. E.g.: I deposit 1 ounce of gold in Bank A. Bank
A gives me a bill stating that I get one ounce of gold if I make a claim
with this bill in bank A. I use this bill to purchase a radio. The radio
salesman uses the bill to pay his rent. The landlord uses the bill to pay
... → the bill works as currency.
Why does a bank issue such a bill? As long as it is not required to
keep 100 per cent reserves, it can make an income on the interest rate
differential. 100 per cent reserves would imply that the bank keeps one
unit of gold for each unit of gold backed currency issued. However, it
is not likely that everyone will claim their bills at once. So the bank
can keep less than 100 per cent of the gold as actual reserves. It can
10
therefore invest some of the gold deposited in activities with a positive
return, and thereby get an interest rate. The return on issuing currency
is the difference between this interest rate and the interest rate paid on
the bill (usually zero). So why do I give my gold to the bank? A bill
of credit is easier and safer to carry than gold.
– As a unit of account: if everyone understand the denomination, i.e.
how much gold one unit refers to, it should work well. However, it
is clearly most useful if every bank uses the same denomination.
– As a means of payment: bills of credit are easy to carry. However,
here the value depends on the bank that has issued the bill. If
you don’t trust the bank, you don’t trust the money.
– Store of value: In the case of gold we had uncertainty about the
future value of gold. Here we must add the uncertainty about the
bank. And we still (normally) get no interest rate. So this bill is
probably dominated as a store of value.
The currencies above are all based on commodities. That means that
the currency have a potential value even if it is not used as a currency.
However, there are problems with such currencies. The supply of money is
exogenous—it is mostly decided by factors outside the economy. This is not
perfectly true: the mining activity for gold would to some degree depend on
its monetary value. However, over time the gold supply is independent of
how much money the economy actually needs.
• Fiat currency
Fiat money is an asset that only has value as a medium of exchange. An
example of fiat money is a bill issued by a national monopoly stating
11
that it is the standard means of payment in a given country. The bill is
however not redeemable in any commodity from the side of the issuer.
Norges Bank is not obliged to give anything else in return for paper
money than new paper money—a 50 NOK bill will only return you a
new 50 NOK bill. It only has value because it is accepted as a means
of payment.
– As a unit of account? Actually fiat money is not very good.
The problem is that the issuer, in theory, can issue as much such
currency as he likes. But of course, it an infinite amount of currency is issued, then the currency loses all value. So in practice
the issuer will limit the amount issued. However, inflation is or
has been a problem in almost every country with a fiat currency.
If inflation is high or unpredictable, the currency is no longer a
good unit of account. In countries with extreme inflation one often changes the unit of account to a foreign currency, although
the national currency is still the means of payment. E.g. in many
high inflation countries the USD is used as a unit of account.
– As a means of payment: fiat currency works good, as long as
people trust the issuer. But it depends on how many uses the
currency. If everyone accepts it, it is very handy. If no-one accepts
it, it has no value—the value of a currency depends on its use.
– As store of value: very uncertain, and clearly dominated by a
number of other goods, including gold and bonds.
12
1.2.2
The creation of a national currency
In modern times we have seen a movement from gold backed currency to fiat
currency, and a movement from the use of currency issued by private banks
to currency issued by a state monopoly.
Those two movements probably depended on each other. The issuer of
a currency need to be trustworthy, stable and have good credit. The modern state came to fulfill these criteria during the 19th-century, as national
governments were firmly established, and tax systems were implemented.
The private banking system seems to have worked in a satisfying manner.
As an example the USA had no national currency from 1838 to 1863. All
currency was issued by private banks. The Federal Reserve System was first
established in 1913. However, there are potential problems:
• “Wild-cat banking”—banks issues bills with no backing, or they keep
insufficient reserves.
• Potential instability. A currency becomes more valuable the more people who uses it. However, to extend the use of its currency, the bank
needs to extend the number of customers. More customers generally
means more bad customers as well. So a big bank might become more
unstable, and the currency more unsafe. We get the potential of currency crashes.
• Private banking creates uncertainty among general users, as it is difficult to evaluate if a bank is safe or not.
• The state loses possible income from seignorage—the profit from issuing
money.
13
Figure 1.1: Norwegian CPI from 1835 to 2000. Log of index value. 1920=100
8
Pure fiat currency
7
Bretton Woods
Gold standard
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3
These factors brought forward the nationalisation of the “currency industry” and centralisation of currency issuance by “central banks”. Note that a
central bank is not always public. The only requirement is that it gets the
monopoly to issue valid currency for a country. Norges Bank was a private
institution in the first years of its existence. However, after some time most
central banks were nationalised.
A state backed monopoly issuer has less need for gold to back the value
of its currency. Why? A government back the currency on the trust of the
people and the income generated from future taxes. However, it is much
easier to impose inflation if the currency is issued by a monopolist than if
one has private issuance of currency.
14
1.3
Money versus currency
Is money and currency the same thing? Currency is money, but money is
not only currency. Currency is very liquid money, money used as means of
payment and unit of account. However, other forms of money exists:
• A short term bank deposit is money. But it is not as liquid as currency
(there are stores that do not accept a debit card).
• A savings account is money. However, these money are more illiquid
than the primary account. One can not make purchases directly on a
traditional savings account.
• If one holds long term bonds, these can be bought and sold, but is not
redeemed before after a certain number of years.
Different types of assets have different degrees of liquidity. One moves
one’s holding between different types of money all the time. Traditionally,
and everything else equal, the return of an asset is decreasing in the degree
of liquidity. Currency, i.e. very liquid money, usually returns no interest.
Money has been divided into groups, like M1, M2 and M3. M1 is the most
liquid money (currency and short term deposits), M2 is less liquid money
and so on.
Note: in modern banking the distinctions between different types of
money is falling. My credit card offers an account with free debit card access
and an interest rate formerly only expected on long term deposits. More and
more money is stored electronically as we extend the use of bank cards. Most
people no longer holds large holdings of non-interest bearing currency.
15
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Notes and coin in the Norwegian economy
NOK)
Figure 1.2: Notes and coins in (Millions
the Norwegian
economy. Millions of NOK
45 000
43 000
41 000
39 000
37 000
35 000
33 000
31 000
29 000
27 000
25 000
Figure 1.3: M1 versus notes and coins
450 000
400 000
All numbers in million NOK
350 000
300 000
250 000
M1
200 000
150 000
100 000
50 000
Notes and coins
0
16
International Monetary System
2. Banking system
The QTM in Argentina, 1974-1991 (log scale)
Figure 1.4: Inflation and money growth in Argentina, 1974-91
Annual CPI Inflation Rate
100000
10000
1000
100
10
10
100
1000
10000
Annual Money Growth Rate
1.4
Money and prices—the Cagan model
In the IS-LM model the relationship between money and prices is given by
the LM-curve,
Md
= L (Yt , it+1 ) ,
Pt
(1.1)
where M d is money demand, Pt is the price level at time t, Y is output and i is
the nominal interest rate. The LM curve assumes that real money demand is
8
rising in Y (because when output grows
on needs higher real money holdings)
and falling in i, as a higher interest rate rises the alternative cost of holding
money (remember that money here is the same as currency).
Phillip Cagan argued that during a period of hyperinflation expected
17
inflation would swamp all other influences on money demand. Figure 1.4
illustrates the relationship between money growth and price inflation in Argentina over the period from 1974 to 1991. This was a period with very high
inflation. As we can see, as inflation gets higher, the relationship between
money growth and inflation becomes stronger. Under high inflation one can
therefore ignore the effect of output and interest rates, and instead write
Mtd
= Et
Pt
Pt+1
Pt
−η
.
(1.2)
Equation (11.48) tells us that if expected inflation rise, we reduce our demand
for real money balances. If we know that prices will rise tomorrow, we want
to hold less money today, as these money will lose value tomorrow.
Et shows us that we look at expectations at time t. η is the semielasticity
of demand for real balances with respect to expected inflation. It is parameter
that tells us how much demand for real balances—the money stock divided
by the price level—reacts to a change in expected inflation. If η is large this
indicates that we would make a large adjustment in money balances if we
know that prices will change tomorrow. If η is close to zero we do not care
about inflation when deciding the level of real money balances.
If we take logarithms on both sides we obtain
mdt − pt = −ηEt (pt+1 − pt )) ,
(1.3)
where small letters are the logarithms of large letters. We will use the equation on logarithmic form, as this simplifies the analysis.
18
1.4.1
Solving the Cagan model
We want to study the relationship between money and prices. So we need to
find the equilibrium of the model.
We have an equation for money demand. However, we know that in
equilibrium supply must equal demand. So we must have
md = mt .
(1.4)
We can then restate equation (11.48) as
mt − pt = −ηEt (pt+1 − pt ).
(1.5)
Further, let us assume that all agents are rational and have perfect foresight.
If so we can eliminate the expectation term. We get
mt − pt = −η(pt+1 − pt ).
(1.6)
Equation (11.53) is a first order difference equation. We want to find the
relationship between p and m, in other words we want an expression of the
type
pt = γm.
(1.7)
The easiest way to solve a first order difference equation is by iteration.
First, write equation (11.53) with pt on the left hand side. We get
pt =
1
η
mt +
pt+1 .
1+η
1+η
(1.8)
We see that today’s price level depends on the unforseen price level of tomorrow. What does the price level of tomorrow depend on? Lead equation
19
(1.8) with one period, and we get
pt+1 =
1
η
mt+1 +
pt+2 .
1+η
1+η
(1.9)
We can now substitute the expression from equation (1.9) into equation (1.8).
Doing so we obtain
1
pt =
1+η
η
mt +
mt+1
1+η
+
η
1+η
2
pt+2 .
(1.10)
If we repeat this procedure, eliminating pt+2 and then pt+3 and so on, we
will in the end get
s−t
T
∞ 1 X
η
η
pt =
ms + lim
pt+T .
T →∞
1 + η s=t 1 + η
1+η
(1.11)
How shall we interpret equation (1.11)? We often choose to assume that
lim
T →∞
η
1+η
T
pt+T = 0.
(1.12)
This is the same as assuming that there is no “speculative bubbles” in the
price level. Indeed, equation (2.10) will be zero unless the level of prices
changes at an ever increasing proportional rate.
Bubbles
What is a speculative bubble? One can say that a bubble is an explosive
path which brings the level progressively farther away from economic fundamentals. However, “economic fundamentals” is something we define—it is
a “model specific term”.1 A better definition is probably that a bubble is
1
What do I mean with “model specific term”? When we build a model we define a
relationship between variables. The only thing we know about the relationship between
20
a movement that leads to increasing divergence from the equilibrium value
defined by an economic model.
Notice that in this model we assume perfect foresight and rational agents.
Despite this quite strong assumptions we can not rule out the existence of
rational bubbles. We can only assume that they do not exist. However, it is
reasonable to believe that rational bubbles exist?
Bubble can not exist if we know that it will “burst” at a given point of
time. Why? If we know the price level will revert to its “true value” at a
given time, we will try to make a fortune going short in the asset. However,
if everyone does this, prices must fall today. A bubble can never exist if there
is certainty about when the bubble will collapse.
It is easier to see this if think about e.g. stocks instead of the general
price level. Assume that there is stock price bubble. If we expect the prices
to fall at time t, we will go “short” today—i.e. we will sell assets for delivery
at time t + 1. Why? Because we expect that we can buy stock to a much
lower price than in the forward contract when time t + 1 arrives. At t + 1 we
buy stock in the spot market at a low price to fulfill our forward contract.
However, if the timing of the crash of the bubble is uncertain, a bubble
can exist even if everyone knows it is a bubble. If we expect prices to rise
in this period, and the next period, and the period after that, we can make
money by buying the asset today. But doing so, we just fuel the bubble—the
more people who buy the asset, the more do prices rise. In fact everyone
find it profitable to let the bubble exist—although everyone knows that a
some time in the future the prices need to revert to a lower level. “Rational
bubbles” are models where the there is much uncertainty about when the
the price level and money is what we have defined in economic models. If the price level
does not behave as in the model we say that it does not behave according to “economic
fundamentals”. However, notice that we do not know if the behaviour of the price level
defies logic, or if it is our model that is flawed.
21
bubble will collapse.
Note that it is very difficult to test if a bubble really exists. If we test for
the existence of a bubble, we will simultaneously test whether
1. there is a divergence from the values predicted by the economic model,
and
2. whether the economic model in fact is the true model, or if the divergence only is the product of bad modelling.
It is more or less impossible to distinguish these two issues from each other.
Prices and money—a solution?
We assume no bubbles. We can then rewrite equation (1.11) as
s−t
∞ 1 X
η
ms .
pt =
1 + η s=t 1 + η
(1.13)
We can draw several interesting conclusions from equation (1.13):
• First, note that2
s−t
∞ 1 X
η
1
1
=
(
η ) = 1.
1 + η s=t 1 + η
1 + η 1 − 1+η
2
(1.14)
Here I use the rules of summations. Remember the following two results from your
classes in mathematics:
∞
X
1
ks =
1−k
s=t
T
X
s=t
ks =
1 − k T −t
1−k
22
If the money supply is constant, i.e. m = m we have that
pt = m.
(1.15)
Not only is inflation zero for all periods, the price level is also fixed at
the level m. However, if the money supply makes an unexpected jump
at time t to a new level, i.e.
mt =


m t < t
(1.16)

m0 t ≥ t, (m0 > m),
this implies that
pt =


m, t < t
(1.17)

m0 , t ≥ t.
As we see, if there is an unexpected shock to m the price level will
change immediately. The change in the price level will be equiproportionate with the change money stock.
These results implies that in this model, money is fully neutral. Changes
in the level of money supply or changes in the denomination used, i.e.
a change in the unit of account, leads to an immediate equal proportional change in the price level. For example, exchanging 8 “old NOK”
with 1 “new NOK” will only lead to all prices being divided by 8. This
result will be found in all models that have no nominal rigidities, such
as sticky prices, and no “money illusion”.3
• Real variables are not affected by a change in money supply—we have
3
Money illusion is the idea that people do not understand the consequences of a change
in the money supply immediately).
23
real-monetary dichotomy—money affect only prices. Money is a “veil”—
and rational agents are able to look through it without letting it affect
their decisions.
• Notice that prices depend on expectations of the future. This implies
that
– it will matter whether a shock is expected to be temporary or
permanent, and
– it will matter whether the shock is expected or unexpected.
Above we illustrated the case of an unexpected shock. Assume instead
that at time t the government announces a change in the money supply
at some future time T . Suppose
mt =


m t < T
(1.18)

m0 t ≥ T, (m0 > m).
One will then find that the path of the price level becomes4
pt =


m + ( η )T −t (m0 − m), t < T
1+η
(1.19)

m0 , t ≥ T.
The price level will make a small jump when the news is announced.
It will so accelerate over time until it reaches its new level at time T .
News will immediately be incorporated in the price setting.
Last, consider the case when the money supply grows at a fixed rate.
Assume that mt = m + µt. It is reasonable to believe that if money grows at
4
A proof is provided at the end of the lecture notes.
24
Figure 1.5: A perfectly anticipated rise in the money supply
Price level
m’
m
m
t
T
time
the rate µ, prices must grow at the same rate, so that inflation also equals
µ. If we insert this in the real money demand function, equation (11.48), we
have
mt − pt = −ηµ,
(1.20)
pt = mt + ηµ.
(1.21)
or
This result will be used later in the course.
Does the Cagan-model fit Norwegian data?
According to the above model an unexpected increase in the money stock
should lead to
• an immediate, equiproportionate increase in the price level, and
25
• causality should go from money to prices, not the other way around.
One empirical methodology to identify unexpected shocks is to do a socalled Vector Auto Regression (VAR) and find impulse response functions. A
VAR is a system of equations estimated simultaneously. An impulse response
function estimates how the variables in the system will react to a shock in the
error term of one variable. The error term is something that is not explained
in the model. A shock to the error term is therefore by definition unexpected.
Figure 1.6 illustrates the impulse response functions from a shock in the
12-month growth rate of M1. The results can be summarised as follows:
• Prices react to a change in the money stock. However, the reaction
occurs with a lag of between 4 and 10 months.
• We see that a shock to money affects prices, but a shock to prices do
not affect money. This should imply that causality runs from money
to prices.
There is a correlation between money and prices. However, the prediction
of an immediate jump in the price level is not reflected in the data. This
might have two causes:
• the shocks in the model are not “unexpected”, or
• prices only react to a shock in money with a lag.
The first explanation is not implausible, as we only estimate a model containing lagged values of changes in the CPI and M1. However, it is reasonable
to believe that prices do indeed only react with a certain lag. Three explanations are offered for why prices do not react immediately to a shock to
money:
26
Figure 1.6: Money growth versus inflation—Norway 1987-2001
Response to One S.D. Innovations ± 2 S.E.
Response of DCPI to DCPI
Response of DCPI to DM1
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0.0
0.0
-0.1
-0.1
5
10
15
20
25
30
35
5
Response of DM1 to DCPI
10
15
20
25
30
35
30
35
Response of DM1 to DM1
3
3
2
2
1
1
0
0
-1
-1
5
10
15
20
25
30
35
5
10
15
20
25
DCPI is the 12-month change in CPI, and DM1 is the 12-month change in
M1.
27
1. Sticky prices. This is the traditional assumption in Keynesian models.
It is built on the argument that contracts take time to adjust.
2. Money illusion. When people get more money between their hands,
they are not able to conclude if this is the result of increased productivity on their part, or of more money in circulation.
3. Portfolio balancing. People will not adjust their money holdings immediately. As a result the effect of increased money supply will take
time to dissipate through the economy.
These theories have different implications. However, on one account they all
agree: if prices do not adjust immediately, a change in money growth might
have real effects on the economy. Money will no longer be neutral.
1.4.2
Seignorage
Seignorage is the revenue the government acquires by using newly issued
money to buy goods or repay debts. It is assumed that most hyperinflations
are results of the government’s need for seignorage revenues.5 Seignorage in
period t is defined as
Seignoraget =
Mt − Mt−1
.
Pt
(1.22)
This is the real increase in the money supply from period (t − 1) to period t.
However, above we saw that the price level depends on the present money
supply and future expected money growth. This implies that there must be
a limit to how much the government can collect as seignorage. To see this,
5
A hyperinflation is a period when prices rise at a rate averaging 50 per cent per month.
The highest monthly inflation recorded is in Hungary in July 1945 when prices rose 19800
per cent in one month.
28
rewrite equation (1.22) as
Seignoraget =
Mt − Mt−1 Mt
.
Mt
Pt
(1.23)
If higher money growth leads to higher expected inflation, demand for real
balances (M/P ) will fall. So higher money growth might not always increase
seignorage revenues.
We can use the Cagan model to find the of money growth will maximize
seignorage revenues. We had that
Mt
= Et
Pt
Pt+1
Pt
−η
.
(1.24)
If we substitute (1.24) into (1.23) and rearrange a little, we get
Mt−1
Seignoraget = (1 −
)
Mt
Pt+1
Pt
−η
.
(1.25)
We now assume that the government can commit itself to a certain rule
for money growth. More specifically, we assume that money growth is given
by
Mt
= 1 + µ ⇔ mt+1 − mt = µ.
Mt−1
(1.26)
If money supply grow at a constant rate µ, we have seen that prices grow at
the same rate µ, so we have that
Mt
Pt
=1+µ=
.
Mt−1
Pt−1
(1.27)
Substituting (1.27) into (1.25) we obtain
Seignoraget = (1 −
1
)(1 + µ)−η = µ(1 + µ)−η−1 .
1+µ
29
(1.28)
We find the µ that optimises seignorage by taking the first-order condition
of (11.73) and setting equal to zero, so that
(1 + µ)−η−1 − µ(η + 1)(1 + µ)−η−2 = 0.
(1.29)
The revenue maximising net rate of money growth must equal
1
µM AX = .
η
(1.30)
This is the inverse of the semielasticity of real balances with respect to money.
In fact, we have just found out that an optimising central bank will behave
in exact the same way as monopolist with zero marginal cost of production
(we simplify by ignoring the cost of printing currency). That should not
be a surprise; after all a central bank is just a monopolist in the “currency
issuance market”.
An other way to see the result from equation (1.30) is illustrated in figure
1.7. We can draw a “Laffer-curve” for seignorage revenue. There will be
a level of money growth that maximises seignorage revenue—to issue more
money than this will only be counter productive.
In a hyperinflation it is reasonable to believe that the government exceeds
this optimal level of money growth. But why? If expectations are not forward
looking, but backward looking, the government might earn money by printing
money at an increasing speed. If expectations are backward looking, everyone
believes that last periods money growth will be next periods money growth.
Increasing money growth in the next period over the money growth in this
period will by definition exceed expectations. It is however doubtful if one
can fool the public for a long time in this way.
A problem with the above analysis is that we assume that the government
30
Figure 1.7: “Laffer-curve” for seignorage revenue
Seignorage revenue
1/n
Rate of money growth
Note that n in the figure equals η in the model.
can commit itself to a given rate of money growth for an infinite future.
However, if this is credible, the government has an incentive to fool the public
by increasing the rate of money growth for one period, thereby getting an
extra revenue. If the public does not trust the government, the optimal rate
of money growth might be less than what implied from the above analysis.
In the end, how large is actual seignorage revenue? For most industrialised countries the yearly revenue is about 0.5 per cent of GDP. In the case
of Norway that would be about 500 million USD. In developing countries it
can be much more of total government expenditure, however it reportedly
rarely exceeds 5 per cent of GDP on a sustained basis.
31
1.5
The balance sheet of the central bank
The government is often seen as one entity in economic models. It should
not matter that one public institution has a surplus on its books, if another
public institution has a deficit. What matters are the net position over all
government institutions.
However, in monetary matters it is useful to distinguish between the
“fiscal authority” and the “central bank”. In fact this distinction is artificial.
As long as the central bank is publicly owned, it is part of the governments
balance sheet. Money, a liability on the central bank, is at the same time
a liability on the government. However, because money is so important for
the workings of the modern economy, there tends to be a separation between
government expenditure and the central bank.
If there was no separation between the central bank and the government,
the government would have two choices if it needed to finance a deficit:
• it could issue more money, or
• it could issue bonds.
An independent central bank is supposed to be a guarantee against monetary
financing of public expenditure. However note that the distinction between
issuing bonds and money is only a “veil”. If the central bank issues money
to purchases government bonds, the two cases are exactly the same.
In most advanced economies there is a tight wall separating the fiscal
and monetary authorities. If the government uses money to finance public
deficits, the money will loose value, and no longer fulfill its purposes as unit
of account, means of payment and store of value. In the long term the cost of
undermining the value of money exceeds the potential gains from financing
public deficits by printing money. However, leading experts on monetary
32
economics (like Michael Woodford) have argued that a target for inflation
will only be credible if there is some target for public spending as well.
Over time the one needs to see the government accounts from a consolidated
standpoint—and one can not expect that the central bank balances its book
if other parts of the government do not balance their books.
A central bank typically holds four types of assets. These are
• claims on foreign entities, i.e.
– foreign currency, and
– foreign-currency-denominated bonds.
• gold (although the stock of gold has been reduced in the later years) and
SDR’s (claims on the International Monetary Fund, so-called “paper
gold”), and
• home-currency-denominated bonds.
On the liability side the central bank has two types of assets,
1. currency and
2. required reserves.
Required reserves are accounts domestic banks must hold in the the central
bank to be able to borrow money from the central bank. Currency plus
required reserves make up what is called the “monetary base”. The liability
side will also contain an accounting term, “net worth” to assure that the
accounts balance. The balance sheet is presented in figure 2.3.
If the central bank want to reduce the monetary base, it sells one of its
assets to the public. When it wants to increase the money supply, it buys
assets from the public.
33
Figure 1.8: The balance sheet of the central bank
Assets
Liabilities
Net foreign-currency bonds
Monetary base
Net domestic-currency bonds
Net worth
Foreign money
Gold
1.5.1
Models without money
Although we have spent much time in this lecture on the topic of money, one
will usually find that discussions of monetary policy is conducted in models
that do not contain the term money at all. The reason is that is very difficult
to establish stable econometric relationships between the money and other
variables in the economy. The lack of stable money aggregates make money of
little use in practical policy. Indeed, attempts to focus on the money supply,
as was conducted by e.g. the Bank of England in the early 1980’s, failed.
Instead of targeting money, most central banks today target the inflation
rate, and use the interest rate as instrument, not the money supply.6
However, the central bank’s control of short term nominal interest rates
ultimately stems from its ability to control the quantity of base money in
existence. If some power different from the central bank could control M ,
6
The ECB makes one important exception. They have continued the tradition from
the Bundesbank, and keep an official target for money growth.
34
then this power could directly affect monetary policy. One should also note
that although modern monetary theory looks like a theory with no money,
it still rests on the assumption that in the long run inflation is a monetary
phenomena.
1.6
Appendix
Proof of equation (1.19).
T ∞ 1 X
η
1 X
η
pt =
m+
m0
1 + η s=t 1 + η
1 + η s=T 1 + η
∞ ∞ η
1 X
η
1 X
pt =
m+
m0 − m
1 + η s=t 1 + η
1 + η s=T 1 + η
∞ 1 X
η
m0 − m
pt = m +
1 + η s=T 1 + η
"∞ X
#
T X
1
η
η
pt = m +
m0 − m
−
1 + η s=t 1 + η
1+η
s=t

pt = m +
η
1+η
T −t 
1−
1 

(1 + η) −
 m0 − m
η
1+η
1 − 1+η
"
T −t #
1
η
pt = m +
(1 + η) − (1 + η) + (1 + η)
m0 − m
1+η
1+η
"
T −t #
1
η
pt = m +
(1 + η)
m0 − m
1+η
1+η
35
pt = m +
η
1+η
T −t
36
m0 − m
Chapter 2
International money
2.1
Some final remarks on the importance of
money
In Lecture 1 we discussed the nature of money. The value of the currency
we hold at a given point of time depends on how much we can purchase for
this amount. If the price level increases, our currency loses value. The value
of money depends on the price level. Currency is an asset were the level of
return is given by inflation. The higher inflation, the lower the return on
holding currency, as high inflation implies a falling value of your currency
holdings.
Several points were made in the first lecture:
• For all types of money, even for a commodity currency, there is a need
for trust between the issuer of a currency and the holder of currency
for the currency to be accepted.
• The Cagan model showed us that the trust in a currency depends on
the future expected supply of the currency. This implies that money is
an asset—its value depends on expectations of the future.
37
• Our example of seignorage revealed that a fiat currency is indeed only
a product supplied by a monopolist. However, for this monopolist to
maximise profit, given perfect foresight, there is an absolute limit to
how fast money supply can grow. This limit depends on the semielasticity of money demand in expected inflation.
The value of money depend on the credibility of the issuer of money. In
that respect money does not differ from other assets we are holding, like
bank deposits, bonds or equity. However, why are money special? Two
things make the credibility issue of special importance when we talk about
money:
1. Money is one of the few assets that encompass the whole economy.
2. For many people money the only financial asset they hold. For them
money is an asset with no alternatives.
For a large group of people, especially among the poor, financial markets
are incomplete. Most important are perhaps that the poor have difficulties
getting loans. This implies that they do not posses the credit necessary to
buy e.g. their own home.
For these people money or short term deposits are the only store of value.
Further, almost all expenses are based on nominal prices. If prices rise very
fast, wages tend to lag prices. At the same time their holdings of money are
diminished by inflation.
Loans are and real assets are both a hedge against inflation. Even though
interest rise, the cost of a loan tends to fall if inflation is high, because a loan
is fixed in nominal terms. The price of real assets should be expected to rise
with inflation. The value of the holdings of money is however diminished by
inflation.
38
The problem of incomplete financial markets grow the less sophisticated
the financial market is. One implication is that instability in the value of
money might is especially costly in developing countries.
2.2
Introduction to a discussion on international money
In the first lecture we argued that the economy needed money; something
that could work as a unit of account, means of payment, and also be a store
of value. It was also pointed out that the value of money depended on the
use of money. However, why are money national?
There has always (i.e. as long as there has existed money) existed international money—means of payment accepted across borders. However,
generally small change and money used in daily transactions have been national currency. That is probably a question of both trust, standards and,
with the emergence of a national state, the ability of a government to impose
a monopoly.
• If e.g. gold is used as a currency, everyone must agree on a weight unit
if gold is going to work as a unit of account. However, weight measures
have traditionally differed between countries.
• The value of money is a question of trust in the institution that has
issued the money. Proximity traditionally increases the ability to trust.
• The revenue from seignorage has been an important factor when governments have imposed a state monopoly in currency issuance.
Would it be optimal to have only one currency? One has compared a
currency to a language: the more people who use a language, the more useful
39
does it get. But would it be optimal for everyone to speak the same language?
In a world where communication is difficult, languages get specialised. Even
if one starts up with one language, the different needs of different areas
turn a common language into different dialects, and over time into distinct
languages.
In the current world, with easy communication over long distances a
common language could probably be an option. However, is it optimal?
Perhaps one would have created only one language if we could redraw the
world from scratch. Given that multiple languages already exist it would
probably not be optimal to impose one language on everyone. However,
for international communication only a few languages are in fact actively
used. These function as “international languages”. This is also the case with
money: side by side there exists national currencies and international monies.
In this lecture we will discuss what determines the use and value of currencies in international markets. How is the value of national currencies
determined? How does monetary policy affect the value of an exchange rate?
And what is the role of international money?
2.3
The relationship between the national currency and the international currency
In the last lecture we used the Cagan model to say something about the
relationship between money and prices. However, one can also use the Cagan
model to get an understanding of how a currency is priced in international
markets. This is a starting point for our discussion of monetary policy and
exchange rates.
40
2.3.1
A model of the exchange rate
General assumptions
We can use the Cagan model to derive a monetary model of the exchange
rate. However, we want the model to be more general than the one we
discussed in the first lecture, so we reintroduce nominal interest rates and
real income in the equation. If we assume that expected inflation is low or
non-existing, we can write the demand for real money balances on log-form
as
mt − pt = −ηit+1 + φyt .
Here i is the nominal interest rate
1
(2.1)
and y is real output.
We want to find a link between the model of money and the exchange
rate. Let us first define the exchange rate , as the price of one unit of
foreign currency denominated in domestic currency. This is the standard
denomination in most countries2 . It implies that
· (domestic currency) = (one unit f oreign currency).
(2.2)
Note that seen from the point of view of the home country, a higher exchange
rate implies that the home currency has depreciated, or has lost value. A
higher exchange rate means that it takes more units of the home currency to
buy one unit of the foreign currency. Similarly, a lower exchange rate implies
an appreciation of the home currency. Also note that the log of will have
the label e.
To be able to say anything about an exchange rate we need to make two
assumptions, linking the value of local money to the value of foreign money.
1
Formally measured as log of 1+i, where i is the nominal interest rate.
One exception is Great Britain, where a currency is usually quoted as units of foreign
currency that is needed for the purchase of GBP 1.
2
41
If we shall be able to say something about relative prices we must assume
• free trade, and
• free capital mobility.
Unless these two requirements are fulfilled, the monetary model will not
give a good empirical fit. However, what does these two assumptions imply
for our model?
1. The assumption of free trade makes it possible to assume purchasing
power parity, or PPP. PPP implies that the exchange rate between two
countries shall equal the relative ratio of the price levels between two
countries,
Pt = t Pt∗ ,
(2.3)
where is the exchange rate and P ∗ is the foreign price level. On logs
(2.3) can be expressed as
pt = et + p∗t .
(2.4)
The PPP states that the price level should be the same in all countries
if prices are re-calculated to one currency. One way to look at this is
through the “law of one price”. LOP states that if a good is priced
differently in two countries, arbitrage would assure that the good is
bought in the country where it is cheap, and transported to the country
where it is expensive. Over time this should trade away the price
difference.
There is a number of problems concerning the PPP. Although there
is free trade of many physical products, there are e.g. restrictions on
the trade of labour, so one should assume it to be considerable price
42
differences in labour intensive products. This is taken account of in
the “Balassa-Samuelson” model, presented in your prior macro course.
However, for the time being we assume the PPP to hold.
2. If markets are efficient, free capital mobility should assure that the
return on capital assets are equalised between currencies. This relationship is formalised in the uncovered interest rate parity (UIP), that
can be written as
1 + it+1
= Et
1 + i∗t+1
t+1
t
.
(2.5)
What does the UIP say? It states that the expected return on investment should be independent on the currency the bond is denominated
in. If I hold NOK I should get the same return if I invested my money
in a Norwegian bond, or if I exchanged NOK for EUR today, invested
in a perfectly similar bond in the Euro zone, and exchanged back to
NOK after the bond came up for payment. Why should this hold? If
there is perfect foresight it should hold by pure arbitrage. If one expected a higher return in EUR-bonds than in NOK bonds, everyone
would buy EUR-bonds, depressing the interest rate on such bonds. On
logs the UIP can be written as
it+1 − i∗t+1 = Et et+1 − et .
(2.6)
Deriving the exchange rate
If we substitute equations (2.4) and (2.6) into equation (11.31) we obtain
mt − (p∗t + et ) = −η(Et et+1 − et + i∗t+1 ) + φyt .
43
(2.7)
Again we assume perfect foresight, so that we can dispose of the expectation
term. Then equation (2.7 can be rewritten as
et =
1
(mt − φyt + ηi∗t+1 − p∗t ) + ηet+1 .
1+η
(2.8)
If you remember back to lecture 1, you will see that this is the same difference
equation as we derived in the stochastic Cagan hyperinflation model. The
only change is that we have exchanged p with e and m with (m−φy+ηi∗ −p∗ ).
In the same way as we solved for p in lecture 1 we can now solve for e. The
solution will be
s−t
T
∞ η
η
1 X
∗
∗
et =
(ms − φys + ηis+1 − ps ) + lim
et+T .
T →∞
1 + η s=t 1 + η
1+η
(2.9)
As in the case of the solution for the price level we obtain two terms. The
last term is a potential bubble term. A rational model with perfect foresight,
and where the PPP and the UIP hold at every point of time is not enough to
be certain that bubbles does not exist. However, it is usual to assume that
lim
T →∞
η
1+η
T
et+T = 0.
(2.10)
If so we can express the exchange rate as
s−t
∞ 1 X
η
et =
(ms − φys + ηi∗s+1 − p∗s ).
1 + η s=t 1 + η
(2.11)
We see that an increase in the money stock will lead to a higher exchange
rate. In other words, an increase in the money stock leads to a depreciation
as a higher rate implies that you must pay more for foreign currency because
the local currency loses value. A lower money stock will imply a stronger
exchange rate. Higher output will imply a stronger currency. However, if
foreign interest rates rise, the currency will depreciate.
44
Implications
As we will later discuss, this model does not have a very good empirical fit
in the short term. Whether this is due to
• the fact that the assumptions of free trade and free capital mobility do
not hold,
• whether it is due to a bad model specification,
• whether it is due to bubbles actually being a factor,
• whether it is due to public interference not captured in the model,
• whether we do not understand how expectations are formed, or
• whether markets are just not as rational as this model assumes,
is not easy to tell. These are important questions in current economic research.
However, a monetary model of this type is not an unreasonable approximation to the exchange rate in the long term. And there are several important implications that can be derived from the monetary approach.
1. The exchange rate must be seen as an asset price—the exchange rate
depends on the expectation of future variables. That is a very important finding. One should analyse the exchange rate in the same way
as one analysis e.g. a stock or bond. In fact, we still know very little
about how asset markets are actually priced. As we will find later in
this course, this is also the case for exchange rates.
2. The exchange rate is determined by stocks, not flows. Up till the 1970’s
45
most models of supply and demand in the FX-market3 was based on a
flow approach. Foreign exchange was seen as medium of exchange for
executing international trade transactions. In this model the currency
is treated as an asset—something that is infinitely durable, which can
be transferred but not destroyed. One important implication of this
shift:
• in the flow approach exchange rate movements are expected to be
sluggish, as flow specifications would be slow to change.
• in the stock approach exchange rate movements are expected to
be quick to reflect new information.
The last is clearly a better description of a floating exchange rate than
the first.
3. It is important to distinguish between different types of shocks. The
consequence of a temporary shift in a variable will differ from the consequence of a permanent shift. Likewise, the consequence of an anticipated shock will be differ from the consequence of an unanticipated
shock.
In the last lecture we distinguished between an unexpected and expected
shock. Let us see how a permanent shock will differ from a temporary shock.
• Let y, i∗ and p∗ all equal zero4 , and assume that there is no bubble. Assume that at time T the government announces a permanent change in
the money supply. Then the exchange rate must rise equiproportionate
3
This is the short term for “the foreign exchange market”—the markets where currencies are traded.
4
As these are on logarithmic form, setting a value equal to zero implies setting the
actual value equal to one. As you know, ln(1) = 0.
46
with the money stock, i.e.


m, t < T
mt =

m0 , t ≥ T , (m0 > m).
(2.12)
implies that
et =


m, t < T
(2.13)

m0 , t ≥ T .
• Assume that at time T the government announces a temporary increase
in the money supply. However, at T the money supply reverts to its
level before T :




m, t < T



mt = m0 , t ∈ T , T
(m0 > m)





m, t > T .
We find that the path of the exchange rate becomes5




m, t < T



T −t
0 − m) < m0 , t ∈ T , T
et = m0 − η
(m
1+η





m, t > T .
(2.14)
(2.15)
The price level will make a jump in period T . However, the jump will
be less than if the shock was permanent. The exchange rate will then
fall, just to reach its previous level at time T . Both cases are illustrated
in figure 2.1.
5
Proof provided in the appendix.
47
Figure 2.1: Temporary vs. permanent shock to the money supply
e
m'
m
T_
2.3.2
T
time
Choice of exchange rate regime
Let us assume two extreme cases.
1. The government fixes the exchange rate, i.e.
et+1 = et .
For simplification we set = 1, which implies e = 0 ⇒
(2.16)
pt = p∗t and
it+1 = i∗t+1 . It follows that
mt = p∗t − ηi∗t+1 + φyt .
(2.17)
→ the money stock that is necessary to support a fixed exchange rate is
determined by changes in real output, foreign prices and foreign interest
rates. The central bank must adjust the money supply accordingly. For
the fixed exchange rate regime to be credible the central bank must let
48
the money supply be endogenous.
2. The government fixes the money supply. The money supply is the only
variable the central banks can control directly in this system. Fixing
the money supply is the most extreme example of an exogenous rule
for money supply.
For simplicity we assume the central banks sets m = 0.6
Using the equations above, we obtain that the exchange rate is given
by
s−t
∞ 1 X
η
(−φys + ηi∗s+1 − p∗s ).
et =
1 + η s=t 1 + η
(2.18)
The central bank can not influence any of the variables in equation
(11.43). This implies that the exchange rate become an endogenous
variable—it is determined within the system. The exchange rate is
outside the control of the central bank. The central bank can not
control the money supply and the exchange rate at the same time.
2.4
The central bank and the supply of money
A choice of exchange rate regime is the same as a choice of a rule for money
growth. But how do the central bank affect the money supply in the first
place?
2.4.1
The balance sheet of the central bank
The government is often seen as one entity in economic models. It should
not matter that one public institution has a surplus on its books, if another
6
This is not the same as setting money supply to zero. Remember that m = log(M ),
and that log1 = 0.
49
Figure 2.2: Fixed exchange rate vs. fixed money supply. Consequences of a
shock to output
Fixed exchange rate
e
y0
y1
e
y2
Fixed money supply
y0
e0
m0
m1
m2
e1
y1
e2
y2
m
m
m
A shock to output will have different consequences depending on the choice
of target in the monetary policy.
public institution has a deficit. What matters are the net position over all
government institutions.
However, in monetary matters it is useful to distinguish between the
“fiscal authority” and the “central bank”. In fact this distinction is artificial.
As long as the central bank is publicly owned, it is part of the governments
balance sheet. Money, a liability on the central bank, is at the same time
a liability on the government. However, because money is so important for
the workings of the modern economy, there tends to be a separation between
government expenditure and the central bank.
If there was no separation between the central bank and the government,
the government would have two choices if it needed to finance a deficit:
• it could issue more money, or
• it could issue bonds.
50
An independent central bank is supposed to be a guarantee against monetary
financing of public expenditure. However note that the distinction between
issuing bonds and money is only a “veil”. If the central bank issues money
to purchases government bonds, the two cases are exactly the same.
In most advanced economies there is a tight wall separating the fiscal
and monetary authorities. If the government uses money to finance public
deficits, the money will loose value, and no longer fulfill its purposes as unit
of account, means of payment and store of value. In the long term the cost of
undermining the value of money exceeds the potential gains from financing
public deficits by printing money. However, leading experts on monetary
economics (like Michael Woodford) have argued that a target for inflation
will only be credible if there is some target for public spending as well.
Over time the one needs to see the government accounts from a consolidated
standpoint—and one can not expect that the central bank balances its book
if other parts of the government do not balance their books.
A central bank typically holds four types of assets. These are
• claims on foreign entities, i.e.
– foreign currency, and
– foreign-currency-denominated bonds.
• gold (although the stock of gold has been reduced in the later years) and
SDR’s (claims on the International Monetary Fund, so-called “paper
gold”), and
• home-currency-denominated bonds.
On the liability side the central bank has two types of assets,
1. currency and
51
Figure 2.3: The balance sheet of the central bank
Assets
Liabilities
Net foreign-currency bonds
Monetary base
Net domestic-currency bonds
Net worth
Foreign money
Gold
2. required reserves.
Required reserves are accounts domestic banks must hold in the the central
bank to be able to borrow money from the central bank. Currency plus
required reserves make up what is called the “monetary base”. The liability
side will also contain an accounting term, “net worth” to assure that the
accounts balance. The balance sheet is presented in figure 2.3.
2.4.2
Central bank interventions
If the central bank want to reduce the monetary base, it sells one of its assets
to the public. When it wants to increase the money supply, it buys assets
from the public. The central bank can adjust money supply in two ways:
1. it can intervene in the FX-market by buying or selling currency, or
2. it can change the short-term interest rates.
52
The first alternative implies a change in the holdings of the foreign currency
denominated assets held by the central bank. The second alternative implies
a change in some of the domestic currency denominated assets of the central
bank. However, in theory these types of interventions are equivalent.
To see this, remember that for every change made on the asset side of
the central bank’s balance sheet, an equivalent change needs to made on
the liability side. If the central bank intervenes in the FX-market by selling
foreign currency, it must at the same time reduce its liabilities. So the stock
of currency falls. This implies an increase in the interest rate
Likewise, a change in the interest rate will be an indirect change in the
money supply. When the central bank increases an interest rate it offers
government bonds in the market at the new rate. When the central bank
sells a bond, it gets domestic currency in return. The supply of domestic
currency in the market will fall, and the supply of bonds will increase. The
money supply will contract.
In fact the central bank will not set an exact target for neither exchange
rate nor money supply. In a fixed exchange rate regime the exchange rate
will be allowed to fluctuate inside a defined target zone. If demand for the
currency increases, the currency will appreciate. If demand shift so much
that the going rate will be at the boundary of the target zone, the central
bank will adjust money supply to keep the exchange rate within the target
zone.
In a inflation targeting regime the central bank will (indirectly) target the
money supply. The money supply shall be kept inside a certain band. the
central bank will no longer intervene in the markets because of fluctuations
in the exchange rate. Rather it will intervene because of fluctuations in the
money supply. The choice between an inflation target and an exchange rate
53
Figure 2.4: A fixed exchange rate target
e
D
ehigh
elow
S
m
54
Figure 2.5: A price level target
e
D
S
m
low
m
high
m
target will therefore imply a choice between price volatility and exchange
rate volatility.
Sterilised vs. unsterilised interventions
In the discussion above I assume that the central bank uses interventions to
change the domestic money supply. Such an intervention will affect prices
and interest rates. However, in many instances the central bank would like
to influence the exchange rate without affecting prices and interest rates.
A sterilised intervention means that while the central bank e.g. buy NOK
55
in the foreign exchange market it will simultaneously buy bonds (or in the
Norwegian case, something called F-loans). In other words, when the central
bank reduces its holdings of foreign currency assets, it will at the same time
increase its holdings of domestic currency assets. That way it leaves the total
supply of NOK unaffected. However, in our model only an actual change in
m can affect the exchange rate. In the monetary model presented above,
sterilised interventions make no sense.
Two reasons have been presented for why sterilised interventions might
work.
1. Portfolio balance effects: if investors believe that foreign and domestic assets are imperfect substitutes, a change in the relative supply of
foreign and domestic assets might have real effects.
2. Signaling: an intervention, even if it is sterilised, can signal to the
market that the central bank believe the exchange rate to be out of
bounds. Unless the market corrects this itself, the central bank might
go in with real interventions in the future.
Economist often argue that the effect of sterilised interventions are low.
However, central banks continue to use them. Making things even more
curious, most interventions are done in secret, which should in fact reduce
the signaling effect.
2.5
Appendix
Proof of equation (2.15).
T ∞ X
1 X
η
1
η
pt =
m0 +
m
1 + η s=t 1 + η
1+η
1+η
s=T
56
International Monetary System
2. Banking system
. LOUIS
EDERALSt.
RESERVE
BANK of STFed):
A discussion of sterilized intervention (from Fthe
Louis
Figure 2.6: From the Federal Reserve Bank of St. Louis:
STERILIZED INTERVENTION
Stylized Balance Sheet of the U.S. Monetary Authorities
Assets
Liabilities
Foreign exchange reserves
1$100 million (1)
U.S. government securities
2$100 million (2)
Because exchange rates are important prices that
influence the time path of inflation and output, central
banks often intervene in the foreign exchange market,
buying and selling currency to influence exchange
rates. Such intervention typically is sterilized, meaning
that the central bank reverses the effects of the foreign
exchange transactions on the monetary base.1 For
example, if the Federal Reserve Bank of New York—
following the instructions of the Treasury and the
Federal Open Market Committee—purchased $100
million worth of euros, the U.S. monetary base—composed of U.S. currency in circulation plus deposits
of depository institutions at the Federal Reserve
Banks—would increase by $100 million in the absence
of sterilization. This transaction is illustrated in the
stylized balance sheet items marked as (1). To prevent
changes in domestic interest rates and prices, the
Federal Reserve Bank of New York also would sell
$100 million worth of government securities—sterilizing the intervention by reducing deposits with
the Federal Reserve—to absorb the liquidity. This
transaction is marked as (2) in the balance sheet.
To prevent euro-denominated short-term interest
rates from rising, the European Central Bank would
have to conduct similar open market purchases of
euro-denominated securities to increase its money
stock to completely sterilize the original transaction.
The final net effect of such a sterilized intervention
would be to increase the relative supply of U.S.
government securities versus euro-denominated
securities on the market.
Because sterilized intervention does not affect
the U.S. monetary base or interest rates, it cannot
Currency plus deposits held
with the Federal Reserve
1$100 million (1)
2$100 million (2)
influence the exchange rate through price or interest
rate channels. It might, however, affect the exchange
rate through the portfolio balance channel and/or the
signaling channel. The reasoning behind the portfolio balance channel is that if foreign and domestic
bonds are imperfect substitutes, investors must be
compensated with a higher expected return to hold
the relatively more numerous bonds. In the example
in which the Federal Reserve purchases euros/sells
dollars (USD), the intervention must result in an immediate depreciation of the dollar that creates expectations of future appreciation, increasing the expected
future return to dollar-denominated assets and convincing investors to hold the greater quantity of them.
The signaling channel, on the other hand, suggests
that official intervention communicates to the market
information about future monetary policy or the
long-run equilibrium value of the exchange rate.
A purchase of euros/sale of dollars may signal to
the markets that the central bank considers the
dollar’s current value to be too high given current
and expected future policy. The consensus of the
research on sterilized intervention is that any
influence intervention has on the exchange rate is
weak and temporary.2
1
2
Unsterilized intervention is equivalent to domestic monetary policy
and therefore is often implicitly excluded from discussions of the
efficacy of intervention.
Humpage (1999) provides some evidence that U.S. intervention may
influence dollar exchange rates.
central banks keep interventions secret? Taylor
possibility that central banks are reluctant to release
(1982a and 1982b) suggests that the practice dates
such information because they are trying to avoid
back to the Bretton-Woods era of fixed exchange
accountability. Finally, it is possible that secret interrates, when reports of intervention could trigger a 15 ventions—or at least concealing the size of interrun on the currency. Given that the practice has
vention—may make the transaction more effective
persisted for more than 25 years after the end of 57 in influencing the exchange rate in certain circumfixed exchange rates, one also must consider the
stances (Bhattacharya and Weller, 1997).
S EPTEMBER /O CTOBER 2000
21

T −t 


X
∞ T 1
−
X
η
1 
η
1 
0
m

−
pt =
m +

η
1
+
η
1
+
η
1
+
η
1+η
1 − 1+η
s=t
s=t
η
1+η
"
pt =
1
(1 + η) − (1 + η)
1+η
pt = m0 −
pt =
η
1+η
T −t #
η
1+η
T −t
η
1+η
m0
−
"
m0 +
1
(1 + η)
1+η
T −t
m0 +
58
η
1+η
T −t
m0 − m
m
η
1+η
T −t #
m
Chapter 3
Exchange rate regimes
3.1
Relating the national currency to the international currency market
If a country wants to trade with an other country without adopting the other
country’s currency, there needs to be some mechanism that assures that a
currency can be used for international transactions. Most important, it must
be some system for converting the local currency into other currencies.
The government has three measures to assure international convertibility.
1. It can use coercion or control—all trade with abroad must be approved,
and conducted at a given rate. This was the system in Europe after
the Second World War, in the Soviet Union and Eastern Europe until
1989, and is still the case in some developing countries.
2. It can commit to a certain fixed exchange rate, and guarantee that it
will use all measures to defend that rate.
3. It can depend on the trust of the markets, and let the market set the
rate.
If trade is severely restricted, coercion is the only way to assure some
59
balance in currency flows. However, most developed economies allow a relatively high degree of free trade. This leaves the choice between commitment
and a free float.
Classical economic doctrine argues that markets will give the optimal
solution. However, for this to be true markets need to have a certain degree
of liquidity and a sufficient number of participants to work effectively. If these
requirements do not hold, markets can be manipulated. Whether this is a
real problem in the FX-market is uncertain. But remember that the financial
market of small and/or developing countries are often very small compared
to the financial markets of large and/or developed countries. There are a
number of American funds managers that control resources that exceeds the
total Norwegian GDP—and measured in GDP Norway is a large country.
Second, and perhaps more important for political decision makers, open
markets might imply serious limitations on the degrees of freedom in national
policies, as the exchange rate is vulnerable to swings in the moods of market
participants. This have lead governments to limit the mobility of capital.
If capital flows are limited, it is possible to achieve some degree of freedom
in monetary policy at the same time as the exchange rate is fixed This is
because the UIP will not hold if capital can not move freely. However, most
economist believe that it is impossible to have both an independent monetary
policy, a fixed exchange rate and free mobility of capital at the same time.
For the markets to work properly, the national economy must be developed and financial markets sufficiently sophisticated. In fact, the combination of a fiat currency and free convertibility was first introduced in the early
1970’s. Before that all forms of currency exchange across boarders had imposed either coercion or commitment to guarantee the value of the currency.
60
3.1.1
A short history of exchange rate regimes
“The gold standard” describes a system where national currencies were convertible to gold at fixed rates. This implied that the exchange rates were
fixed as well. The gold standard was in existence from about 1870 to 1914,
although it worked properly only in the first part of that period. This was a
period with very strong commitment. Even if a “crisis” of some kind made
a country unable to fulfill the requirements of the gold convertibility for a
certain period, it was usual for governments to make a strong effort to return
to the previous parity after the crisis had ended. At the same time it was
little or no coercion, as there existed no limitations on capital flows.1
During the First World War most countries abolished the convertibility
to gold, and instead imposed strong coercion, as trade flows was restricted.
After the war many countries attempted to return to their old parity values.
However, as prices had risen quite extensively during the war, a return to
parity implied that prices had to be deflated. This became a very costly affair
for a number of countries, Norway included. Britain, the leading country in
international relations up till the First World War, managed to restore the
old parity in the late 1920’s, only to be forced of gold in 1931. Commitment was soon again replaced by control and coercion. During the 1930’s
many countries restricted the flow of goods, and limited trade to bilateral
agreements.
In 1944 a number of economists met at the Bretton Woods Hotel in upstate New York. There it was worked out an agrement on how the exchange
1
As we will see later in this course, according to some measures capital flows was larger
per unit of output in the year 1900 than in the year 2000. It can also be noted that Great
Britain, which as the leading economy of the world at that time had a vested interest in
a stable foreign exchange market, intervened heavily in support of other currencies under
pressure. Great Britain worked as a stabiliser in the world markets, to some degree filling
the role the IMF has today.
61
Figure 3.1: Commitment versus coercion in the exchange rate system
coercion
Norway, 1945,
Early Bretton Woods
Most small open economies today
USA,
Japan,
Germany
after 1973
Norway, 1990,
USA 1945-1973
commitment
62
rate system should work after the war. To make a long history very short,
the gold standard (where every currency was convertible into gold) was exchanged with a “dollar-gold” standard: all currencies was to be convertible
into USD, and USD was to be convertible into gold at a given rate (USD 35
per ounce of gold).2 The International Monetary Fund (IMF) was founded
to oversee the international currency system.
After the Second World War there was a large demand for investments
in most European countries. At the same time many people had money they
wanted to spend on luxury imports from abroad (i.e. the US). European
governments were afraid that if they let people exchange home currency into
USD without restrictions, to much of private spending would be used on the
imports of luxury goods, and not enough on more important investment. It
was therefore enforced quite strong restrictions on capital movements and
the private exchange of currency.
As currencies was not freely convertible balance in international trade
could not be left to the markets. To balance trade between two countries can
be compared with a barter economy on the country level—each country must
accept what the other has to offer, or there will be no trade. To make the
system more flexible one therefore institutionalised a multilateral payment
system—e.g. if Norway had a trade deficit versus Denmark and trade surplus
versus Great Britain, while Denmark had a deficit versus Great Britain, this
could be netted out in the system. Payments and receipts were handled by
the Bank of International Settlements (BIS) in Basel. By the end of the
1950’s the financial system was stable enough to allow for free convertibility.
By the end of the 1960’s great strain was put on the system. Bretton
Woods collapsed in early September 1971. In 1973 the big currencies (USD,
2
This was a natural solution, as 70 per cent of all gold reserves in 1945 was held by the
Federal Reserve System.
63
JPY, DEM and GBP) was allowed to float. It was predicted that this would
result in reduced international trade and more financial uncertainty. That
does not seem to have happened. By 1973 the major economies had established trust in their economic policies. Increased volatility could probably
be handled as long as there was certainty about the long-term value of the
currencies.
However, in parallel with the experience of floating exchange rates between the large currencies, one saw an co-operation to stabilise exchange
rates at the regional level. European economies worked out an “exchange rate
snake”, a system that was supposed to reduce volatility between European
currencies. The “snake” evolved into the European Monetary System—a system of stabilising the currencies of the member countries towards a common
currency basket, defined as the ECU. On paper all countries in the EMS was
supposed to support each other if any one country faced pressure against
the fixed rate. However, in practice EMS was a fairly flexible system, that
allowed for frequent changes in the exchange rates between countries. And
while Germany was the country in the EMS with the lowest inflation, and also
the most credible monetary policy, Germany became “first among equals”.
In practice the EMS looked like a system for fixing European currencies to
the value of the DEM.
In the end of the 1980’s EMS changed character. EMS was now described
as the forerunner to the future European currency union that was expected
to be established sometime during the 1990’s. As a first step in this process the flexibility in the EMS was reduced. From 1987 until 1992 the EMS
worked as a pure fixed exchange rate system. However, in 1992 severe speculative attacks forced many countries to leave the EMS. Despite this seeming
setback the process towards the EMU continued, and a common European
64
currency with 11 (currently 12) members was established January 1, 1999.
The national bills and coins where exchanged with bills and coins denominated in EUR from January 1, 2002. The transformation was completed
within the end of February 2002.
3.1.2
Types of exchange rate regimes
A country can choose between a number of different regimes for the exchange
rate. Note that when we e.g. say that the USD is a floating currency, we mean
that the federal Reserve will not attempt to reduce short-term volatility in the
USD. However, the USD might still be fixed against a number of currencies,
simply because many countries choose to stabilise their currencies against
the USD. This will be unilateral pegs. Also note that an exchange rate
regime must be defined not for a currency, but for an exchange rate cross.
If Argentina has fixed its currency to the USD this does not imply that the
the ARP (Argentinean peso) has a fixed value in the market. It only means
that the currency cross ARP/USD will be fixed. The ARP will be floating
with regard to all currencies that are floating with regard to the USD. E.g
the ARP/EUR will be a floating rate, as the USD/EUR rate is floating.
One can describe seven different types of exchange rate regimes:
1. A floating rate. The central banks make no attempt to stabilise the
exchange rate in the short run. (Examples: USD/EUR, JPY/USD)
2. A managed float. There exist some statement that the central bank
will not allow to much fluctuation in the exchange rate. If the exchange
deviates much from a target value, the central bank might make limited
interventions, either in the form of interest changes or in the form of
direct currency interventions. (Example: NOK/ECU (1993-1998(?)))
65
3. Multilateral exchange rate pegs. Several countries agree to stabilise their currencies against each other. The currencies shall fluctuate within predetermined bounds. All countries retain an independent
monetary policy. However for the country to remain in the system,
monetary policy must be adjusted according to the monetary policy
of the system as a whole. Mostly a multilateral peg is dominated by
a single country. The countries are obligated to support each other if
there is a speculative attack against any one country. If one country
wants to make an adjustment in its exchange rate, the other countries
in the system must be informed in advance. (Example: the European
Monetary System (EMS)—European currencies were stabilised against
ECU)
4. Unilateral peg. One country fixes its currency to some other currency. There is no obligation from the other country with regard to
interventions. (Example: NOK/ECU from 1990 to 1992).
However, more often a country fixes the value of its currency to a
“currency basket”—an index value of several currencies. The basket
weights are often based on the composition of trading partners. (Example: NOK, SEK and FIM in the 1980’s)
5. Currency board. The currency is fixed completely to the value of
another currency. There is no allowance for a target zone as in a multilateral or unilateral peg. The central bank promises to exchange the
local currency into the foreign currency at the fixed rate, and must have
sufficient reserves to make this promise credible. There is no longer an
independent monetary policy. The only role of the central bank is to
adjust the level of reserves to assure that the fix remains credible at
66
every point of time. The central bank can no longer adjust the money
stock in periods of e.g. banking crises, and can therefore no longer
work as credible lender of last resort. A speculative attack against a
currency board can therefore often take the face of a speculative attack
against banks (as in e.g. Argentina).
6. Dollarisation. The local economy adopts a foreign currency as its
own. All local currency must be exchanged at a given rate, and destructed. All contracts must be re-denominated in the foreign currency.
There is no central bank in the sense of a monetary authority. All monetary policy is made in the country of the adopted currency, without
consideration for local needs. (Examples: Ecuador and Panama have
adopted the USD. The Jugoslav province of Montenegro has adopted
the EUR.)
7. Currency unions. Several countries come together and create a common currency. A new central bank is created. Monetary policy is to
be adjusted for the best of the currency union as a whole. (Example:
EMU)
Note that the distinctions between these groups are not strict. Even in a
floating currency like the USD monetary authorities will from time to time
make interventions to adjust what is perceived as “extreme misalignments”.
One example is the so called Louvre Accord in 1985 when the G-7 agreed
that the USD was overvalued. In the following months the USD depreciated
extensively. A currency board will often be followed by dollarisation of much
of the economy. There will almost always remain uncertainty about the
long-term prospects of the board. Many will therefore chose to use foreign
currency instead of the home currency as a store of value.
67
If any exchange rate peg shall be successful, one must keep the inflation
close to the inflation in country to which the currency is targeted. In shorter
periods, an exchange rate peg can survive even if monetary policy is not
fixed. In the long run a fixed exchange rate does demand a common monetary
policy. As most exchange rate pegs are in reality unilateral, that will normally
imply that the smaller country must adopt the monetary policy of the larger
country if a fixed currency shall be credible. Over longer periods of time this
only observed in very few cases. The Austrian peg to DEM is one of a few
such instances. Obstfeld and Rogoff (1995) find that only a few so-called
fixed exchange rates indeed had been fixed for more than 10 years.
Unilateral exchange rate system will generally be unstable, as a fixed
exchange rate by definition demands some sort of common monetary policy.
This is first solved if the unilateral system evolves into a currency union.
3.1.3
Optimal currency areas
Lack of credibility has made governments turn to fixed exchange rates to
assure convertibility. However, a fixed exchange rate might leave the open
for sudden adjustments, so-called currency crises (to which we return in the
next lecture). Although day-to-day volatility is less than in a flexible regime,
the volatility over time might be high if one has to leave the exchange rate
system at some time. This leaves us with the question of why a country
needs an independent currency at all.
In general one would at least keep a currency area as large as the area of
political independence—i.e. an optimal currency area will at least contain the
national borders of one country. That is not to say that the borders of this
“political area” necessarily comprise the borders of the “optimal currency
area”. From the OCA theory it might well be that e.g. the US should have
68
had more than one currency. In practice political realities always overrule
the OCA-theory. If multinational organisations get a strong hand in national
decision making, one can extend the optimal currency area to the extension
of the whole (or parts) of the organisation, as has been done in the EU
through the European Monetary Union, EMU.
The main benefits of entering a common currency have been listed to be
that a currency union
• reduce transaction costs from currency conversion,
• reduce accounting costs and give greater predictability of relative prices
for firms doing business with firms in the other countries of the currency
area,
• if prices are sticky, insulate from monetary disturbances that could
affect real exchange rates, and
• reduce political pressure for trade protection based on swings in the
exchange rate.
For a small open economy the first two points are probably the most important.
The potential costs of joining an optimal currency area include to
• forgo the possibility to use monetary policy to respond to regionalspecific real shocks. Remember that if the exchange rate is fixed, the
money supply is endogenous. It can no longer be adjusted by the
government.
• Further, one can no longer inflate away public debt or increase revenues
by extracting more seignorage.
69
In the end the choice of the size of currency unions remains a political
one. The more integrated an area is, the less will the costs of a common
currency be, and the higher will the potential gains be. However, areas
that are tightly integrated economically, are often tightly integrated in other
dimensions as well. How integrated an area needs to be for a currency union
to work is uncertain. However, with increasing ease of communication, many
of the traditional arguments for national currencies disappear. There is for
example difficult to see why the citizens of EMU should trust the ECB less
than they trusted their former central banks.
3.1.4
The death of fixed exchange rates?
To assure an efficient flow of trade it is necessary that there is some sort of
convertibility between the national currency and the international currency.
If the national currency is not accepted abroad the country reverts to defacto
barter trade. This is the case for e.g. North Korea. Almost all trade with
North Korea is in the form of bilateral trade agreements—North Korea gets a
certain amount of one good against the delivery of a certain amount of North
Korean goods. Until the early 1970’s it was accepted that to assure growth
in trade there had to some sort of fixed relationship between currencies to
avoid to much uncertainty.
The actual experience after 1970, with more liberalised capital flows, has
shown us that
• floating exchange rates, although volatile, does not seem to be destabilising for world trade nor financial flows as long as there is sufficient
trust in the governments issuing the currencies. For most developed
countries a floating exchange rate does not seem to reduce national
welfare.
70
• With free capital flows speculative attacks cause abrupt adjustments in
fixed exchange rates. These adjustments might be very destabilising.
Many economist argue that the danger of such adjustments make fixed
exchange rates very unfortunate.
A popular argument today is that one no longer can make a unilateral
decision to peg a currency. According to this argument, there is only two
options:
• to float, or
• to “super-fix” the exchange rate, either through a currency board, dollarisation or by joining a currency union.
This view is captured by the following quote made by then U.S. Secretary of
the Treasury, Larry Summers in 2000:
“[F]or economies with access to international capital markets,
[the choice of the appropriate exchange rate regime] increasingly
means a move away from the middle ground of pegged but adjustable rates toward the two corner regimes of either flexible
exchange rates, or a fixed exchange rate supported, if necessary,
by a commitment to give up altogether an independent monetary
policy. ... [This policy prescription] probably has less to do with
Robert Mundell’s traditional optimal currency areas considerations than with a country’s capacity to operate a discretionary
monetary policy in a way that will reduce rather than increase
the variance in economic output.”
From a historical perspective this view seems to be based more on a disillusionment with the intermediate alternatives—like pegged-but-adjustable
71
rates or managed floats, than the historical merits of either of the two corners.
In fact, there are only a small number of countries that have attempted to
“super fix” their exchange rate. Likewise, with the recent exception of Mexico, one has no good example of a developing market with a long experience
of a floating exchange rate.
The super-fixed exchange rate
A super fixed exchange rate includes a currency board and dollarisation. Supporters of super-fixed exchange rates have argued that these arrangements
provide
• credibility,
• transparency
• very low inflation, and
• financial stability.
In addition, as in principle a super-fixed rate should reduce the risk of speculation and devaluation, domestic interest rates should be lower than under
alternative regimes.
The argument in favour of a super-fixed exchange rate is made even
stronger if one can argue that there is a correlation between country risk
and currency risk. Country risk is the risk of investing in a given country.
This can be measured as the premium on long-term domestic government
bonds relative to foreign government bonds. Country risk should, among
other things depend on the long term prospects of a country.
Currency risk is the risk of devaluation. This can, assuming the UIP to
hold, be measured as the premium on short-term domestic interest rates over
72
foreign short-term interest rates. The argument is that a stable exchange rate
results in an environment that is more conductive to long term growth. So
low currency risk should lead to lower country risk. As can be seen from
figure 3.2, it does seem to be a relationship between these two measures in
the case of Argentina.
However, several things must be in place for a super-fixed rate to be
credible.
• Fiscal solvency. In a super-fixed rate regime the government can no
longer reduce the burden of public debt through inflation. This increases the need for fiscal responsibility. Also, as monetary policy can
not be used for stabilisation purposes, there must be in place an ability
to run counter-cyclical fiscal policy.
• The lender of last resort function, which under flexible and pegged-butadjustable regimes is provided by the central bank, has to be delegated
to some other institution. This can either be a consortium of foreign
banks or some international organisation.
• Related to the point above, there is a need for a very solid domestic
banking sector, as the lender of last resort function will not function
properly.
• A currency board requires that the central bank holds enough reserves,
an amount that in fact will exceed the monetary base.
For a super-fixed exchange rate to succeed, all the above points need to
be satisfied. However, even then super-fixed regime will not be without
problems. There will always remain the possibility of a regime switch. If the
cost of the regime increases, e.g. due to an external shock, this can create
73
61
Figure 4:
Currency vs Country Risk Premia:
Argentina, 1994-1999
Figure 3.2: Currency risk vs. country risk, Argentina 1994-1999
Country Risk Premium
15
10
5
0
-5
0
500
1000
1500
2000
Currency Risk Premium
Source: Edwards, 2000
74
2500
uncertainty about the future of the regime. If investors start to move money
out, domestic interest rates will increase, thereby further increasing the cost
of maintaining a fixed regime.
Argentina adopted a currency board early in 1991. At that point the
Argentinean peso had lost confidence. In the late 1980’s the USD had become
the de facto unit of account. For many types of purchases the USD worked
as means of payment as well.
The currency board fixed the exchange rate between ARP and USD at 1:1.
The currency risk from 1993 to 1999 is illustrated in figure 3.3. In the early
years of the board, Argentine inflation exceeded US inflation, leading to a
real appreciation of the the ARP. Argentina was hit hard by the ripple effects
of the Mexican devaluation (the “Tequila-crisis”) in late 1994. However, as
the board survived this event, the confidence grew. Inflation stabilised, and
Argentina faced deflation in 1999 and 2000.
Argentina addressed the lender of last resort issue in three ways:
• Banks were required to hold a very high level of reserves.
• The central bank negotiated a substantial credit line with a consortium
of international banks to be used in times of financial pressure.
• Many of the domestic banks were taken over by foreign banks. Seven
out of eight of Argentina’s largest banks were in 2000 owned by major
international banks.
An important problem in the case of Argentina was probably fiscal solvency. The Argentine government was not able to reform government in an
efficient manner. Attempts of privatisation did not result in increased productivity, mainly because public monopolies were often exchanged for private
monopolies.
75
62
Figure 3.3: Interest differential between peso and dollar denominated deposits
20
15
10
5
0
2/09/93
1/10/95
12/10/96
11/10/98
ARG_DIF
Source: Edwards, 2000
Figure 5: Argentina, Interest Rate Differential between
Peso and Dollar Denominated
Deposits
76
(Weekly Data 1993-1999)
Figure 3.4: Fiscal balance in Argentina, 1991-2001
Source: The Economist, 2002
77
At no time did expectations of devaluation disappear completely. The
result was a certain interest differential between the ARP and the USD.
One implication was that Argentineans choose to deposit money as ARP—
as ARP’s got the highest interest rate. However, if they borrowed money,
they borrowed USD, as the interest rate in USD was lower. This made the
banking sector very vulnerable to the effects of a change in the currency
board.
So what happened in Argentina? We will return to that question in the
next lecture. Argentina’s government did fulfill most requirements of a stable
currency board. However, it evidently failed on two important accounts: it
was not able to get full control of fiscal policy, and it was never able to remove
all doubts about the long term viability of the regime, not even among their
own people. In the end these two things terminated the regime.
The floating exchange rate?
If a super-fixed regime is so difficult to achieve, a floating exchange rate
remains the alternative. Table 3.5 shows that over the last twenty years more
and more countries have chosen managed or flexible exchange rate regime
instead of a regime with an exchange rate peg or limited flexibility. However,
recent empirical studies show that this apparent “floating” of exchange rates
might not be as clear cut as the IMF data suggests. In fact, ? find that most
developing countries that claim to have a float or a managed float do not
let their exchange rate fluctuate much outside a band of +/-2.5 per cent—
equivalent to pegged regime. This is even true for a number of industrialised
countries including, until recently, Norway. Floating regimes resemble noncredible pegs—an observation Calvo and Reinhart attributes to a “fear of
floating”.
78
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3.5: Choice
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Why should there be a fear of floating in emerging markets? This can
probably be attributed to a lack of credibility.
• A fixed exchange rate provides a more clear-cut nominal anchor, as the
exchange rate is observable today. An inflation target will depend on
expectations about future inflation rates—and if credibility is low this
might result in higher interest rate volatility.
• In emerging markets debts are often denominated in foreign currency.
Large swings in exchange rates might impair the access to financial
markets. Sharp depreciations can be very expensive as the cost of
servicing debt rise.
• The pass through from exchange rates to inflation is traditionally higher
in emerging markets than in developed markets.
There is an ongoing debate on the issue of fixed versus flexible exchange
rates. Mainstream academic economists in the US and Europe, and the IMF,
79
Figure 3.6: Exchange rate volatility in recent of current “floating” exchange
rate regimes
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80
Figure 3.7: Exchange rate volatility in recent of current “managed floating”
-
exchange
rate regimes
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81
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argue in support of flexible rate regimes. Many economists from developing
countries, and some western economists as well, are in support of more fixed
rates. As an example, several Asian countries have recently signed agreements to secure common interventions in the case of speculative attacks—
certainly not what one would do in a floating exchange rate regime. For many
countries some sort of fixed exchange rate regime is still the only option for
gaining credibility in their monetary policies.
3.2
Why a fixed exchange rate system might
be unstable
As we seen in the above discussion, there are benefits and costs of having
a fixed exchange rate. However, even if a fixed exchange rate seems like an
optimal solution, it is difficult to retain a stable exchange rate. As we have
noted, few exchange rates remain fixed for a long period of time.
The n-1 problem illustrates a problem that occurs if two countries fix
their common exchange rate. A fixed exchange rate implies that if one country changes its money supply, the other country must do so as well if the
fixed exchange rate shall survive. The second problem occurs when different shocks implies different policy strategies in the two countries. The third
problem occurs because the two governments might have different goals for
their monetary policy.
3.2.1
The n-1 problem
In the last lecture we found that if the exchange rate was fixed, money supply
would be determined by real output, the foreign interest rate and the foreign
price level:
mt = p∗t − ηi∗t+1 + φyt .
82
(3.1)
The central bank must adjust the money supply to assure that equation (3.1)
hold.
In a unilateral exchange rate regime the country that fixes its exchange
rate will take the interest rate and the price level in the other country as
given. However, in a bilateral fixed exchange rate regime this becomes more
tricky. The fixed exchange rate determines the ratio of the money stocks
in the two countries, but not the level of the money stock. Either the two
countries must agree on how the money stock shall be determined, or one
country must accept the money stock set by the other country.
To see this we can use the following example. From the UIP we know that
if exchange rates are fixed between two countries, the nominal interest rate
must be the same in both countries. From the real money demand functions
discussed in the Cagan model we know that there is a relationship between
the interest rate and the money stock. For every level of the money stock
there will be a certain interest rate. We illustrate this relationship in figure
3.8.
If we have a fixed exchange rate, and the UIP hold, then the following
relationship must hold: if the interest rate in the foreign country fall because
the foreign country increases the money stock, then the domestic interest
rate must fall as well. This can only be achieved by increasing the money
stock in the home country. So a change in the money stock of one country
must imply a similar change in the money stock in the second country.
This is the n-1 problem. One has two countries, but only one exchange
rate. The basis of a multilateral exchange rate agreement is that the two
countries agree on how interest rates and money stocks shall be set. However,
often a multilateral fixed exchange rate regime is containing countries that
are not willing to compromise their opinion of what is the optimal money
83
Figure 3.8: Interest rates and money stock
Country A
ia
ib
Country B
ma
mb
supply. If the two countries can not agree, the fixed exchange rate will break
down.
Most fixed exchange rate systems has a de facto “base country” that is
supposed to work as a “nominal anchor”—i.e. set the money stock. In the
Bretton Woods the US was the base country. In the European Monetary
System (EMS) Germany was the base country. In both cases this worked
fine as long as the interests of the base country were the same as the interest
of the countries who took part in the exchange rate system. However, in
both instances situations occurred when that were no longer the case.
The breakdown of Bretton Woods
In the end of the 1960’s the USA were running considerable trade deficits.
When a country run a trade deficit, we must expect the currency to be overvalued. As the exchange rate was fixed, an overvaluation can be alleviated
either through deflation in the home country or by inflation abroad. Accord-
84
ing to the rules of the Bretton Woods system such deficits should not cause
a problem to the exchange rate.
The process was supposed to proceed as follows: if a country was running
a trade deficit, there is increased demand for foreign currency in the home
country. To meet this demand for foreign currency, the local central bank
must sell foreign exchange reserves. When the foreign exchange reserves are
reduced, this should cause a proportionate change in the money base. When
the money base falls, the local price level shall fall. A falling price level will
reduce the overvaluation. Over time the trade deficit will disappear.
A trade deficit in one country should be reflected in a trade surplus in
another country. The country with a trade surplus will experience excess
demand for the domestic currency. This will imply that the central bank
increases its holdings of foreign reserves. An increase in the holdings of
foreign reserves should imply an increase in the money base, and a rise in
the domestic price level. The real exchange rate should appreciate.
The US experienced a an increase in home demand mainly due to the
welfare reforms conducted under the Johnson administration, and due to the
increasing costs of the Vietnam war. The US government financed its public
deficit by printing more money. This money was used to purchase goods
abroad. To reduce the money base would reduce the US ability to run a
public deficit. The US administration was not interested in paying such a
cost.
The countries running trade surpluses were countries like Germany, Japan
and Switzerland. The US money stock had increased. To alleviate the misalignments in the system, these countries had to allow their money stocks to
increase as well.
However, a country like Germany was not interested in importing US
85
inflation. When the demand for DEM increased, the Bundesbank chose to
sterilise the increase in its currency reserves. At the same time as currency
reserves rose, it sold domestic bonds. This way the German money base
remained stable. However, at the same time the automatic stabilisation in
the Bretton Woods system broke down.
The real problem here was perhaps not that Germany did not want to
import inflation. In fact, the Bretton Woods system was supposed to include
an additional check to assure that the US should use its all important position
to impose inflation on other countries. Remember that the USD was fixed
to gold at the rate of USD 35 per ounce of gold.
If the holdings of USD increased to much, central banks in other countries
was supposed to bring these dollars to the Federal Reserve and claim gold in
return. Doing so, they would reduce the asset holdings of the Federal Reserve.
The Federal Reserve was supposed to react to such claims by reducing the
money base.
However, the most important holders of excess USD reserves, Japan and
Germany, chose not to do this. The reason was that both countries depended
on the US for both political and military reasons. They did not want to
endanger these relationships by forcing the US to reduce its money supply.
The only country that to some degree did claim gold for USD was France.
Over time it became “evident” to speculators that countries like Germany,
Japan and Switzerland rather would revaluate their exchange rates at a new
level than stay at a fixed level with an increased money stock. At this time
speculators started to move from USD to DEM, CHF and JPY. As no country
was willing to compromise about the optimal money supply in the Bretton
Woods system, the system was posed to break down. In early September 1971
US president Richard Nixon declared that the US was no longer committed
86
Figure 3.9: Money supply shock in the US...
USD/DEM
DUSD
S1 USD
S0 USD
M DEM
US money supply increased as a result of more public spending, due to welfare
reforms and the Vietnam war.
to fixed parity between USD and gold. With this declaration the Bretton
Woods system was de facto dead.
3.2.2
The adjustment problem
The point is this: If a country has a fixed exchange rate, it can not use
monetary policy for stabilising the economy. However, assume that there is
a shock to only one of the countries in the exchange rate mechanism. Then
the government must make a choice. Either it can use fiscal policy to stabilise
the economy, or it can leave the fixed exchange rate and use monetary policy.
Why might it choose the last strategy?
87
Figure 3.10: And the consequences for Germany
DEM/USD
Do DEM
D1 DEM
SDEM
M DEM
A money supply shock in the US increases demand for DEM. To hold the exchange rate within the target zone Germany has two alternatives: exchange
USD-reserves for gold, and thereby contract the US money supply (however
this was not politically feasible), or increase their own money supply (which
they did not want to do, as this would imply importing US inflation to Germany).
88
There will be a cost of leaving a fixed exchange rate. E.g. the government
might loose credibility if it wants to go back to a fixed exchange rate at a later
stage. However, there might also be a cost of not using monetary policy for
stabilisation. This will especially the case if prices and wages are sticky—i.e.
that they adjust only slowly.
Example: Assume that the cost of producing in the home country increases. This might e.g. be due to a restriction of working hours that have
a negative effect on labour productivity. Implicitly this is a wage shock that
will affect the domestic price level. If the domestic price level increases, Q
will fall. The country experiences a real appreciation.
A real appreciation implies that domestic goods are less competitive on
international markets. This will have a real economic cost. However, to
alleviate the real appreciation the government has two choices:
1. it can force the price level down, or
2. it can devalue the nominal exchange rate.
The last option will however imply a break with the fixed exchange rate
policy. Why would a government choose this option over the option of deflating the economy? In fact it is very difficult to impose a downward change
in wages. It is also a process that might take a very long time, as most wages
are set by long term contracts. By devaluing the exchange rate home goods
will become cheaper abroad over night, without lowering wages at home. One
should however note that the purchasing power of home wages of course will
fall—as imports become more expensive.
Note that if the shock is symmetric, i.e. both countries in the system get
the same shock, monetary policy can be used for adjustment. Both countries
now have incentive to move the money supply in the same direction. This
89
can be done without affecting the fixed exchange rate. Remember that the
fixed exchange rate can be sustained for an infinite number of different money
supplies, but only for one ratio of home money over foreign money. However,
in this case the real exchange rate will of course not be affected.
3.2.3
The problem of a credible policy—the Barro Gordon model
From your former lessons in macro, you know the concept of a Phillips curve.
The Phillips curve implies a relationship between unemployment and inflation. In “modern macroeconomics” one thinks about the Phillips curve as
a fluctuations around a “non-accelerating-inflation-rate-of-unemployment”
(the NAIRU). The NAIRU is seen as the long-run rate of unemployment.
In the short term unemployment can be higher or lower than the NAIRU,
depending on whether inflation is higher or lower than expected inflation. If
we call unemployment for u, the NAIRU for un and inflation for π, and we
let π e be expected inflation, we can express the Phillips curve as
u = un + a(π e − π).
(3.2)
If inflation exceeds expected inflation, the unemployment rate can for a short
period be less than the NAIRU. However, one can not expect inflation to
exceed expected inflation over time.
We assume that the government has two policy goals: to keep inflation
stable, and to keep unemployment low. In fact, the government has as a
goal to keep unemployment at a level u∗ < un . This can be rationalised if
ne think there are some sort of inefficiencies in the labour market that lead
to an increase in the NAIRU rate. As a second best policy the government
90
target an unemployment rate below the NAIRU. We specifically assume that
u∗ = σun ,
(3.3)
where 0 < σ < 1.
The government minimises a loss function, L, that contain these two
elements:
L = π 2 + b[u − u∗ ]2 ,
(3.4)
where b (assumed to be > 0) is the weight on holding unemployment at u∗ .
If we substitute in for the equations (11.85) and (11.86), we obtain
L = π 2 + b[(1 − σ)un + a(π e − π)]2 .
(3.5)
The government want to set inflation such that it minimises the value of
L. To do so we must take the derivative of L with regard to π, and set equal
to zero. This gives us
δL
= 2π − 2ab[(1 − σ)un + a(π e − π)] = 0
δπ
(3.6)
If we solve with regard to π we get
π opt =
ab(1 − σ)un
ba2 π e
+
.
1 + ba2
1 + ba2
(3.7)
Assume that the government set π = 0, and that this is fully credible (the
public believes the government, so that π e = 0 as well). The the loss would
be
L = b[(1 − σ)un ]2 .
(3.8)
However, if π e = 0 we know that the optimal inflation rate from the point of
91
view of the government would be
ab(1 − σ)un
,
1 + ba2
(3.9)
1
b[(1 − σ)un ]2 .
1 + ba2
(3.10)
π=
which would give a loss of
L=
One can show that
b[(1 − σ)un ]2 >
1
b[(1 − σ)un ]2
1 + ba2
(3.11)
for all values of b > 0. So, in a one period game—if the government only
cares about today, and not about the future, it will always be rational for
the government to try to fool the public by setting inflation higher than they
expect.3
However, if the public have rational expectations they will look through
this strategy. In fact the public will understand which inflation rate will
minimise the loss of the government, and expect this inflation rate. Indeed,
equilibrium if we assume rational expectations must be that π opt = π e . We
therefore know that
πe =
ab(1 − σ)un
ba2 π e
+
,
1 + ba2
1 + ba2
(3.12)
which implies that the equilibrium rate of inflation will be
π = π e = ab(1 − σ)un .
3
(3.13)
Why should the government play one period games? Very simplified: because an
elected government is supposed to only think about the next election.
92
This will give the government a loss of
L = [ab(1 − σ)un ]2 + b[(1 − σ)un ]2 > b[(1 − σ)un ]2 .
(3.14)
The government will in other words be worse of than if it could follow a
credible policy of no inflation. However, it can not, because if a zero inflation
policy is indeed credible, the government has incentive to cheat be setting
inflation above zero for one period. The government is not able to tie itself
to the mast.
How should this affect a fixed exchange rate regime? Assume that country
A (e.g. Norway) has fixed its exchange rate to country B (e.g. Germany),
and that Germany follows a “zero inflation” policy. That is, Germany has
a bG = 0. If we assume the PPP to hold, the results from the Cagan model
implies that Norway must follow a zero inflation policy too. However, if the
Norwegian government has a bN > 0, such a policy will not be credible for
Norway.
3.2.4
Appendix: The real exchange rate
One reason why exchange rates are important for international trade is that
they are closely related to the real relative price of foreign goods. For example, let P ∗ be the price, in foreign currency, of a bushel of foreign wheat,
and let P be the dollar price of a bushel of domestic wheat. We assume that
the quality of foreign and domestic wheat is the same. Which good is more
expensive? The relative price of foreign to domestic wheat is the ratio
Q=
P∗
.
P
(3.15)
This makes sense. P ∗ is the price of foreign wheat, and is the domestic price
of foreign currency, so P ∗ must be the price of foreign wheat in domestic
93
currency. We then find the relative price by taking the ratio.
Q is often referred to as the real exchange rate. This is another way
of saying ‘relative price of imports’. Also, in practice we often use prices of
larger baskets of goods, such as the country specific CPI’s, to form the relative
price. Loosely speaking, the real exchange rate indicates how competitively
priced foreign goods are in terms of domestic goods: higher real exchange
rates tend to make a country’s exports more attractive on world markets.
If you think domestic and foreign goods are very similar, and that there
are relatively few barriers to trade it is reasonable to expect little variation
in the real exchange rate. The extreme case is to assume Q = 1. To see why
this is reasonable, assume that Q < 1, This implies that imported goods are
less costly than domestic goods. Consumers will therefore tend to purchase
foreign goods, creating a downward pressure on either (or both) the price
of domestic goods or the value of the domestic currency, until Q = 1. In
other words, prices of common goods should, expressed in units of a common
currency, be the same. When we talk about one good, price equalisation is
called the law of one price. When we talk about basket of goods, we call this
assumption purchasing power parity, PPP. Remember that when we defined
PPP in lecture 2 as
=
P
,
P∗
(3.16)
we implicitly assumed that Q = 1.
Although in theory a fixed exchange rate can only be viable if the PPP
holds, in practice on will find that the PPP does not hold exactly all the time.
More specifically, if shocks differ between countries, Q might at any point of
time be bigger or smaller than one. If Q exceeds one, domestic goods improve
their competitiveness abroad, and we should expect that there evolves a trade
surplus. If Q < 1, domestic goods have lost competitiveness abroad, and the
94
country should turn to trade deficit.
95
Chapter 4
Currency crises
4.1
Introduction
Some definitions:
• A “devaluation” is the move taken by the government to change the
target value of the fixed exchange rate regime to a weaker (higher)
exchange rate. A “revaluation” is the move taken by the government to
change the target value of the fixed exchange rate regime to a stronger
(lower) exchange rate.
• A speculative attack is a situation where a large number of market
participants go “one way” in the market—all participants either sell
or buy the asset. In a speculative attack on a fixed exchange rate the
central bank is obliged to stand as counter party to all transactions
within the target zone, unless someone else takes the deal. The central
bank will either do so by intervening in the markets directly, or by
changing interest rates. Changing interest rate might induce private
investors return to the currency to profit on the interest differential.
At the same time higher interest rates increase the cost of speculation.
When (if) the central banks pulls out the price of the asset will fall (or
96
rise). Often a period of turbulence occurs before a new equilibrium is
established.
• A “currency crisis” is a situation where a speculative attack forces the
central bank to make a change in the fixed exchange rate not actually
intended by the central bank.
What is the difference between a “controlled” change in the exchange
rate and a currency crisis? If the markets believe that the central bank will
change the target rate, rational investors would only trade on one side of
the markets—i.e. behave like in a speculative attack. The central bank has
incentive to present this as if it was forced to abandon the fixed exchange
rate, although its own behavior actually caused the markets to behave as
they did.
Note that a currency crisis might occur even if the exchange rate is not
fixed. If the markets bring forth a large change in a floating exchange rate
over a short period of time, the central bank will be expected to intervene, as
large changes in an exchange rate might destabilise financial markets. The
inability of the central bank to keep the exchange rate at the wanted target
can be considered a “currency crisis”, even if it does not induce a formal
devaluation.
There are three sides to all currency crisis: the government, investors with
liquid assets and investors with illiquid assets. For the government a currency
crisis is a question of credibility, of flexility in political decision making and
about a possible fallout because of negative implications of a sudden change
in the exchange rate. For a liquid, well informed investor a currency crisis is
a question of potential financial gains.
The illiquid investors are the most vulnerable to currency volatility. They
might not have the financial strength to diversify investments, or they might
97
be contained to long term contracts. Further, these investors also tend to be
smaller and perhaps less informed than the liquid investors. The presence
of illiquid investors is especially a problem in countries with underdeveloped
financial markets.
In this lecture we will discuss the interaction between government incentives and the behavior of the markets, by which we mean the liquid investors.
We will return to issue of the illiquid investors in the last part of the course.
4.2
Speculative attacks
In the last lecture we discussed three reasons for why a fixed exchange rate
might break down. They were all based on the fact that in a fixed exchange
rate system monetary policy is outside the full control of the central bank.
Changes in the money supply must be symmetric between the countries involved in the system. If optimal policy makes for asymmetric monetary
policy, a fixed exchange rate is not sustainable.
1. The n-1 problem: the countries involved can not agree on a proper rate
of growth in the money supply.
2. The adjustment problem: if we have asymmetric shocks and sticky
prices, it might be optimal with leave the fixed rate regime.
3. The credibility problem: a fix is not sustainable if the governments
involved have different loss functions, i.e. they care about different
things.
If these were all the reasons why fixed exchange rate systems broke down,
one should expect that governments chose to leave such systems by purpose.
However, countries often first leave a fixed exchange rate system after a
98
“speculative attack”, an event where the whole market has sold the currency
to the central bank because everyone believes that the central bank soon will
break its promise of a fixed rate.
An example of this is the EMS-crisis in 1992-93. After 1990 the countries
in the European Monetary System had attempted to limit fluctuations in
their exchange rates more actively—they had agreed on a less lenient use
of the escape clause. Some countries outside the EMS, as Norway, Sweden
and Finland also attempted to fix their currencies closer to the ECU. In the
August of 1992 the currencies came under great stress. First, investors sold
ITL and FIM. Both countries choose to devalue (or more exact—they let the
value of the currency float). In early September Great Britain left the EMS.
This attack is famous for the role of George Soros. His Quantum Funds is said
to have increased its value with 25 per cent due to exchange rate movements
in the fall of 1992. The speculators then turned to Scandinavia. Sweden came
under pressure. However, the Swedish government, eager to build credibility
in a new monetary policy, attempted to defend the exchange rate by rising
over night interest rates to 500 per cent. This policy was not sustainable,
and when the rates came down the attack continued. In November Sweden
devalued. Norway devalued in December after heavy interventions.
In a fixed exchange rate regime the central bank has promised to buy and
sell the currency at specified levels. The distance between the sell and buy
price will be the “target zone”, the room for fluctuations in the exchange
rate. The target zone is usually about +/- 2.5 per cent around the stated
“fixed rate”. However, a central bank can only buy the local currency in
exchange for foreign currency as long as it has foreign reserves available. In
theory it can borrow reserves for interventions. However, one rarely sees this
in practice. If the level of reserves become too low, the cost of standing by
99
Figure 4.1: Swedens exit from the EMS—1992
100
80
60
40
20
0
6/01/92
10/19/92
3/08/93
7/26/93
12/13/93
7/26/93
12/13/93
SEINT1W
5.2
4.8
4.4
4.0
3.6
3.2
6/01/92
10/19/92
3/08/93
DEMSEK
100
the promise of a fixed exchange rate might become to expensive—and the
currency is devalued.
There has been much effort to understand the nature of speculative attacks. Some of what we know about speculative attacks can be summarised
in these points:
• From the “first-generation model” (the Krugman model), we have that
– A currency crisis will occur if the “shadow exchange rate”—the
exchange rate that would have been if the rate was floating—is
sufficiently different from the fixed rate ⇒ there must be some
relationship between the fixed rate and a “fundamentally sound”
rate.
– If there are any kind of “trend” that will affect the shadow exchange rate the timing of an attack can be calculated. The time
will be independent of “news”—it will only be a function of the
rate of growth in the trend and how this affects the shadow exchange rate.
• If there is no trend affecting the shadow rate, the shadow rate might
still fluctuate due to shocks.
– If fundamentals are very strong (the shock is weak) the government will probably defend the currency no matter what.
– If fundamentals are very weak (the shock is strong) the government will probably choose to devalue anyway.
– Between these levels there will be a “window of uncertainty”. For
a speculative attack to occur in this window, a sufficient number
of speculators must believe in a crisis at the same time. If only
101
a few investors speculate against the currency, they might lose
money. For a speculative attack to succeed many investors must
act simultaneously.
This is the so-called “second generation model, or the “Obstfeld model”.
In this case speculation can cause a devaluation even if the government
did not intend to devalue if there had been no speculation.
In the last couple of years (after the Asian crisis) new questions have been
raised.
• Originally a trend that affected the shadow rate, as described in the
Krugman model, was understood as growth in the money supply or
depletion of foreign reserves. However, new models have emphasized
the role of implicit obligations of the government: if the government
has growing obligations to e.g. the banking sector, this might have the
same implications for the shadow exchange rate as a fall in the actual
level of foreign reserves.
• There has been much discussion on the question of contagion: why do
currency crises tend to occur in “batches”—why do several countries
experience currency crises at the same time?
• One has investigated whether e.g. hedge funds play a special role under speculative attacks. One can show that this might be the case if
different investors have different information. If hedge fund have more
information than others, and this is known to everyone, the presence
of hedge funds might increase the volatility of capital flows.
• Last, much has been done on the role of regulating the exchange rate
market. This is an issue we return to at the end of the course.
102
4.3
The Krugman model
We consider a small open economy where both the PPP and the UIP holds,
and all investors have perfect foresight. Further, we assume for simplification
that y = 0, i∗ = 0 and p∗ = 0. If we use a continuous time setting, and we
·
let e be the rate of change in e, we can write the Cagan equation from the
lecture 2 on the form
·
mt − et = −η e.
(4.1)
It follows from equation (11.96) that if the exchange rate is fixed at e, the
money stock is fixed at
m = e.
(4.2)
We now assume that the money stock is composed by two parts, domestic
credit, D, and foreign reserves, R, such that
Mt = Dt + Rt ,
(4.3)
when R is denominated in foreign currency terms. Let us further assume
that the government follows a policy that expand domestic credit at a fixed
rate µ, such that
·
·
D
= d = µ.
D
(4.4)
This can be thought of as a fiscal deficit monetisation by the central bank,
i.e. that the central bank issues money to pay for government expenditure.
However, if the central bank at the same time follows a fixed exchange rate
policy, if can not let the expansion of domestic credit affect the exchange
rate. So by definition we must have that
·
·
D = −R,
103
(4.5)
⇒ expansion of domestic credit must be followed by a fall in the level of
reserves.
Such a policy can not last. Domestic credit can increase forever. Foreign
reserves have only a limited supply. At some point of time the foreign reserves
must be zero. At this time the central bank will no longer be able to stand by
its obligations in the fixed exchange rate regime—with no foreign reserves the
central bank can not fulfill the promise to exchange the domestic currency
into foreign currency at a given rate. So a policy of domestic credit expansion
must necessarily lead to the fall of the fixed exchange rate system.
When will such a collapse happen? Will it be when the inconsistent
policy is introduced? Or will the the exchange rate first collapse when the
the reserves are zero? In fact we observe that “currency crises” often seem
to occur independent of new information. How can we explain that in this
framework?
Let us define a “shadow exchange rate”, ee, as the exchange rate that would
have been if the speculative attack had already occurred. After a speculative
attack, foreign reserves must be zero. In this case the money stock will only
contain domestic credit, so we must have that mt = dt . However, we assume
that domestic credit continues to grow at the rate µ. If the money supply
grows at a fixed rate, the exchange rate must depreciate at the rate ηµ, as
we found Lecture 1. This implies that the shadow rate of the exchange rate
will be
eet = mt + ηµ = dt + ηµ = d0 + µt + ηµ.
(4.6)
The Krugman model argues that by arbitrage the fixed exchange rate
must collapse at the moment when the shadow rate equals the fixed rate,
ee = e. Why? Assume that the fixed exchange rate equals the shadow rate
at time T . Let the fixed exchange rate collapses at a T + 2. In this case
104
the shadow rate will exceed the fixed rate. The fixed rate is terminated at
this point, the exchange rate must make a jump from e to ee. A discrete
jump in the exchange rate will imply infinite profit opportunities for rational
speculators. As everyone have perfect foresight, everyone will try to sell the
domestic currency at time T + 1. Hence, the speculative attack will take
place at T + 1. However, at T + 1 the jump will still be discrete. So everyone
will sell at T .
Why not sell at T − 1? Simply because one would lose money by doing
so. If everyone sell at T − 1 the exchange rate actually will appreciate, as
the shadow rate at this time is lower than the fixed rate.
If we know when a speculative attack will occur, we can calculate the
exact timing of an attack. We know that the attack will occur when
e = d0 + µT + ηµ.
(4.7)
e = mo = ln(D0 + R0 )
(4.8)
ln(D0 + R0 ) = d0 + µT + ηµ.
(4.9)
Further, we know that
so that
T will then be given by
T =
ln(D0 + R0 ) − d0 − ηµ
.
µ
(4.10)
We see that the larger the initial holdings of reserves, the higher must T be.
Further, T will decrease in the rate of growth in domestic credit.
T must occur at a time when R > 0. The speculative attack will occur
when the central bank still has some foreign reserves left. The result will
105
be a fall in the money supply at time T as the central bank must sell its
foreign reserves during the attack. The reason why the money stock must
fall is because the investors expect the growth in domestic credit to continue
after the attack. Before the attack we had e = m. After the attack we have
e = m + µη. The money stock must fall so that
m = mT + µη ⇒ m − mT = µη.
(4.11)
There are a number of weaknesses in the Krugman model. These include
that we assume perfect foresight, that we assume the UIP to hold at every
point of time and that we assume that the government follow a totaly inconsistent policy over time. One relevant question is why, when everybody has
perfect foresight, should the government care to follow an inconsistent policy
of this kind? However, the model tells us that if we want to understand why
a seemingly “irrational” event occurs—remember, here a speculative attack
occurs even if the central bank still controls foreign reserves—it is important to understand long term underlying trends, and how these affect the
expectations of market participants.
4.4
Crises with no trend?
In the August 1993 the French franc, the Belgian franc and the Danish krone
all experienced severe speculative attacks. As a result of this the countries
agreed to widen their target zones within the EMS system from +/-2.5 per
cent to +/-15 per cent. However, within two years of the attack all three currencies were not far from the edge of the original band. Figure 4.3 illustrate
the movements of the BEF over the period from 1990 to 1999.
Over this time period little changed in the Belgian economic policy. Belgium had with success followed a low inflation policy in the late 1980’s.
106
Figure 4.2: Anatomy of a speculative attack
log exchange rate
T
Shadow floating rate
Fixed rate
log money supply
time
time
log foreign reserves
Level of foreign reserves at
time of attack
time
107
BGF TO DEM
Figure 4.3: The BEF against
DEM—1990 to 1999
22.5
22
21.5
21
20.5
20
24.10.99
24.07.99
24.04.99
24.01.99
24.10.98
24.07.98
24.04.98
24.01.98
24.10.97
24.07.97
24.04.97
24.01.97
24.10.96
24.07.96
24.04.96
24.01.96
24.10.95
24.07.95
24.04.95
24.01.95
24.10.94
24.07.94
24.04.94
24.01.94
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24.07.93
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24.01.93
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24.01.92
24.10.91
24.07.91
24.04.91
24.01.91
24.10.90
24.07.90
24.04.90
19.5
Inflation remained low. The Belgian state debt was high—it was (and is)
well above 100 of GDP—however it remained stable over the whole period.1
There was strong support in Belgium for the long term goal of joining a
common European currency. There was no obvious “trend” in Belgian policy that could be considered as incompatible with the commitment to a fixed
exchange rate.
The Krugman model is clearly not able to explain events such as those
we observed in Denmark, France and Belgium in 1993. In fact, a number of
more recent currency crises have aspects that are similar to what we observe
in these three countries. The Norwegian devaluation in 1992 happened in a
country that at the time of attack had lower inflation than Germany and a
very sound fiscal position.
A new line of currency crises models therefore emerged to suggest that
1
One should note that the Belgian debt is mainly debt issued in domestic currency to
domestic residents. This makes the high debt levels less of a problem with regard to the
exchange rate.
108
even sustainable currency pegs could be attacked and even broken. These
models focus on the choice of governments: they assume that the government
will make a continuous comparison of the net benefits from changing the
exchange rate versus the net benefits of defending it. When costs become to
high the fixed rate is abandoned. An important aspect is that speculation
itself will affect to the cost of holding an exchange rate fixed.
4.4.1
The strategy of speculators
The following game theoretic approach2 illustrates the case of how speculative attacks might occur even in situations when the exchange rate peg is
sustainable. The basis of the argument is that there is a correlation between
the “discomfort” a government will feel about a devaluation and the level of
reserves the government chooses to hold.
Assume that if fundamentals are very strong, the government is not under
any circumstances willing to give up the fixed rate. In this case the level of
reserves the government is willing to commit to defending the exchange rate
is high. If fundamentals are very weak—think e.g. about a period when
the real exchange rate is overvalued—the government might be willing to,
or even interested in devaluing the exchange rate. So the level of reserves
committed to defending the rate will be low.
The problematic case is the “grey zone”. Where do “good” fundamentals
end and “bad” fundamentals start? Assume that the currency is slightly
overvalued in real terms. However, there are reasons to believe that one can
adjust this through lower inflation and tight fiscal policy. So the exchange
rate peg is sustainable. However, given the economic difficulties, the government is not willing to put its full force behind the exchange rate peg.
2
From Obstfeld, 1995.
109
In the model we assume that at such “intermediate” levels of fundamentals
the government is only willing to commit an intermediate level of reserves to
defend the exchange rate.
More specific, we assume three possible states of the economy. In the
good state the governments commits reserves equal to 20 “domestic money
units”, e.g. 20 billion NOK. For simplicity we assume that this equals the
total monetary base. In fact, such a commitment will make it impossible for
speculators to topple the exchange rate.
In the intermediate stage the government commits reserves equal to 10.
In this situation it is possible for speculators to topple the regime, but only if
the whole markets reacts at the same time. In the bad state the government
commits reserves equal to 6. In this case one large trader can topple the
regime alone.
We assume the existence of two traders. Each trader control resources
of 6 domestic money units. The traders incur a cost of −1 by attacking
the exchange rate. Figure 4.4 presents the result of alternative strategies
in the “good state”. In this case the traders will not be able to topple the
regime under any circumstances. They will gain 0 by doing nothing, and
lose −1 by speculating against the currency. The case of “hold, hold” can be
characterised as a “Nash equilibrium”.3
Assume that we are in the low state, and that one trader attack the
exchange rate. Then the central bank will offer this trader its whole portfolio
of reserves, equal to 6. Assume the currency depreciates with 50 per cent.
The trader makes a profit of 2—the income from the speculation is 34 and
3
A Nash equilibrium is a state where nobody, when the behaviour of everyone else is
taken as given, can improve on their outcome by changing their own strategy.
4
Assume that the peg was on the level 1:1. The trader exchanges 6 domestic currency
units in 6 foreign currency units at the rate 1:1. After the devaluation she can exchange
back at the rate 1.5:1—for her 6 units of foreign currency she will get 9 units of domestic
110
Figure 4.4: Attack when fundamentals are strong. Committed reserves=20.
Trader 1
Hold
Sell
Hold
0,0
0,-1
Sell
-1,0
-1,-1
Trader 2
111
Figure 4.5: Attack when fundamentals are weak. Committed reserves=6.
Trader 1
Hold
Sell
Hold
0,0
0,2
Sell
2,0
1/2,1/2
Trader 2
the cost of speculation is −1. However, if both traders sell at the same time,
the traders will share the central bank reserves between each other. Both
will make an income of 3/2, and a profit of 1/2. This case is illustrated in
figure 4.5. In this case the “sell, sell” strategy will be a Nash equilibrium.
The most interesting case is made up by the intermediate fundamentals.
In this case no trader can topple the regime alone. So if a trader acts alone,
she will gain nothing, and lose the cost of speculation. However, if both
traders attack at the same time, both will gain 5/2 − 1 = 3/2, as they will
share the committed reserves of the central bank between them. This case
is illustrated in figure 4.5. Her we have two Nash equilibria—it will be an
equilibrium to “hold, hold”, but it will also be an equilibrium to “sell, sell”.
currency. She will make a profit of 9 − 6 = 3 units of domestic currency.
112
Figure 4.6: Attack when fundamentals are “intermediate”. Committed reserves=10.
Trader 1
Hold
Sell
Hold
0,0
0,-1
Sell
-1,0
3/2,3/2
Trader 2
In this situation we have possible instability—the peg might survive or it
might not, depending on whether the traders are able to co-ordinate their
attack or not.
4.4.2
The role of large speculators
Of course, the investor will never know exactly what commitment the central
bank is ready to offer. So the investor must first observe some signal that
gives her an opinion about the economy. Then she makes up her mind about
a speculation strategy. If she finds that she have positive expected returns,
she will attack. If expected returns are negative, she will not attack.
One question that has been asked is what role large speculators play in
113
determining the fait of fixed exchange rate regimes. Above, I referred to the
story of George Soros and the devaluation of the GBP in 1992. Soros is said
to have made billions of USD during this attack.
What is a large speculator? There exist funds that control enormous
amounts of money. Several American pension funds have resources in excess
of the Norwegian GDP. However, when we talk about a “large player” in
the FX-market, it is not necessarily market capitalisation that is interesting.
Rather it is the ability to take high risk positions. Most banks and pensions
funds have strong restrictions on the level of risk they can take.
However, there exists a type of institutions that have no juridical restrictions on their risk positions. These are the so-called hedge funds. Hedge
funds are financial institutions that specialise on making money on potential mis-pricing in financial markets. The hedge fund will form an opinion
of what it perceives to be the “shadow exchange rate”. If the fixed rate
and the “shadow rate” diverges, there are potential profits to be gained by
speculating in this market.
The main difference between a hedge fund and a e.g. mutual fund is that
while public regulators will take some responsibility for checking up on the
practices of a mutual fund, the investors in a hedge fund is perceived to be
able to take care of themselves. There is no restrictions on how a hedge fund
can invest.
The fast way to make money in financial markets is by gearing risk. That
is to gamble with loaned money. Assume that you expect the stock of firm
A to increase with 50 per cent over a year. You have NOK 100. If you invest
all you have in the firm, you expect to make NOK 50. However, assume
that you gear your investment 10 times. That is, you offer a bank 100 as a
security, and borrow 1000 for investment in the stock. The cost of the loan
114
is 10 per cent, i.e. 100 for a year. If your expectations go in you gain 500 on
your investment, and earn 400 after loan cost are paid. So you increase your
profits by 800 per cent. However, the risk is of course considerable. Say that
the firm actually goes bust. Then you lose 500 plus the cost of the loan, a
total of 600. That is 500 more than you have...
An institution that basis its investment strategy on gearing is called a
highly leveraged insinuation. Most hedge funds fall in this category. This
implies that even a relatively small fund can take very large positions during
e.g. a speculative attack.
How can an American hedge fund with no NOK assets attack a currency
peg involving the NOK? It can do so by going short—i.e. sell currency in
the forward market. When the hedge funds sells a forward contract on the
delivery of NOK, the opposing party will be a bank. The contract implies that
the bank must take a delivery of NOK sometime into the future. However,
the bank does not want to expose itself to currency risk. So it will cover the
contract by selling NOK today. If there is no market for this NOK today,
the central bank must intervene, and foreign reserves will be depleted. The
hedge fund can force a spot sale of NOK today by intervening in the forward
market. However, one should note that this strategy is not risk free. The
cost of the forward contract is the same as the interest differential between
the two currencies of the contract. To short sell NOK is equivalent to taking
a loan in NOK. If Norges Bank increases its interest rates to stop the attack,
the cost of such a contract can be high.
Hedge funds have been accused of trying to destabilise financial markets.
The accusors are both politicians and economists, and they include, in a random order of importance, the former French president Francois Mitterand,
the Malaysian prime minister Dr. Mathahir and the head of Norges Bank
115
Svein Gjedrem. The central banks of Hong Kong and Australia have both
issued reports where they accuse hedge funds of manipulating the local exchange rates. In the case of Norway, it has been reported that the fund
Tiger Management has been actively involved in speculation against NOK.
The same is the case of Chase Manhattan, although Chase is not a hedge
fund.
The idea is that a “large player” could generate profits by secretly selling
the currency forward and then deliberately trigger a crisis by making a large
spot sale combined with some public statements of how weak the currency is.
One example of manipulation might have taken place in Hong Kong in 1998.
It is said that funds short sold both the HKD and the Hang Seng index at
the same time. The idea was that by selling HKD they would force the Hong
Kong Monetary authority to leave the currency peg. Then they would make
money in on the currency contracts. Short selling the stock market would
increase the pressure for a devaluation. However, if the authorities raised
interest rates to defend the pegged rate one should expect the stock market
would fall. Then the investors would make money on the stock contracts
instead.
Was this a case of manipulation? “Fundamental analysis” probably could
justify both going short in the currency, and short in the stock market. Of
course by taking such positions, investors might contribute to making such
events inevitable. But whether this is “manipulation” or not is hard to say.
In fact the Hong Kong authorities pulled of a “double defence”. They
increased interest rates to defend the peg. However, at the same time they
intervened in the stock market to boost prices. This way investors lost money
on both their contracts. Hong Kong authorities might have fooled potential
speculators. The question is how this willingness to intervene in the markets
116
affected the perception of other potential investors in Hong Kong.
How should we analyse the role of large investors? Take the example of
speculation given above. Assume that the two traders have unequal size. E.g.
let one investor control resources equal to 9 domestic currency units, and the
small investor controls resources equal to 3 units. What would change? The
“good state” remains as before. No devaluation would occur. In the bad
state the small investor could no longer attack the currency alone. In fact,
the “large player” gets a proportional share of the central bank reserves—
i.e. 75 per cent of the reserves, as she has 75 per cent of the market, then
the small investor would not care about the currency markets at all. The
small investor would lose money by selling anyway, given the high costs of
speculation. This is illustrated in figure 4.7.
In the intermediate case however, there would be no real change. The
large trader needs the support of the small trader to succeed. Only the
payoffs would be different from the case where the traders were of equal size.
If size is the only difference between two traders, this might affect who
takes part in an attack when the central bank has only a low commitment
to a fixed exchange rate. However in these cases an attack is probably due
to happen anyway. In the cases when fundamentals are stronger, the whole
market still needs to take part for an attack to succeed.
If the large trader is different from the small trader on other counts than
just size, this argument will of course change. If the large player is perceived
to have superior information, that might increase her ability to influence the
behavior of the market. If the large player has less cost of speculating than
the small investor, this might also affect the results. An extreme version of
this case is reflected in figure 4.9. Here we assume the large trader has no
cost of speculating. In this case it would be optimal for the large trader to
117
Figure 4.7: Attack when fundamentals are weak. Committed reserves=6.
Trader 1 controls 9 units, trader 2 3 units.
Trader 1
Hold
Sell
Hold
0,0
0,-1
Sell
2,0
5/4,-1/4
Trader 2
118
Figure 4.8: Attack when fundamentals are intermediate. Committed reserves=10. Trader 1 controls 9 units, trader 2 3 units.
Trader 1
Hold
Sell
Hold
0,0
0,-1
Sell
-1,0
11/4,1/4
Trader 2
119
Figure 4.9: Attack when fundamentals are intermediate and the large trader
has no cost of speculation. Committed reserves=10. Trader 1 controls 9
units, trader 2 3 units.
Trader 1
Hold
Sell
Hold
0,0
0,-1
Sell
0,0
15/4,1/4
Trader 2
always speculate—and therefore for the the small trader to speculate as well.
If the costs of speculation is very small, the volatility of the exchange rate
might increase.
4.4.3
A short note on the Tobin tax
A Tobin tax is a proposed tax on on all transactions in the foreign exchange
market.
Intention: to reduce excess volatility caused by low costs of transaction.
Will it work? Yes—and no.
• Hinder currency crises? If the cost is high relative to expected gains
120
a tax will reduce the probability of crises. However, the tax necessary
must probably be high. And there are possible problems, see example
below.
• A tax would make the markets less liquid. It is not perfectly clear how
that will effect the price process. However, short term volatility might
fall.
• It has been argued that for a Tobin tax to be effective it must be
implemented in all territories—if only a tiny bit of land is excluded one
could move all FX transactions there to avoid the tax. However, a tax
that covers the OECD countries will probably still have a substantial
effect.
• The real problem is financial derivatives. It is possible to speculate
in the FX-market without being in the FX-market—one can create
financial derivatives that reflect the risk in the FX market.
4.5
Contagion
Figure 4.11 depicts the development of Asian currencies over the period from
1996 to 1998. As we see, during 1997 there occurred a period of severe
volatility that lead to a shift from fixed exchange rate regimes to floating
exchange rate regimes.
In figure 4.12 we take a closer look at the period from May 15 to December 31 1997. We observe that the crises did not occur simultaneously.
Rather they occurred one after another. There is signs of some sort of regional “spread”. This phenomena is often referred to in the literature as
“contagion”.
121
Figure 4.10: Example of how a Tobin tax can be destabilising (note that
this is an extreme case). Trader 1 controls 6 units, trader 2 6 units. Cost
increases from 1 to 2.
Trader 1
Hold
Sell
Hold
0,0
0,2
Sell
2,0
1/2,1/2
Trader 2
Trader 1
Hold
Sell
Hold
0,0
0,1
Sell
1,0
-1/2,-1/2
Trader 2
Attack when fundamentals are weak. Committed reserves=6. In first case
cost of speculation is set to -1. In second case cost of speculation is set to
-2. In the first case we have one Nash equilibrium, in the lower, right corner.
In the second case we have two Nash122
equilibria, in the upper right and lower
left corner. This creates the possibility of a more unstable situation.
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Figure 4.11: Asian currencies against USD, 1996-98
Indonesian rupiah
1.5
1
South Korean won
Malaysian ringgit
0.5
Thai bath
0
Taiwan dollar
-0.5
Figure 4.12: Asian currencies against USD, May 15, 1997-December 31, 1997
1
Indonesia
0.8
South Korea
0.6
0.4
Malaysia
0.2
0
Why do contagion occur? Four reasons have been presented:
1. Several countries can be similarly affected by a common shock.
2. Trade linkages can imply that a crisis in one country weakens fundamentals in other countries.
3. Financial interdependence.
4. A currency crisis in one country can change market participants’ perceptions of other countries, resulting in the withdrawal of capital.
Argument one is providing a “fundamental” explanation of the spread of
crises. Argument number four favour the perception of crisis as “self-fulfilling”.
This argument does however depend on assumptions of limited rationality
among market participants. It is no reason why a crisis in one country should
affect rational expectations of other countries unless there are real links between the two economies. Arguments two and three are therefore perhaps
the more interesting, as they provide explanations of why a crisis can be
transmitted between countries even if there are no common shock.
4.5.1
Transmission of currency crisis via trade channels
It is important to point out that transmission via trade channels do not
depend on the existence of trade channels between the countries affected. In
fact, in the case of Asia one common feature is the relatively small trade
flows between the countries affected by the speculative attacks.
The important feature is to which degree the exports of two countries
are competing in foreign markets. In table 4.3 we illustrate the case with
countries A and B exporting to countries C and D. Country A sends most
124
of her exports to country C, while country B sends most of her exports to
country D.
Assume that country A devalues with 10 per cent. What is the effect on
the exports of country B? To say something about this we must make some
assumptions about how close substitutes the goods of A and B are in C and
D. We assume that there is a one-to-one relationship between a devaluation
and an change in demand in the importing country. If the price of goods
from country A falls with 10 per cent, the demand for goods from country B
falls with 10 per cent. The relative price elasticity ρ, is set equal to 1.
The total effect of a devaluation in country A on the exports of country
B will be given by
∆exshareB =
X
[ρ(k) · exshareB (k) · marketshareA (k)] · dev,
(4.12)
k=C,D
where exshareB (k) is the export share of country B in market k, k ∈ {C, D},
and dev is the devaluation in per cent. If we substitute in from table 4.3 we
obtain
∆exshareB = [1 · 0.1 · 0.9] · 0.1 + [1 · 0.9 · 0.1] · 0.1 = 1.8%.
(4.13)
The exports of country B will fall by 1.8 per cent.
However, assume that country A and B are competing in the same markets. An example is given in table 4.2.
In this case the effect of a 10 per cent devaluation in country A will be
∆exshareB = [1 · 0.1 · 0.5] · 0.1 + [1 · 0.9 · 0.5] · 0.1 = 5%,
(4.14)
a 5 per cent fall in the exports of country B.
In the case of South East Asia, these countries were all competing in
125
126
Initial trade flows
value
C D
From A
10 90
B
10 90
trade flows
Market share
D
percent
C D
10
A
90 10
90
B
10 90
Table 4.2: Competing trade flows
Export share
Market share
percent
C D
percent
C D
A
10 90
A
50 50
B
10 90
B
50 50
Table 4.1: Non-competing
Initial trade flows
Export share
value
C D
percent
C
From A
90 10
A
90
B
10 90
B
10
foreign markets. They all specialised on electronics and computer components, sending their goods to Japan, the USA and Europe. The actual trade
between these countries was of lesser importance. However, in this case the
actual devaluations were not 10 per cent. Thailand, Malaysia and South
Korea experienced devaluations of close to 50 per cent. If we assume a 50
per cent devaluation in country A, we get a 9 per cent fall in exports in
country B in the “little competition case”, and as much as 25 per cent fall
in the exports of country B in the “strong competition case”. Effects of that
magnitude would certainly create a “fundamental” basis for a devaluation in
country B as well.
4.5.2
Transmission via a credit crunch
We consider a case where two banks, bank 1 and 2, lend to three different
countries, A, B and C. However, the dependence on the two banks differ
between the three countries. This is not an unrealistic assumption. Often
banks will specialise on lending to specific geographical regions.
No assume that there is a speculative attack in country A, and that
country A defaults on its foreign debt. Both bank 1 and 2 will lose all they
have lent to country A. As a result both banks need to recall loans to satisfy
the demands of their creditors. Bank 1 have total loans of 40 (20+20) after
the default of A. It must recall a total of 20, which makes up 20/(20+20)=50
per cent of its loan portfolio. Bank 2 had an exposure of 10. It must no
recall 10, which makes up 10/(10+80)=11.1 per cent of its portfolio.
For country B this means that total loans are reduced from 30 to
20 ∗ 0.5 + 10 ∗ 0.899 = 18.9.
That implies a reduction in total loans of (30-18.9)/30=37 per cent. For
127
128
Initial portfolio
From:
Bank 1
Bank 2
To:
A
20
10
B
20
10
C
20
80
Total:
Table 4.3: Bank dependence
Exposure
Dependence
Bank 1
Bank 2
Bank 1
Bank 2 Total:
33
10
33
10
66
33
100
33
80
20
80
100
100
100
country C we find that total loans are reduced from 100 to
20 ∗ 0.5 + 80 ∗ 0.899 = 81.1.
That implies a reduction in total loans of (100-81.1)/100=18.9 per cent.
The point here is that a default in one country might have large effects
on the financing of other countries if there are some kinds of concentration
in lending. If credit channels and trade channels are both regional specific
the transmission effects can be substantial. In other words, a shock to one
country might have substantial implications for other countries, even though
these countries before the crisis had “strong fundamentals”, and even if we
assume investors to be fully rational. Through trade and credit channels
economies can be interdependent despite no direct links between them.
129
Chapter 5
The FX-market
5.1
Some definitions
5.1.1
Instruments
• Spot market: Spot transactions in the FX-market are transactions
made today that shall be completed within two days, i.e. formal delivery of the currency will take place in two days.
• Outright forward: transaction that contract delivery of the currency at
some point beyond two days.
• Option: The right to buy (or sell) an asset at a predetermined value.
• Swap: Bundles two FX transactions that go in opposing directions.
Usual to combine a spot transaction and an outright forward.
Example: buy 100 million EUR today for USD at spot exchange rate.
At the same time agree to sell EUR 100 million in one month. Purpose:
Lock in interest rate differential. If I need EUR 100 million from now
and one month into the future, I can reduce the cost of holding this
sum to the interest differential between EUR and USD by doing a swap
today. I will remove all exchange rate risk.
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Swaps come in two types.
– “Short swaps” are contracts that give delivery today or tomorrow—
i.e. before the delivery in a standard spot contract. Short swaps
are used for liquidity purposes.
– “Long swaps” are swaps with spot contracts and future contracts
with delivery beyond two days.
5.1.2
Bid-ask
All exchange rates are quoted as two prices—a bid and an ask. On the
Reuters screes you will see quotes of the type:
USD/EUR 0.8810-0.8812
0.8810 will be the price where the bank is willing to buy EUR. This is the
bid price for EUR.
0.8812 will be the price where the bank is willing to sell EUR. This is the
ask price for EUR. The seller asks 0.8812 USD to give you one EUR.
Note that the bid price for EUR will be the aks for USD—the price of
one USD is after all only the inverse of the price of one EUR. This might be
confusing...
Table 5.1: Example of bid-ask. Assume that CAD/USD=1.5858/1.5865
Bid
Ask
Price of USD 1.5858 1.5865
Price of CAD 0.6303 0.6306
Trading in the market, dealers will only quote the last two numbers of
the exchange rate. In the above transactions, dealers will say they have a
bid of 10 and an ask of 12.
131
The spread is measured in basis points. One basis point is one 1/10000 of
the unit, that is one point in the fourth decimal of the quote. In the above
example the spread is two basis points.
The spread is the only ‘transaction cost’ in non-brokered interbank foreign
exchange transactions. The spread is a ‘fee’ on the trading. Note that the
spreads in the sport FX-market is much lower than what you will expect
in most financial markets. E.g. a standard fee in equity trading can be 1
per cent of amount transacted—if the fee is symmetric (same for sell and
purchase) that amounts to the the equivalent of 200 basis points. In the FX
market spreads are seldom above 10 points in liquid markets.
5.2
What we know for certain about the FXmarket
The FX-market is riddled with “puzzles”—things we do not understand.
However, there are a few things we do know will hold for certain. In both
examples bellow we will ignore the bid-ask spread. This simplifies things
considerably. However, the logic still holds it we assume the existence of
spreads.
5.2.1
Triangular arbitrage
Let us ignore the bi/ask spread. Assume that we have
• HKD/USD 7.70 (HKD-Hong Kong Dollar)
• ZAR/USD 11.9 (ZAR-South African Rand)
What is the HKD/ZAR rate?
HKD/U SD
7.70
=
= 0.6471 HKD/ZAR.
ZAR/U SD
11.9
132
(5.1)
Suppose not. Suppose e.g. that HKD/ZAR=0.75. This means that we
can make a profit by arbitrage. How? Sell one ZAR and get 0.75 HKD. Sell
0.75 HKD and get 0.0974 USD. Sell 0.0974 USD and get 1.159 ZAR ⇒ you
have made a profit of 16 per cent!
Such profits can not exist for long in a free market. They will be traded
away. In the end triangular arbitrage must hold.
5.2.2
Covered interest rate parity—CIP
Let F be the forward exchange rate. Consider two portfolios:
1. Invest 1 USD at the US 1 year interest rate of i. In one year you will
have U SD · (1 + i).
2. Convert 1 USD to GBP at the spot rate today. This gives you a total
of GBP=U SD/. Invest this at the UK 1 year interest rate of i∗ . In
one year you will have the equivalent of (U SD/) · (1 + i∗ ). However,
you measure your money in USD, so you want to convert back to USD
in the end of the year. To lock in the profit you buy a forward contract
at the price F for delivery of USD in one year. The contract should
cover an amount of GBP=(U SD/) · (1 + i∗ ). The amount earned will
then be (U SD/) · (1 + i∗ ) · F .
These two transactions are equivalent. If the UK and the US assets are
similar, there is no risk difference involved by doing one transaction versus
the other. So we should expect that:
(1 U SD) · (1 + i) =
(1 U SD)
· (1 + i∗ ) · F.
133
(5.2)
It follows that we must have
F
(1 + i)
=
.
(1 + i∗ )
(5.3)
CIP should hold at every point of time unless there are restrictions on
the trade in capital assets.
To sum up: it should not be possible to lend riskless dollars at different
rates in two different markets. A covered international investment is the
same as a domestic investment: they both involve no currency risk. Ergo,
the return should be the same. The forward rate should reflect this.
In logarithmic terms the return of the covered international investment
will be
i∗ + f − e.
(5.4)
The return on the domestic investment must be i. So we must have that
f − e = i − i∗ .
5.3
(5.5)
How the FX-market is organised
Assets are traded in three different types of markets:
1. Auction market. Customers submit orders. These can either be
• market orders—buy or sell at the current market price, or
• limit orders—buy or sell at a the in the contract predetermined
price. When the market reaches the limit price, the order is executed. If the market never reaches the limit price, the order is
never executed, or at least not at that price.
There will be no dealers in this market, only a system for organising
the stream of orders.
134
An example of an auction market is to be found at the Paris Stock
Exchange.
2. Single-dealer market. In this market we have one dealer who offers a
best bid and a best ask. The customer must accept the offer of the
dealer. FX markets in some developing countries will work as single
dealer markets, with the central bank acting as the single dealer.
3. Multiple dealer market.
• Centralised. Quotes from many dealers will be available at one
screen at the same time. Example: NASDAQ.
• Decentralised. Many dealers will offer quotes. However, there is
no system to keep track of all offers in the market at the same
time.
The FX-market can best be described as a decentralised multiple dealer
market. There exists no exchange and no common screen for all quotes.
This means that trading will be partly fragmented—it is not possible
to observe the price in all simultaneous transactions.
Note that there are two types of traders that are active in the FX-market:
1. brokers, and
2. dealers.
These groups offer slightly different services.
Dealers will offer two-way prices (both bid and ask). Direct trade between
dealers will be conducted over a computer system, or over the telephone.
Mostly they will use something called Reuters D2000-1. An example of
communication over Reuters D2000-1 is provided in figure 5.1. One dealer
135
Figure 3 provides an example of a D2000-1 conversation when a trade takes place. A
conversation starts by a dealer contacting another dealer. The contacting dealer usually
asks for bid and ask quotes for a certain amount, for instance USD one million. 4 When
seeing the quotes, the contacting dealer states whether he wants to buy or sell. Sometimes he asks for better quotes, or end the conversation without trading. However, most
conversations result in a trade (70%). All D2000-1 transactions in the data set take place
at quoted bids or asks.
Figure 5.1: Interdealer
communication
Figure 3: D2000-1
conversation on D2000-1
From ‘‘CODE’’ ‘‘FULL NAME HERE’’ *0728GMT ????98 */7576
Our Terminal: ‘‘CODE’’
Our user: ‘‘FULL NAME HERE’’
DEM 1
# 45.47
BA> I BUY
# TO CONFIRM AT 1,8147 I SELL 1 MIO USD
# VAL ??(+2)??98
# MY DEM TO ‘‘FULL NAME HERE’’
# THANKS AND BYE
TO CONFIRM AT 1,8147 I BUY 1 MIO USD
VAL ??(+2)??98
MY USD TO ‘‘FULL NAME HERE’’
THANKS FOR DEAL FRDS. CHEERS
#
# END REMOTE #
^
^
^
## TKT EDIT OF CNV 7576 BY ‘‘CODE’’ 0728GMT ????98
STATUS CONFIRMED
##ENDED AT 07:27 GMT#
(
293 CHARS)
An example of a D2000-1 conversation when a trade takes place. The first word means that the call came “From”
another dealer. There are information regarding the institution code and the name of the counterpart, and the time
(Greenwich Mean), the date, and the number assigned to the communication. DEM 1 means that this is a request
for a spot DEM/USD quote for up to USD 1 million, since it is implicitly understood that it is DEM against USD.
At line 4, we find the quoted bid and ask price. Only the last two digits of the four decimals are quoted. In this
case, the bid quote is 1.8145 and the ask quote is 1.8147. When confirming the transaction, the communication
record provides the first three digits. In this case, the calling dealer buys USD 1 million at the price 1.8147. The
record confirms the exact price and quantity. The transaction price always equals the bid or the ask. There is also
information regarding the settlement bank. “My DEM to “Settlement bank” identifies the settlement bank of “our
bank”, while “My USD to “Settlement bank” identifies the settlement bank of the other bank. It is usual to end a
conversation with standard phrases, such as “thanks and bye,” “thanks for deals friends.”
Source: Bjønnes and Rime, 2001
3.2.2
Electronic broker systems
will
contact
another,
and
for afunctions
price quote.
These quotes
are
considered
Electronic
broker
systems
fill ask
the same
as voice-brokers,
but are
more
efficient.
A bank dealer with access to one of the electronic broker systems can enter his buy and/or
to
be binding. A market maker is a dealer that is supposed to always be
sell price into the system as a market maker. D2000-2 and EBS show only the highest
bid and
the lowest
ask, thereby
minimizing
the spread.
These
normallyparty
be entered
able
to give
a quote.
In direct
interdealer
contact
thewill
opposing
will by
be
different banks, but the identity of the inputting bank is not shown. The total quantity
known.
entered for trade on these quotes is also shown. This means that when more than one
bank input the same best bid (ask) price, the quantity shown is the sum of that offered by
A banks.
single This
dealer
will ismostly
specialise
only
currency
cross.
The
these
quantity
shown as
integers of in
USD
one one
million,
and in some
bilateral
cases DEM one million. When the quantity is at least ten million, “R” is entered on the
dealer
might take considerable positions in this currency intra-day. However,
D2000-2 screen. EBS shows two set of bid and ask quotes, for amounts up to ten million
USD or
DEM, close
and fortheir
amounts
of at least
millions.
This information
is optional
on
most
dealers
positions
overtennight.
Figure
5.2 illustrate
observed
4
In some rare cases, the contacting dealer also tells whether he wants to buy or sell.
dealer inventories for four different dealers in two different markets over one
week, collected from a Norwegian bank.
As we see, dealer strategies can
9
136
Figure
5.2:
DealerInventory
inventory
Figure
2: Dealer
6
20
4
10
USD
USD
2
0
0
-10
-2
-20
Mon
Tue
Wed
Thu
-4
Fri
Mon
a) Dealer 1: DEM/USD Market Maker
60
Thu
Fri
5
20
0
USD
DEM
Wed
10
40
0
-5
-20
-10
-40
-60
Tue
b) Dealer 2: DEM/USD "Nintendo-dealer"
Mon
Tue
Wed
Thu
-15
Fri
c) Dealer 3: NOK/DEM Market Maker
Mon
Tue
Wed
Thu
Fri
d) Dealer 4: DEM/USD
The evolution of dealers inventory over the week. Dealer 1 (panel a), 2 (panel b) and 4s (panel d) inventory are
in USD million, while Dealer 3s inventory is in DEM million. The horizontal axis is in“transaction”-time. Vertical
lines indicate end of day. The numbers are in USD million.
Source: Bjønnes and Rime, 2001
be described as “individual”.1 In this sample we see that dealer might take
intra-day positions of up to 20 million USD. It is not unusual for dealers to
trade for USD 1 billion a day. As a comparison US equity traders trade for
an average of USD 10 million a day.
A broker is a pure matchmaker. Dealers will submit limit orders to the
broker. The broker will post these orders on a screen. One such system is
8
the Reuters D2000-2. In the broker system traders can observe the quotes
available in the market on one screen. However, it is not revealed who has
1
The dealer consistently making most money of these four is supposed to have been
the “Nintendo-dealer”—a guy who never held a position for more than two minutes.
137
posted the quote. This is first revealed after the trade has been completed.
A difference between the direct trade and the broker system is that the as
the broker system is based on limit orders, one will post a maximum size of
the order at a given price. Further, one needs not post limit orders on both
sides of the market. A dealer can choose to post orders a bid or an ask.
The cost of trades will depend on the counterparty. Direct interdealer
contact has the lowest spreads. Brokers take somewhat higher spreads, not
least because brokers only make money through transaction costs. Customer
get the highest spreads. The market is illustrated in figure 5.3
Three characteristics of the FX market:
1. A very high volume,
2. high intra-dealer volume, and
3. low transparency.
In all these regards the FX-market is different from other multiple dealer
asset markets. The daily volume in the FX spot market in April 1998 was
600 billion USD, of which about 2/3 is supposed to have been intradealer
trade. As a comparison, the daily volume in the New York Stock Exchange
in this period was 30 billion USD, and average daily world trade in goods
and services was about 15 billion USD.
One way to explain the high amount of trade in the FX-markets is the
“hot-potato-hypothesis.” Assume that a dealer gets an order from a customer. However, the dealer wants to keep his inventory as close to zero as
possible. So the dealer makes a trade with another dealer. This dealer will
keep a little, and trade the rest. And so on. That way every customer trade
gets multiplied when we look at the FX-market as a whole. One question
might be why dealers conduct such trading. Seemingly they could try to seek
138
Figure 5.3: The FX-market
Customer à dealer
Spread: 3-7 basis points
Brokered interdealer
Spread: 2-3 basis points
Direct interdealer
Spread: 2 points
Why use a broker?
1. Do not have access to direct
market
2. Do not have to reveal identity
before trade is completed
3. Access to a larger market
Source: Lyons, 2001
139
a better match for their orders, thereby reducing the number of rounds before
the currency risk is spread thin enough to satisfy the market. The willingness
to trade might be explained through the low transparency in these markets.
The only way dealers can obtain information about the flows in the market
is by trading themselves.
The FX-market has evolved almost with no government intervention.
This might point to low transparency being in the interest of the dealers.
Low transparency gives active dealers an advantage in the markets—and it
might be an advantage for their customers as well, as they always get the best
quotes. The smaller and less informed loose out however. In fact we have
seen an increasing concentration in the FX-market over the last 10 years.
The largest 10 firms did in 1998 control about 50 per cent of the market.
5.4
Data from the FX-market
In April every three years Bank of International Settlements, BIS, collect
data on transactions in the FX-market from 48 national central banks. The
total volume reported in the survey for 2001 is found in figure 5.4. As we can
see, after years of increase in FX-volume, the volume has fallen considerably
over the last three years. This is probably fairly simple to explain—with
the introduction of the EUR the number of heavily traded currencies fell
dramatically.
Figure 5.5 summarises the types of instruments used in the market. We
see that most deals are made with ‘reporting’ dealers—dealers that are ‘registered’ by the central bank as reporters. We also see that most swaps are
conducted as transactions with a life of less than 7 days—short-swaps are
the leading type of swap transactions in this market.
140
Table5.4:
1
Figure
Global foreign exchange market turnover1
Daily averages in April, in billions of US dollars
Instrument
1989
1992
1995
1998
2
2001
Spot transactions
317
394
494
568
387
Outright forwards
27
58
97
128
131
190
324
546
734
656
56
44
53
60
36
590
820
1,190
1,490
1,210
570
750
990
1,400
1,210
Foreign exchange swaps
Estimated gaps in reporting
Total “traditional” turnover
Memorandum item:
Turnover at April 2001
3
exchange rates
1
Adjusted for local and cross-border double-counting. 2 Revised. 3 Non-US dollar legs of foreign currency transactions were
converted into original currency amounts at average exchange rates for April of each survey year and then reconverted into US dollar
amounts at average April 2001 exchange rates.
Source: BIS, 2001
5.4.1
International currency
Just as domestic currency is the reference in the domestic economy, there
needs to be a point of reference in the international currency markets as
well. In a flexible currency system this point is not clear. However, at different times Greek coins, Roman coins, Florins, bills of credit on German
banks or British pounds have worked as accepted means of payment in international transactions. Since the Second World War USD has filled this role,
although some observers now predict a larger role for the EUR. How do we
define an international currency? What will determine which currencies are
dominating the world markets?
Factors that the determine the international use of a currency is
• size of the economy,
• importance in international trade,
• size, depth, liquidity, and openness of domestic financial4/13markets,
141
Table 2
Figure 5.5:
Reported foreign exchange market turnover by instrument, counterparty
and maturity1
Daily averages in April, in billions of US dollars
1992
Instrument/counterparty
1995
1998
2
2001
.......................................................
394
494
568
387
With reporting dealers ...............................
With other financial institutions ..................
With non-financial customers.....................
282
47
62
325
94
75
348
121
99
218
111
58
Outright forwards ....................................
58
97
128
131
With reporting dealers ...............................
With other financial institutions ..................
With non-financial customers.....................
Up to 7 days ..............................................
Over 7 days and up to 1 year ....................
Over 1 year................................................
21
10
28
…
…
…
33
28
36
50
44
2
49
34
44
66
59
5
52
41
37
51
76
4
Foreign exchange swaps ........................
324
546
734
656
With reporting dealers ...............................
With other financial institutions ..................
With non-financial customers.....................
Up to 7 days ..............................................
Over 7 days and up to 1 year ....................
Over 1 year................................................
238
39
47
…
…
…
370
108
68
382
155
7
512
124
98
529
192
10
419
177
60
450
197
8
Total..........................................................
776
1,137
1,430
1,173
With reporting dealers ...............................
With other financial institutions ..................
With non-financial customers.....................
541
96
137
728
230
179
909
279
241
689
329
156
Local..........................................................
Cross-border..............................................
316
391
526
613
658
772
499
674
Spot
1
Adjusted for local and cross-border double-counting.
2
Revised.
Source: BIS, 2001
REVIEW
Table 1
Figure 5.6: The roles of international money
Functions of an International Currency
Sector
Function
Private
Official
Unit of account
Invoice
Store of value
Financial assets
Exchange rate peg
Reserves
Medium of exchange
Vehicle/substitution
Intervention
reserves in this
currency
and (ii)
as a medium of
Korean economy, U.S. exports comprise a much
Source:
Pollard,
2001
larger share of world exports.
exchange if it is used for intervening in currency
Clearly the dominance of the U.S. economy
markets.
and the decline of the U.K. economy in the twentieth
The three functions of an international currency
reinforce each other. For example, the use of a
142century were related to the rise of the dollar and
the decline of the pound as international currencies.
currency for invoicing trade and holding financial
Likewise, the growth of the German and Japanese
assets increases the likelihood that the currency
5/13
economies in the last several decades of the twenwill be used as a vehicle currency. In the official
tieth century prompted the use of their currencies
sector, if a country pegs its exchange rate to another
in international markets. As a result, the overwhelmcurrency, it is likely to hold reserves in that currency
ing dominance the dollar held in international
and conduct its interventions in exchange markets
markets in the 1950s and 1960s diminished.
in that currency. In addition, the use of an interTable 2 compares the relative size of the U.S.,
national currency by one sector reinforces its use
euro-area, and Japanese economies. The U.S. econby the other sector. For example, using a currency
omy is the largest in the world, accounting for about
as an exchange rate peg facilitates the use of that
FEDERAL RESERVE BANK OF ST. LOUIS
Table 2 5.7: Factors that determine the international use of a currency
Figure
Comparison of United States, Euro-Area, and Japanese Economies in 1999
United States
Euro area
Japan
Share of world GDP (%)
21.9
15.8
Share of world exports (%)
15.3
19.4
9.3
40,543.8
24,133.4
20,888.5
6,662.5
Financial markets ($ billions)
Bank assets ($ billions)
7.6
7,555.3
12,731.3
Domestic debt securities outstanding ($ billions)
15,426.3
5,521.9
6,444.9
Stock market capitalization ($ billions)
17,562.2
5,880.2
7,781.4
NOTE: GDP is based on purchasing power parity equivalents. World exports excludes intra-euro-area trade.
SOURCE: GDP: IMF, World Economic Outlook, October 2000. Exports: IMF, Direction of Trade Statistics Quarterly, September 2000.
Bank assets: European Central Bank, Monthly Bulletin; Board of Governors of the Federal Reserve System, Flow of Funds Accounts;
IMF, International Financial Statistics. Debt securities: Bank for International Settlements, Quarterly Review of International Banking
and Financial Market Developments. Stock market: Eurostat.
exchange a currency
for other2001
currencies limits its
this currency; (ii) if this currency is used to facilitate
Source: Pollard,
the exchange of other currencies; and (iii) if this
global use. At the end of World War II almost every
currency is used as a substitute currency.
country, with the exception of the United States,
restricted the convertibility of its currency. This
Invoice Currency
• convertibility
ofthecurrency,
and
inconvertibility
persisted for
first decade after
the
war. The convertibility of the U.S. dollar prompted
The dollar is the main currency that functions
its use as the currency in which international trade
as a unit of account for private international transwas
• conducted.
macroeconomic policies. Policies actions.
fostering
lowdatainflation
(i.e.of invoice
a stable
Although
on the currency
Macroeconomic policies also play an imporin international trade are limited, the available data
tant role
in determining
whether
cur- important.
confirm the dominance of the dollar. In 1995 the
value
of money)
area country’s
especially
rency will be used internationally. These policies
U.S. dollar was used as the invoice currency for more
affect a country’s economic growth and its openthan half of world exports, down only slightly from
ness to the world economy. Policies fostering a low
1980, as shown in Table 3. The Deutsche mark was
So what
currencies
are actually
international
currency
markets?
inflation
environment
are especially
important. usedthein
next
most popular invoice
currency, used
for
Countries experiencing hyperinflation and/or
approximately 13 percent of world exports, followed
crises
often
see the
use of their
Aspolitical
can be
seen
from
tables
5.8currenand 5.9 the
most
traded
is the
USD,
by the
French
franc andcurrency
the British pound.
While
cies collapse not only internationally but also
the yen’s use in world trade lagged behind these
within
domestic
economy,
as residents
turn is the
European
currencies, its share had more than
and
thethemost
traded
currency
pair
USD/EUR.
to a substitute currency.
doubled since 1980. The combined share of the
Clearly the size and openness of the U.S. econfour major euro currencies was less than half that
omy have been major factors in encouraging the
of the U.S. dollar.
international use of the dollar in the post-World
More importantly, there is a clear distinction
War II period. Its use as an international currency
between the use of the dollar and other invoice
in the private sector and the effect of the emergence
currencies. The U.S. dollar is the only currency
Invoice
of the eurocurrency
in this sector is examined in the next
whose use in world trade far surpasses its country
section.
share in world trade, as shown by its internationalization ratio in Table 3. An internationalization ratio
THE
PRIVATE
USES
OF
AN
Rules for choice of invoice currency:
less than 1.0, as with the yen, lira, and guilder,
INTERNATIONAL CURRENCY
indicates that not all of that country’s exports are
denominated in the local currency. An internationAs stated above, a currency operates as an
alization ratio greater than 1.0, as with the dollar,
international currency in the private sector (i) if
• Between industrialised countries: price
the good in the currency of the
the mark, and the pound, indicates that other couninternational trade and debt contracts are priced in
5.4.2
The roles of international money
exporter.
S E P T E M B E R / O C TO B E R 2 0 0 1
19
• Between industrialised countries and developing countries: price the
good in the currency of the industrialised country, or in a third country
currency (most likely the USD).
143
3
Figure 5.8: Currency distribution of Table
reported
global foreign exchange market
Currency
distribution
of
reported
global
foreign
exchange market turnover1
turnover
Percentage shares of average daily turnover in April
Currency
1989
1992
1995
1998
2
2001
US dollar.................................................
Euro .......................................................
3
Deutsche mark ......................................
French franc ...........................................
ECU and other EMS currencies .............
Japanese yen .........................................
Pound sterling ........................................
Swiss franc .............................................
Canadian dollar ......................................
Australian dollar......................................
4
Swedish krona ......................................
4
Hong Kong dollar ..................................
4
Norwegian krone ...................................
4
Danish krone .........................................
4
Singapore dollar ....................................
4
South African rand ................................
4
Mexican peso ........................................
4
Korean won ...........................................
4
New Zealand dollar ...............................
4
Polish zloty ............................................
4
Brazilian real .........................................
4
Russian rouble ......................................
4
Taiwan dollar .........................................
4
Chilean peso .........................................
4
Czech koruna ........................................
4
Indian rupee ..........................................
4
Thai baht ...............................................
4
Malaysian ringgit ...................................
4
Saudi riyal .............................................
Other currencies.....................................
90
.
27
2
4
27
15
10
1
2
…
…
…
…
…
…
…
…
…
…
…
…
…
…
…
…
…
…
…
22
82.0
.
39.6
3.8
11.8
23.4
13.6
8.4
3.3
2.5
1.3
1.1
0.3
0.5
0.3
0.3
…
…
0.2
…
…
…
…
…
…
…
…
…
…
7.7
83.3
.
36.1
7.9
15.7
24.1
9.4
7.3
3.4
2.7
0.6
0.9
0.2
0.6
0.3
0.2
…
…
0.2
…
…
…
…
…
…
…
…
…
…
7.1
87.3
.
30.1
5.1
17.3
20.2
11.0
7.1
3.6
3.1
0.4
1.3
0.4
0.4
1.2
0.5
0.6
0.2
0.3
0.1
0.4
0.3
0.1
0.1
0.3
0.1
0.2
0.0
0.1
8.2
90.4
37.6
.
.
.
22.7
13.2
6.1
4.5
4.2
2.6
2.3
1.5
1.2
1.1
1.0
0.9
0.8
0.6
0.5
0.4
0.4
0.3
0.2
0.2
0.2
0.2
0.1
0.1
6.7
All currencies........................................
200
200.0
200.0
200.0
200.0
1
Because two currencies are involved in each transaction, the sum of the percentage shares of individual currencies totals
200% instead of 100%. The figures relate to reported “net-net” turnover, ie they are adjusted for both local and cross-border
double-counting, except for 1989 data, which are available only on a “gross-gross” basis. 2 Revised. 3 Data for April 1989
exclude domestic trading involving the Deutsche mark in Germany. 4 For 1992-98, the data cover local home currency
trading only.
Source: BIS, 2001
144
6/13
Table 4
1
Reported
foreign
exchange
turnover
by currency
pairs
Figure 5.9:
Reported
foreign
exchange
turnover
by currency
pairs
Daily averages in April, in billions of US dollars and percentages
1992
Currency pair
1995
1998
2
2001
Amount
%
share
Amount
%
share
Amount
%
share
Amount
%
share
USD/EUR ..............
USD/DEM ..............
USD/FRF ...............
USD/XEU...............
USD/OthEMS ........
USD/JPY ...............
USD/GBP ..............
USD/CHF...............
USD/CAD ..............
USD/AUD ..............
USD/Oth ................
EUR/JPY ...............
EUR/GBP ..............
EUR/CHF...............
EUR/Oth ................
DEM/JPY ...............
DEM/GBP ..............
DEM/CHF ..............
DEM/FRF...............
DEM/XEU ..............
DEM/OthEMS ........
DEM/Oth................
3
OthEMS/OthEMS .
Other currency
pairs.......................
.
192
19
13
43
155
77
49
25
18
48
.
.
.
.
18
23
13
10
6
21
20
3
.
25
2
2
6
20
10
6
3
2
6
.
.
.
.
2
3
2
1
1
3
3
0
.
254
51
18
104
242
78
61
38
29
72
.
.
.
.
24
21
18
34
6
38
16
3
.
22
4
2
9
21
7
5
3
3
6
.
.
.
.
2
2
2
3
1
3
1
0
.
291
58
17
176
257
118
79
50
42
172
.
.
.
.
24
31
18
10
3
35
18
5
.
20
4
1
12
18
8
5
3
3
12
.
.
.
.
2
2
1
1
0
2
1
0
352
.
.
.
.
230
125
57
50
47
197
30
24
12
22
.
.
.
.
.
.
.
.
30
.
.
.
.
20
11
5
4
4
17
3
2
1
2
.
.
.
.
.
.
25
3
30
3
31
2
24
2
All currency pairs
778
100
1,137
100
1,430
100
1,173
100
1
Adjusted for local and cross-border double-counting.
only.
2
Revised.
3
.
The data cover local home currency trading
Source: BIS, 2001
145
7/13
REVIEW
Table 3
Figure 5.10: Invoice currency
Trade Invoiced in Major Currencies
Percent of world exports
Internationalization ratio
Currency
1980
1995
1980
U.S. dollar
56.4
52.0
4.5
3.9
2.1
4.7
0.3
0.6
13.6
13.2
1.4
1.4
6.2
5.5
0.9
1.0
Japanese yen
Deutsche mark
French franc
1995
British pound
6.5
5.4
1.1
1.1
Italian lira
2.2
3.3
0.5
0.8
2.6
2.8
0.7
0.9
24.6
24.8
NA
NA
Netherlands guilder
Euro-4
NOTE: Euro-4 is the share of the four euro-area currencies listed in the table. No data were available for the other euro-area currencies.
World exports includes intra-euro-area trade. The internationalization ratio is the ratio of the share of world exports denominated in
a currency to the share of the issuing country in world exports.
SOURCE: Bekx (1998, Table 3, p. 8).
2001
tries use thatSource:
currencyPollard,
to invoice
some (or all) of
the lower its transaction costs; the lower its transtheir exports.6
action costs, the more likely it is to be accepted.
What determines the currency of invoice in
Related factors that explain these patterns are
world trade? A number of studies including those
convertibility
and the the
expected
stability
of the
•
Between
developing
countries:
most
likely price
good
in USD.
by Grassman (1973), Page (1981), and Black (1990)
currency. As noted above, the use of the dollar as
revealed the following patterns. Trade in manufacan invoice currency was prompted by the lack of
tured goods among the industrial economies is
convertibility of most other currencies in the 1950s.
most
often priced in the(like
currency
the exporter.
use ofpriced
developing
Commodities
oil,of metals
et.c.) The
arelimited
mainly
incountries’
USD. currencies
If the exporter’s currency is not used, then the
in world trade arose in part because many of these
importer’s currency is the most frequent choice.
countries restricted (and some continue to restrict)
Only rarely is a third country’s currency used. Trade
the convertibility of their currencies. Black (1990)
between
and developing
countries
is
• Is industrial
it important
which
currency
isshowed
usedthatasthean
currency?
Yes,
shareinvoice
of a country’s
exports denomgenerally priced in the currency of the industrial
inated in its domestic currency declines the greater
country
that of a reduce
third country.
Trade between
expected depreciation
of itsin
currency.
Thus,
it ormight
currency
risk foris the
businesses
situated
the country
developing countries is often priced in the currency
the currencies of countries with high inflation are
of a third country. When a third country’s currency
seldom used in international trade.
where
thistrade,
currency
belongs.
However,
currency
might
generally
is used
for invoicing
the U.S. dollar
is the
The mere
creation ofrisk
the euro
as a currency
most likely choice. Trade in primary commodities
should provide ample incentive for its use as an
is almost
invoiced
in U.S.cheaply
dollars because
be always
removed
quite
by usinginvoice
options
orReplacing
forward
currency.
the contracts.
currencies of 12
these products are predominantly priced in dollars
countries with a single currency reduces the
on international exchanges.
transaction costs involved in currency exchanges.
According to Hartmann (1996), two factors
Although
only a small
number
of firms within
the
•
Would
it
reduce
risk
if
a
commodity
is priced
in the
national
currency?
that explain these patterns are transaction costs
euro area have already switched to invoicing in
and acceptability. The lower the cost of buying and
euros, the advent of euro notes and coins, along
Norway
oilforeign
price
risk has
two factors: changes in the oil price measellingIn
a currency
in the
exchange
market,
the more likely is its use for invoicing trade. In
6
An internationalization ratio greater than or equal to 1.0 does not
addition,
the more
currency
is for other
that all of the homerate
country’s between
exports are priced in
its currency.
sured
in accepted
USD, aand
changes
in theimply
exchange
USD
and
According to data provided in Bekx (1998) in 1995, 92 percent of U.S.
transactions, the more likely it is to be used as an
exports, 75 percent of German exports, 62 percent of British exports,
invoice currency. Clearly these two factors are mutuand 52 percent of French exports were invoiced in their domestic
NOK. In
onea currency
only has
oil price risk. However, notice that
ally supportive.
The the
more US
accepted
is, the currencies.
20
taking two risks instead of one does only imply increased risk if the
S E P T E M B E R / O C TO B E R 2 0 0 1
fluctuations of the two assets are positively correlated. In fact there is
no reason to believe that the oil price and the USD is positively correlated. In the case of Norway, the volatility of changes in the oil price
measured in NOK is not very different from the volatility changes in
146
Figure 5.11: The oil price in NOK and USD from 1998 to 2001. Indexed
values, index=100 in January 1, 1998
300
250
200
150
100
50
1/01/98
10/08/98
7/15/99
OILNOKI
4/20/00
1/25/01
OILUSDI
Source: Datastream
the oil price measured in USD (a standard deviation on daily data from
1990 to the end of 2001 gives 3.58 against 3.60. Notice however that
this result will be very sample dependent).
Vehicle currency
When making a transaction between e.g. NOK and NZD one will have several
choices available. One can
• buy NZD against the delivery of NOK. This does however assume a
147
coincidence of wants. The bank selling NZD should also want NOK.
• buy USD against the delivery of NOK, and then buy NZD against the
delivery of USD.
• or even more intricate, buy EUR against the delivery of NOK, USD
against the delivery of EUR and NZD against the delivery of USD.
Why should one choose a strategy involving more than one transaction?
Because the transactions costs will depend on the liquidity in each bilateral
currency market. E.g. 80 per cent of all spot trade (that is trades to be
delivered within two working days) in the Norwegian market is conducted
between NOK and EUR. According to table 5.9 in April 2001 91 per cent
of all currency trades included the USD. Most trades in NZD is probably
conducted against USD. So it might well generate the lowest transaction
costs if one makes two or three transactions instead on only one.2
A vehicle currency will emerge each time the indirect exchange costs
through the vehicle currency are less than the direct exchange costs between
non-vehicle currencies. In Norway (and other small European nations) EUR
probably works as a vehicle currency. For most other transactions, the USD
is probably the vehicle currency of choice.
Store of value—the choice of denomination of financial assets
Diversification is an important concept in finance. One wants to diversify
one’s portfolio across interest bearing paper and equity, between different
2
This has very real application in the small scale. If you carry foreign currency to e.g.
Eastern Europe one would normally find a much lower spread (distance between bid and
ask prices—or the sell and buy offers) if one trades with EUR than with NOK. One can
often save money if one exchanged NOK to EUR in a Norwegian bank, and only used
EUR when travelling. In more developed markets, the cost of using NOK instead of other
currencies is however small.
148
REVIEW
Figure 5.12: Vehicle currency
Table 8
Foreign Exchange Market Transactions Involving Select Currencies (Percent of Total) April 1998
Category
U.S. dollar
Japanese yen
Spot
78.8
24.7
Deutsche mark
42.7
French franc
3.3
Euro area*
56.8
Pound sterling
11.6
Forwards
81.4
26.7
28.0
5.1
50.7
12.3
Swaps
95.2
16.7
20.0
6.5
48.8
10.2
Total
87.4
20.8
29.8
5.1
52.2
11.0
*Euro area includes the currencies of the current member countries plus the Danish krone and the ecu.
SOURCE: Bank for International Settlements, Central Bank Survey of Foreign Exchange and Derivatives Market Activity 1998. Basle:
BIS, May 1999.
Source:
Pollard, 2001
kets.” Whereas,
the infrequent
interventions by
the mark and yen taking part in 20 and 17 percent,
respectively, of all trades.
individual European central banks in securities
The use of the dollar in foreign exchange transmarkets “tended to discourage the development of
actions was well above its use in international trade
private securities markets and foster the predomiissuers
of bonds and equity and also between
different currencies. However,
and debt contracts, indicating its role as a vehicle
nance of bank-intermediated finance.” The ECB has
currency. The BIS (1999) notes that evidence of the
continued this practice of infrequent interventions.
the
willingness
invest markets
in a certain
currency
will
on size,
openness,
dollar’s role
as a depend
vehicle currency
is provided
by its
In general,
it is activeto
in securities
only
use in seven of the ten most heavily traded currency
once per week.
pairs.stability
The report also
notescurrency.
that it is standard pracFor now U.S. financial
markets markets
continue to lead
and liquidity
of financial
and the
of the
tice for the dollar to be used as a vehicle currency
the world in both size and liquidity. As a result, the
in swaps, which explains the high percentage of
U.S. dollar remains the major currency in interThe bond
EURmarkets.
will only
behowever,
able tohascompete
with
USDtheasU.S.
the
currency
ofuse
choice
swaps
involving
dollar
and the low
of
national
The euro,
the yen and mark in these trades.
already become a major player in these markets,
The use
of a currency
as a vehicle
currency
is
inand
international
the European
financial
markets
get
the same
its use will likelydebt
expandmarkets
as euro-areaiffinancial
determined primarily by transactions costs. Transmarket integration proceeds. The development of
actions costs
are inversely
related to volume
in eachon
a euro-area
capital market
the U.S. marketmarkets.
size
and liquidity
assimilar
thetoAmerican
This
will probably
depend
bilateral currency market.20 This volume is in turn
should provide benefits to both economies by
determined by a currency’s share in international
increasing the options available to borrowers and
the
levelon of
integration
in the Europeantrade
financial
markets.
and capital
flows. Thus, the use of a currency
lenders
both
sides of the Atlantic.
in invoicing international trade, in international
Vehicle Currency
capital markets, and as a reserve currency lowers
the transactions costs associated with the use of
The There
useareofnoadirect
substitute
currency
data available on vehicle
that currency.
currencies, but this information can be gleaned from
A vehicle currency emerges whenever the
the shares of currencies in foreign exchange transindirect exchange costs through the vehicle are less
18 In 1998 the dollar was
actions,
as
shown
in
Table
8.
If there is loss of trust in the national
currency,
people
will
trytwo
tonon-vehicle
exchange
than direct exchange
costs
between
involved in 87 percent of all currency exchanges.19
currencies. For example, given the depth of the
The euro legacy currencies were involved in 52
exchange market
dollars, itLoss
may beofless
costlycan
their
holdings of this currency into presumably
saferfor
assets.
trust
percent of all exchanges, with the Deutsche mark
the most often traded of these currencies. The yen
18
These
gathered
from a triennialhas
survey of
foreign
exchange
e.g.
under
of hyperinflation,
ordataifarethe
country
an
exchange
wasoccur
used in 21
percentperiods
of all currency
trades. The
markets conducted by the BIS.
dollar’s dominance was especially clear in forward
19
Since there are two currencies involved in an exchange, the total
and regime
swap transactions.
The dollar
was involved
in
rate
that might
break
down.
share of all currencies traded on international exchanges will equal
81 percent of all forward trades compared with the
200 percent. However, a single currency can, at most, be involved in
100 percent of all exchanges.
mark’s and yen’s shares of 28 and 27 percent, respecIn
countries
with
a
weak
legal
system
or a weak central bank, large hold20
tively. In swaps the contrast was even greater. The
The use of transactions cost theory to explain the rise of a vehicle
dollar was involved in 95 percent of all swaps, with
currency was developed by Krugman (1980) and Chrystal (1984).
ings of currency is often kept in foreign currency. In most countries the
26
S E P T E M B E R / O C TO B E R 2 0 0 1
currency of choice will be the USD. In some Eastern European countries the
EUR is more popular than USD, mainly because of the proximity and trade
with the EU countries. Montenegro is probably the most extreme case—they
have adopted the EUR as the means of payment.
149
FEDERAL RESERVE BANK OF ST. LOUIS
Table 6
Figure 5.13: Denomination of international debt
International Debt Securities by Currency of Issue (Percent)
Amounts outstanding
Currency
1993
Share of new issues
1998
2000
1998
1999
2000
Total securities
U.S. dollar
41.1
45.9
48.7
54.1
45.2
44.0
Japanese yen
13.2
11.3
8.2
5.6
5.3
8.3
Swiss franc
7.3
3.8
2.2
3.3
2.0
1.7
Euro area*
24.8
27.2
30.1
24.6
36.8
33.9
Other E.U.†
7.9
8.5
8.2
8.9
8.0
9.2
7.6
7.9
7.8
8.3
7.7
9.1
Pound sterling
Bonds and notes
U.S. dollar
38.9
45.3
48.7
51.1
43.8
42.3
Japanese yen
14.0
11.7
8.6
6.3
6.7
11.4
Swiss franc
7.7
3.8
2.2
2.7
1.6
1.4
Euro area*
25.7
27.6
30.0
28.0
38.3
34.2
Other E.U.†
8.1
8.5
8.1
9.0
7.3
8.4
7.8
7.9
7.7
8.2
7.0
8.2
Pound sterling
Money Market
U.S. dollar
79.4
59.9
49.1
61.0
48.8
47.5
Japanese yen
0.2
2.5
2.3
4.0
1.4
1.9
Swiss franc
1.8
4.5
2.3
4.7
2.9
2.3
Euro area*
8.5
19.2
32.4
17.2
32.9
33.2
Other E.U.†
4.1
8.4
9.5
8.8
9.8
11.0
4.0
8.3
9.3
8.7
9.7
11.0
Pound sterling
*Euro area includes the currencies of the 11 original members of the euro area and currency composites, such as the ecu.
†
Other E.U. includes the currencies of Denmark, Sweden, and the United Kingdom.
SOURCE: Bank for International Settlements, Quarterly Review of International Banking and Financial Market Developments, March 2001.
the 1950s. By the 1970s, however, the currency
Source: Pollard, 2001
denomination of bond issues had become more
diversified, as shown in Table 5. Nevertheless, the
U.S. dollar has remained the most popular currency
choice for issuing bonds in international markets,
as shown in Table 6.9 By the 1960s the euro legacy
currencies, taken together as a group, had become
the second most widely used currency in international bond markets, a status that continues today.
The Japanese yen was not used at all until the 1970s,
and its share of new issues lags far below that of the
dollar or euro. The use of the Swiss franc in international bond markets, which rivaled the Deutsche
mark in the 1970s, declined precipitously in the
1990s.10
In international money markets as well, the
dollar is the currency of choice, but again its
dominance has declined, as noted in Table 6. The
increased use of the euro legacy currencies in these
markets during the 1990s is particularly noteworthy.
In 1993 these currencies accounted for 8.5 percent
of the outstanding debt in international money
markets. By 1998 this share had increased to 19.2
percent.
9
The data in Tables 5 and 6 rely on different sources and hence may
not be directly comparable.
10
Some policymakers in Switzerland were concerned that the creation
of the euro might result in a sharp rise in demand for assets denominated in Swiss francs. See Laxton and Prasad (1997) for an analysis
of this argument.
150
S E P T E M B E R / O C TO B E R 2 0 0 1
23
REVIEW
Figure 2
Figure 5.14: US seignorage revenue
Seignorage Revenues from Foreign Holdings
of U.S. Dollars
Billions of 1996 $
14
12
10
8
6
4
THE OFFIC
INTERNAT
2
0
1973 75
77
79
81
83
85
87
89
91
93
95
97 1999
Source: Pollard, 2001
Percent of federal government expenditures
It1.2is estimated that about 55 per cent (!) of the total U.S. currency
held by the non-bank public was held outside the US in 1995. The same
1.0
number
for the DEM was 35 per cent. The seignorage revenue from foreign
holdings is estimated to an average of about 9 billion USD a year over the
0.8
last decade. That is less than one per cent of US government expenditure.
However it would amount to between 5 and 7 per cent of Norwegian GDP—
0.6
still a reasonably large sum of money.
0.4
0.2
151
0.0
1973 75
to lag behind
Foreign holde
ble, secure cu
value of the e
against the do
existence, wi
the euro as a
If the eur
substitute cur
ECB will rise.
revenues mig
demand for s
euro and the
Emerson et a
age revenues
a year for the
77
79
81
83
85
87
89
91
93
95
97 1999
SOURCE: Department of Commerce, Bureau of Economic
Analysis, and Board of Governors of the Federal Reserve System.
Exchange
Under the
from 1946 to
were tied to t
Bretton Wood
their currenc
their currenc
those countri
continued to
In 1975, 52 m
of the Interna
their currenc
The euro lega
popular choic
the African F
currency use
and the Span
for the curren
Chapter 6
The floating exchange rate
6.1
Introduction
Michael Mussa has summarised our understanding of flexible exchange rates
in the following way:
[T]he largely random character of exchange rate fluctuations
under floating exchange rate regimes is explained by the prevalence of “news” in inducing most exchange rate changes; the tendency for nominal and real exchange rates to move in together
under a floating rate regime is explained by the contrast between
the behavior of nominal exchange rates as randomly fluctuating
asset prices and the behavior of national price levels as relatively
sluggishly adjusting variables; and with respect to the influence of
economic policies on exchange rates, what matters is not simply
what policies governments pursue today, but also to an important
extent, the policies they are expected to pursue in the future.
Despite this progress made over the last 30 years, we still do not have
a good understanding of the observed behavior of exchange rates. Jeffrey
Frankel and Andrew Rose (1995) state that
152
[t]o repeat a central fact of life, there is remarkably little evidence that macroeconomic variables have consistent strong effects
on floating exchange rates, except during extraordinary circumstances such as hyperinflations. Such negative findings have led
the profession to a certain degree of pessimism vis-à-vis exchange
rate research.
6.2
High expectations
During the Bretton Woods era many economist argued in favour of floating
exchange rates. Six main claims were made.
1. Real exchange rates would be more stable with floating than fixed exchange rates. The argument was that since the exchange rate could
adjust faster than the price level, one should expect a floating exchange
rate to allow faster adjustment than a fixed exchange rate, as in the
last case all adjustment was left to the domestic price level.
Outcome: in fact variability in the real exchange rate has increased
considerably with floating exchange rates. Real and nominal exchange
rates tend to move together, and nominal exchange rate changes tend
to increase the variability in the real exchange rate, not alleviate variability.
2. Adjustments in fixed exchange rates tend to be infrequent, but abrupt
and large. They often take a form that can be described as “crises”.
Floating exchange rates was supposed to change slowly, smoothly and
predictably.
Outcome: Flexible exchange rates have been very volatile. Changes
are abrupt and fast. Neither are they predictable, as we will see in the
153
discussion of the UIP below.
3. Floating exchange rates were supposed to adjust to insulate the economy against shocks from abroad. Remember the n-1 problem: in a
fixed exchange rate regime monetary policy had to be adjusted in all
countries if adjusted in one country.
Outcome: In fact, correlation between business cycles have tended to
increase, not fall, over the last three decades. Even in a floating regime
the n-1 problem can not be ignored. If interest rate differentials between
economies are allowed to be to high, we experience changes in real
exchange rates that are not easily accepted. The result is that real
interest rates are highly correlated.
4. In a floating exchange rate the central bank gets complete control over
the money supply.
Outcome: Even in a floating regime the exchange rate can not be ignored. The exchange rate is probably the most important “price” in
every moderately open economy. The stylised example of an independent monetary policy is an illusion.
5. With floating exchange rates, exchange rates would adjust faster to
balance the current account, thereby decreasing the political pressure
for e.g. tariffs an other measures to reduce trade imbalances.
Outcome: if anything, current account imbalances have increased with
floating exchange rates.
6. With a floating exchange rate one did no longer need a foreign exchange
reserve. These money could be freed for other purposes.
154
Outcome: Foreign exchange reserves are in real terms larger today than
in the Bretton Woods era.
How come that we have missed the point so completely? Two possibilities:
either our models have been just plain wrong, or we did not interpret them
correctly. The main problem is probably that floating exchange rates are
much more volatile than was expected. However, this is a feature exchange
rates share with all asset markets—asset prices tend to fluctuate much more
than underlying “fundamentals” should presume.
6.3
“Excess volatility” and some ‘puzzles’ of
exchange rate economics
In the beginning of this course we made two basic assumptions when we
moved from the domestic relationship for money demand to a function for
the exchange rate. We assumed that PPP and UIP would hold. PPP implies
that given the function
P∗
Qt
= t,
t
Pt
(6.1)
we assume Q to be one, or at least stable over time. The UIP states that
Et t+1
1 + it
=
.
t
1 + i∗t
(6.2)
According to the UIP Et t+1 should be our best guess of t at time t.
Table 6.1 give the standard deviations of return for a number of variables.
What we can see from this table is that from week to week one should expect
very limited volatility in prices. The volatility in interest rates are 10 times
the volatility in prices.1 The volatility in the exchange rate is a 100 times
1
Note that as we are looking at the volatility in bond interest rates and not bond prices
we underestimate the risk of investing in long term bonds. A one per cent swing in a bond
with maturity in 10 years implies a substantial swing in the current price of the bond.
155
that of the interest rate. However, we can notice that exchange rate volatility
can only be characterised as “excess” if compared with the volatility of prices
and interest rates. Compared with return in the stock market or in a highly
traded storable good like oil, volatility is in fact rather low.
Table 6.1: Standard deviation of weekly return (weekly change) for different
markets. Sample cover 11.1992-03.2002
St.dev. in per cent
CPI
Norway
0.0003
Germany
0.0002
10 year gov. bond*
Norway
0.003
Germany
0.003
3 month interbank*
Norway
0.006
Germany
0.004
spread (NOK-DEM)
0.005
Exchange rates
NOK/DEM
0.79
DEM/USD
1.37
Stockmarket index
Norway
2.79
Germany
3.44
Traded goods
oil in USD
5.21
*volatility in i
What conclusion can we draw if we combine our results from table 6.1
with the two parity conditions stated above? If price volatility is low, and the
nominal exchange rate volatility is high, the volatility of the real exchange
rate must be highly correlated with the volatility in the nominal exchange
rate. Further, it the volatility in the differential between domestic and foreign
interest rates is low, while the volatility of the current spot rate is high,
then we should expect a very high correlation between the expected future
156
exchange rate and the current exchange rate as well.
These are de facto puzzles. However, they are probably not puzzles only
related to the market for foreign exchange. Rather they are related to all
asset markets. In general changes in asset prices are not well explained by
changes in fundamentals, at least not over a “short time horizon” of say, up
to two years. The reason is that asset prices fluctuate so much more than
other variables in the economy. This volatility can not be well explained with
current economic models. One therefore often hear that asset markets show
“excess volatility”.
We should add a third problem not reflected in the table above. The
real exchange rate tends to fluctuate in long cycles, with a mean reversion
time of between 2 and 6 years, depending on the country and the exchange
rate regime. This implies that over time fundamentals do seem to explain
exchange rates after all. Why is this a puzzle? Because we can not understand why fundamentals should only be reflected in asset prices over a time
span of over two years. Most of the explanations given below for the high
volatility in exchange rates might give a good explanation for a divergence
between fundamentals and the exchange rate for a few months, or maybe a
year. However none of the models can explain why exchange rates are mean
reverting over 4-6 years...
6.3.1
The FX market vs. the stock market
Given the focus on excess volatility in the FX market it is reasonable to
compare this market with the volatility of the stock market. Figure 6.1
depict the log of NOK/DEM exchange rate, indexed to 100 in week 47 1992.
In the figure we have drawn a trend line over the period.2 Figure 6.2 depict
2
The trend line is calculated as with Hodrick-Prescott filter with a smoothing parameter
of 100,000.
157
Figure 6.1: The NOK/DEM exchange rate. Log of index=100 in week 47,
1992. Trend calculated with H-P filter.
4.75
4.70
4.65
4.60
4.55
11/20/92
10/21/94
9/20/96
8/21/98
7/21/00
a similar figure forEURNOKINDEX
the Oslo Stock Exchange.HPNOKEURINDE100
In figure 6.3 we depict only the trend lines. We see that the the two graphs
have many similar features. Both tend to move in long swings. However, as
becomes very clear in figure 6.4, over time the underlying movements in the
stock exchange are of much larger magnitude than the long term changes in
the exchange rate.
Figure 6.5 depict the difference between the actual value and the trend.
As we see both series fluctuate considerably around the trend. Also here the
two series have substantial similarities. When we take the two series into
the same diagram, as is done in figure 6.6, we see that even here the stock
exchange has a much higher volatility than the exchange rate.
158
Figure 6.2: Index of Oslo Stock Exchange. Log of index=100 in week 47,
1992. Trend calculated with H-P filter.
5.8
5.6
5.4
5.2
5.0
4.8
4.6
4.4
11/20/92
10/21/94
9/20/96
OSLOINDEX
159
8/21/98
7/21/00
HPTREND09
Figure 6.3: The H-P trend in NOK/DEM exchange rate and the Oslo Stock
Exchange. Log of index=100 in week 47, 1992.
4.70
4.68
4.66
4.64
4.62
4.60
4.58
11/20/92
10/21/94
9/20/96
8/21/98
7/21/00
HPNOKEURINDE100
5.8
5.6
5.4
5.2
5.0
4.8
4.6
11/20/92
10/21/94
9/20/96
8/21/98
HPOSLOINDEX100
160
7/21/00
Figure 6.4: The H-P trend in NOK/DEM exchange rate and the Oslo Stock
Exchange. Log of index=100 in week 47, 1992.
5.8
5.6
5.4
5.2
5.0
4.8
4.6
4.4
11/20/92
10/21/94
9/20/96
HPNOKEURINDE100
161
8/21/98
7/21/00
HPOSLOINDEX100
Figure 6.5: The difference from H-P trend for NOK/DEM exchange rate the
Oslo Stock Exchange. Log of index=100 in week 47, 1992.
0.10
0.05
0.00
-0.05
-0.10
11/20/92
10/21/94
9/20/96
8/21/98
7/21/00
EURNOKINDEXVOL
0.2
0.1
0.0
-0.1
-0.2
-0.3
-0.4
11/20/92
10/21/94
9/20/96
8/21/98
OSLOINDEXVOL
162
7/21/00
Figure 6.6: The difference from H-P trend for NOK/DEM exchange rate the
Oslo Stock Exchange. Log of index=100 in week 47, 1992.
0.2
0.1
0.0
-0.1
-0.2
-0.3
-0.4
11/20/92
10/21/94
9/20/96
EURNOKINDEXVOL
163
8/21/98
7/21/00
OSLOINDEXVOL
Some tentative conclusions:
• The stock market and the FX market reveal many of the same features.
They both tend to move in long swings, with substantial volatility
around these swings.
• However, both the movements in the trend and the volatility around
the trend tends to be less for the FX market than for the stock market.
• This might indicate that the FX market is slightly more “efficient” than
the stock market. If so, this is not a surprising conclusion. After all,
as we discussed in Lecture 5, transaction costs are lower and volume is
higher in the FX market than in the stock market. Both factors should
contribute to a more efficient market.
6.4
Random walk?—the Meese and Rogoff
results
During the 1970’s much work was done on econometric models for forecasting
exchange rates. Some of these models showed promising results. However,
in 1983 there was published a study by Meese and Rogoff that summarised
the ability of such econometric models to forecast exchange rate changes
out-of-sample. The results were devastating.
To forecast something in-the-sample tells us about the ability of the model
to explain the observations we use in the regression. In out-of-sample forecasts we use the model to forecast time periods that was not included in the
actual regression analysis.
Meese and Rogoff estimated four different models using monthly data.
They had data from March 1973 to June 1981. First they estimated the
164
Table 6.2: Out-of-sample forecasting performance of different exchange rate
models—root of mean squared error of forecasts 1, 6 and 12 months ahead.
Random walk Monetary Dornbusch Portfolio balance
USD/DEM
1 month
3.7
3.2
3.7
3.5
6 month
8.7
9.6
12.0
10.0
12 month
13.0
16.1
18.9
15.7
USD/JPY
1 month
3.7
4.1
4.4
4.2
6 month
11.6
13.4
13.9
11.9
12 month
18.3
18.6
20.4
19.0
USD/GBP
1 month
2.6
2.8
2.9
2.7
6 month
6.5
8.9
8.9
7.2
12 month
9.9
14.6
13.7
14.6
Source: Meese and Rogoff, 1983
models over the period from March 1973 to November 1976. Then they used
the parameters estimated to forecast the changes in the exchange rate 1, 6 and
12 months into the future from November 1976. In this forecast they used
actual realised values of the “fundamental variables”—taking a very strict
assumption of perfect foresight. They then extended the regression with
one month, to December 1976, and reported forecasts. They repeated this
procedure for the whole period till June 1981. Having made these forecasts,
they compared the forecasts with actual outcomes, and reported the squared
errors of the forecasts. A summary of their findings is given in table 6.2.
Meese and Rogoff had estimated three models with “economic contents”—
a monetary equilibrium model, the Dornbusch model and a portfolio balance
model. In addition they had estimated a “naive” model with no economic
content—i.e. a random walk. A random walk is taking the very simple assumption that the current exchange rate is the best predictor of the future
165
exchange rate, i.e.
et+1 = a + et + ut ,
(6.3)
where a is a constant and u is the error term, with the expected normal
distribution u ∼ N (0, σ 2 ). As we can see from table 6.2 the random walk
was the best predictor in eight out of nine cases. This is really equivalent to
stating two things:
• Changes in the exchange rate are unpredictable, and
• the exchange rate is not mean reverting.
This has lead to the idea that exchange rates are in fact following a random walk process. However, one needs to take this with some modifications.
• The result is only valid if we talk about purely floating exchange rate
between industrialised countries in the short term.
• And even here the random walk is not completely satisfying. It shows
up that exchange rate returns—an other word for the change in the
exchange rate—have fat tails. In other words, returns are not normally
distributed after all. What does fat tails mean? While most changes in
the exchange rate are small, some changes are very large. We see more
large changes than we should expect if the errors were drawn from a
normal distribution.
• More specific, the exchange rate tends to follow an ARCH/GARCH
process. This implies that a period of high volatility is usually followed
by more periods of high volatility, and a period of low volatility is
followed by periods of low volatility. Volatility in the exchange rate is
to some degree predictable.
166
6.5
Equilibrium models
Ideally we want to build models that assume rational behavior and complete
information. The rational behavior/perfect information case is in the end the
only real benchmark we have. We need to gain full understanding of what
this framework can tell us before we modify these basic assumptions.
The rational behavior/perfect information was our starting point when
we derived an exchange rate model in Lecture 2. We concluded that the
exchange rate, e, could be expressed as a function of money supply, real
output, foreign interest rates and foreign prices, i.e. as
s−t
∞ 1 X
η
et =
(ms − φys + ηi∗s+1 − p∗s ).
1 + η s=t 1 + η
(6.4)
The above framework is known as a “monetary equilibrium model”. In
this model all volatility should be a result of new information, “news”, as
all history will be reflected in the price at every given point of time. However, given our observations of the very high volatility in the exchange rate
compared to the fundamental variables in this equation, it is tempting to
conclude that this model is no good. There have been attempts to model
exchange rate movements using a reasonable assumption of what is “news”.
Such research tend to find that the exchange rate moves as much in periods
with no “news” as it does in periods with “news”. So “news” do not seem to
explain the exchange rate very well. One should on the other hand not forget
that the monetary equilibrium model does seem to to have some explanatory
power in the long run. The exchange rate is reverting to fundamentals. It
only takes much longer than we are able to explain.
We should ask why our model is no good in the short and medium term.
Some arguments:
167
• The model specification might be no good. E.g. most tests of the
above model are done assuming a linear framework. It is however an
established fact that asset prices have a non-linear relationship to fundamentals. One result from research on “chaos models”, as discussed
in ch. 9 in De Grauwe, is that in a non-linear framework there might
be a relationship between fundamentals and prices even in the short
run. A problem has been that such non-linear models are very difficult
to make intellectually tractable.
• Some of our basic assumptions, like the assumptions of free trade and
free capital mobility might not hold. There might also be public interference not captured in the model.
• In equation (6.4) we have made the very convenient assumption of no
bubbles. However, in the many cases bubbles might be a real problem,
i.e. remember our discussion of rational bubbles.
• More problematic is the fact that we really do not understand how expectations are formed. This is probably the best explanation of why the
equilibrium models do not fit, because it is an explanation that helps
us understand why we do not understand asset market in general—the
FX market is nothing special. What do we not understand? Perhaps
markets are not as rational as this model assumes, or perhaps we do
not fully understand what ‘rational behaviour’ really implies. The economic definition of rationality—to be a forward looking and maximise
some simple utility function—might not be a good description of reality.
Other possibilities exist as well:
• In the above model we assume that all variables, i.e. the price level,
as everything else is given exogenously, will adjust instantaneously to
168
clear all markets. However, we know that prices might be sticky, at
least for periods of up to a year. If we assume that prices take time
to adjust, we must take into regard that it takes time to move from
one equilibrium to another. The economy will spend time “outside
equilibrium”—i.e. the introduction of “disequilibrium models”—the
main tool in the “New Keynesian economics”; dominating much of
current research in macroeconomics.
• When we looked at the FX-market, we saw that different dealers seemed
to follow different strategies. This will be the case for many agents in
asset markets. E.g. we know for certain that many traders will buy
assets based on so-called technical analysis. Technical analysis bases
buy and sell recommendations on graphs of historic prices. Such traders
will by definition be backward looking—they will not fit our forward
looking framework.
• An other feature of the FX market was low transparency. This might
indicate that we as researchers do not have full control over which
information dealers actually use when they set their exchange rates.
We might have a “missing variable” problem.
In the following sections we will investigate whether these three options can
help us understand the “exchange rate puzzle”.
6.6
Disequilibrium models
Disequilibrium models come in many forms. We will focus on the assumptions
that prices are sticky. How will this affect our discussion of the exchange rate?
When we derived the model in equation (6.4) we assumed both the PPP and
the UIP to hold at the same time. However, if prices are sticky this can no
169
longer be the case. In the short term either the UIP or the PPP will not hold.
We will have a state that differs from the long term stable condition—we will
be out of equilibrium.
In the model we will present, due to Rudi Dornbusch, we assume that
while the UIP will hold at every point of times, although the PPP will not.
Assume that there is an unexpected shock to the money supply. Money supply increases. According to the equilibrium model prices should immediately
increase and the exchange rate should depreciate, leaving the real exchange
rate unaffected. The interest rate would not change.
What happens if prices take time to adjust? The long term expectations
will be the same as in the equilibrium model. When the price adjustment
has taken place, the two models have the same implications. The price
level will be higher, and the exchange rate will be higher. However, in the
short term only the exchange rate will adjust. Prices do not change. Hence,
domestic interest rates must fall. This is necessary to induce people to hold
the higher money supply—remember that lower interest rates make people
increase their holdings of currency. If prices had risen immediately people
would have been be willing to hold more money just because prices were
higher, and the interest rate would have been unaffected.
If the exchange rate immediately settles at its long term value, while
interest rates for a period fall bellow the foreign interest rate, the UIP can
not hold. But we have assumed the UIP to hold at every point of time.
So what must happen? If the UIP shall hold when domestic interest rates
are bellow foreign interest rates, we need to expect the exchange rate to
appreciate—as Et et+1 must be smaller than et .
This leads to overshooting—when the money shock occurs the exchange
rate must change by more than its long term expectations. This is the only
170
way the UIP can hold—because only if the exchange rate depreciates “too
much” now, it can be expected to appreciate back to its long term value.
6.6.1
The Dornbusch model
Let us assume a real money demand function of the type we used in Lecture
2. We assume the real money demand, m − p is a function of the expected
interest rate, i, and real output, y. If interest rates increase, you want to
reduce your holdings of currency, so the sign of i is negative. If real output
increases you want to increase your holdings of currency, so the sign of y is
positive. Further, we assume perfect foresight. We an then write real money
demand as
m − p = −ηi + φy.
(6.5)
·
Assume that UIP holds, and that et+1 − et = e so that
·
e = i − i∗ .
(6.6)
Further, we assume that there are both traded and non-traded goods in the
economy. The price of non-traded goods is pd . The price of traded goods is
equal to the foreign price level, p∗ . We can define the price level as a weighted
average of traded and non-traded goods,
p = σpd + (1 − σ)(e + p∗ ).
(6.7)
You see that when σ = 0 the price level evolves according to the PPP.
However, if σ > 0 prices will not adjust automatically to the PPP level.
If we substitute for (6.6-6.7) into (6.5) we obtain
·
m − (σpd + (1 − σ)(e + p∗ )) = −η(i∗ − e) + φy.
171
(6.8)
Figure 6.7: The equilibrium model vs. the disequilibrium model
e
t
time
p
t
time
i
i=i*
t
time
The whole lines give the solution to an unexpected positive monetary shock in
the monetary equilibrium model. This is as discussed in lecture 1 and 2. The
dashed lines give the movements of e, p and i as is expected in the Dornbusch
model.
172
When we reorder we obtain
·
e=
φ
σ
1−σ
1−σ ∗
1
pd +
e+
p − i∗ + y − m.
η
η
η
η
η
(6.9)
We concentrate about p and e. All other variables are exogenous in this
model. For simplicity we define a variable z that includes all exogenous
variables:
z = (1 − σ)p∗ − ηi∗ + φy − m.
(6.10)
·
We can then write e as
·
e=
σ
1−σ
1
pd +
e + z.
η
η
η
(6.11)
This gives us a first order difference equation for the change in the exchange
rate measured in e and p.
To complete the model we need a description of the movement in the
price level. We can define the real exchange rate, q, as3
q = p − p∗ − e.
(6.12)
We define the exchange rate that will assure that q = 0 as ê, i.e.
ê = p − p∗ .
(6.13)
If e > ê the exchange rate is undervalued, if e < ê the exchange rate is
overvalued.
We postulate that the the price level will move up when the exchange rate
is undervalued and that the price level will move down when the exchange
3
De Grauwe includes real shocks into the PPP equation. Such shocks do however not
affect the results we intend to discuss, so we just ignore them. They make no difference
here.
173
·
rate is overvalued. The change in prices, p, can be written as
·
p = δ(e − ê),
(6.14)
where δ > 0. If we substitute (6.13) into (6.14) we obtain
·
p = δ(e − p + p∗ ).
(6.15)
Equation (6.5) describe the domestic price level as a weighted average of
traded and non-traded goods. If we substitute (6.5) into (6.15) and rearrange
we obtain
·
p = σδ(e − pd + p∗ ).
(6.16)
If σ is zero, there will be no over- or undervalued exchange rate, as the PPP
will hold at all times.
·
·
We have two first order difference equations, one for e and one for p. We
·
·
now set e = p = 0. From equation (6.11) we obtain
pd = −
1−σ
1
e + z.
σ
σ
(6.17)
From equation (6.16) we obtain
pd = e + p∗ .
(6.18)
An equilibrium is a situation where variables are stable. Equation (6.17)
defines under what conditions the financial markets are in equilibrium. Equation (6.18) defines under what conditions the goods markets are in equilibrium.
The financial equilibrium is illustrated in figure 6.8. In the financial
market equilibrium we adjust the exchange rate. Assume the price level of
non-traded goods is “too high”—i.e. we are at a point above the line defined
174
Figure 6.8: Financial market equilibrium
p
de=0
e
in equation (6.17). For the real exchange rate to adjust towards PPP the
nominal exchange rate must depreciate—i.e. the direction of the arrow in the
diagram. If prices are “too low”, the nominal exchange rate must appreciate.
The goods market equilibrium is illustrated in figure 6.9. In this equilibrium we adjust the price level. If the exchange rate is “too high”—at a point
to the right in the figure—the price level must rise for the real exchange rate
to adjust. If the exchange rate is “too low”—i.e. we are in the left of the
figure—the price level must fall for the real exchange rate to adjust.
Together the financial market and the goods market define the economy.
If we bring the two equilibrium conditions into one diagram we can identify
175
Figure 6.9: Goods market equilibrium
p
dp=0
e
176
Figure 6.10: Market equilibrium
p
dp=0
de=0
e
e
the equilibrium of the economy. However, outside this equilibrium we have
possible unstable situations. How the market is expected to move in the
different areas is described by the arrows in figure 6.10. The model has a
“saddle point” where the two lines cross. There is only one stable line that
leads from disequilibrium to the saddle point, and this path is defined by
the “saddle path” in the figure. Every other path than the “saddle path”
will lead to increasing deviations from fundamentals. However, as foresight
is assumed to be perfect, it is reasonable to believe that the economy will be
at the saddle path.
Now we can analyse shocks. A money shock is a shock to the financial
177
Figure 6.11: A positive money shock
p
dp=0
de’=0
de=0
e
·
market. An increase in the money supply will shift the line for e out. At the
same time interest rates must fall to bring prices down.
In a phase diagram we will not expect an immediate shift to the new
saddle point. Prices will be sticky in our model. So the price level will take
time to adjust. In the short term only the exchange rate can move. It will
do so by shifting to the right, to the new saddle path. However, this rate
will be higher than the rate in the saddle point. Over time the exchange rate
must appreciate as it moves towards the saddle point. In parallel interest
rates will rise and prices will rise. A new equilibrium will be established with
a higher price level and an interest rate equal to the foreign interest rate.
178
The weakness of the Dornbusch approach
What is the the problem of the Dornbusch model? The model gained attention because the overshooting result gave a possible explanation for the
high volatility in the exchange rate. If the exchange rate tended to overshoot, we should expect exchange rate volatility to be substantially higher
than the volatility in underlying fundamentals. Further, the model gives an
explanation of why we should expect to see a high correlation between the
nominal and the real exchange rate. After all, prices do not move here, while
the nominal exchange rate overshoots. This should imply that even the real
exchange rate will overshoot for a period of time. However, the model only
gives this result in the case of monetary shocks. If there is a shock to de·
mand, through e.g. public spending, this will shift the p = 0 equation. Such
a shift does not lead to overshooting in this model.
Is it reasonable to assume that frequent monetary shocks are the main
cause of the high volatility in the exchange rate? Empirically, monetary
shock are very hard to distinguish, so this is not an easy question to answer.
However, as we pointed out above, the high volatility in the FX market is a
feature it shares with almost every other asset market. It is fairly certain that
monetary shocks does not explain why other asset markets are so volatile.
Probably the Dornbusch model is to specific to give any good understanding
of the high volatility in exchange rates. It is however still important as a
benchmark for much of the current literature in exchange rate economics.
6.7
Chartists and noise traders
The monetary equilibrium model assumes that all traders are using the same
strategy. They have estimated a model for the exchange rate that they are
179
continuously updating, based on expected fundamental underlinings for the
exchange rate. If the exchange rate is “overvalued” compared with their
expectations they sell, it the exchange rate is “undervalued” they buy.
However, different traders might be using different strategies. E.g. most
surveys of traders active in the FX market reveal that at least 30 per cent
tend to use chartist methods to forecast the exchange rate. A chartist will
use historic values of the asset price to predict future movements in the asset
price. They are assumed to use rules that are extrapolative, like “buy when
the 1-week moving average crosses above the 12-week moving average.”
Milton Friedman argued in 1953 that non-fundamental speculators would
over time lose money. However, it has been shown by a number of studies
that one can make money using a chartist strategy. Therefore it might be
perfectly rational to be a chartist, although this implies a trading strategy
that does not care about “fundamentals”. If the exchange rate only reverts
to fundamentals in the long term, much money can be made following the
short term trends. Feedback trading can also be rationalised if one assumes
that the availability of information is limited. If we assume some traders to
have more information than others, the less informed will have to observe
the trading process, as the actual trading is a source of how other agents are
behaving.
If many traders are operating as chartists, this might increase the probability for the exchange rate to move in long swings. If the value of a currency
is appreciating, chartist strategies would probably indicate to buy the currency, thereby fuelling the trend. One the other hand, if this trend is moving
away from fundamentals, should not “fundamental traders” force the rate
back?
At some point they will. However, their total force might not be big
180
enough to do so before the exchange rate has deviated quite substantially
from the underlying rate. Some potential problems:
• There is actual uncertainty about the future. Unless the discrepancy
between the rate and fundamentals become “too large”, there can always occur some unexpected “news” that would justify the current
rate. The fear of such events might hinder a rational investor from
short-selling to bring the exchange rate back.
• Even if the rate is currently overvalued, there is no guarantee for when
the trend will turn. Hence, if you sell today, while the rate continues
to move away from fundamentals, you will miss out on an even bigger
profit opportunity tomorrow.
• Even if you base your predictions on fundamentals, you are never certain that your model is a 100 per cent correct.
The noise trader paradigm is a continuation of the chartist-fundamentalist
approach. A noise trader is defined as someone who responds to random
price movements. Experiments tend to show that investors are overconfident
about their own predictive abilities. Other studies have shown that many
traders believe a large change in the exchange rate to be the most important
“news” over the course of a day—rather odd, given that “news” should be
something generated outside the market. Such findings might indicate that
actual behaviour does not fit the monetary equilibrium model’s definition of
“rational”. Describing noise traders is however difficult. Recent theoretical
studies tend to model noise trading by assuming that noise traders behave
like chartists.
181
6.8
Microstructure theories
In Lecture 5 we discussed the institutional framework of the FX market. We
saw, among other things, that the FX market tended be distinguished by
high volume and low transparency compared with other markets. The microstructure theory is a sidetrack of exchange rate economics that investigate
how institutional factors influence the pricing process in the market.
There have been two lines in the literature. The traditional approach has
been to see whether the trading process, e.g. the use of different trading
system, will have a price impact. These studies are generally restricted to
looking at very short term price fluctuations, mainly basing their findings on
tick-by-thick data, or the continuous flow of orders in the market.4
A more recent strain of the literature focuses on the the lack of transparency. The argument is that different investors will have different information. This information will be reflected to the market through their trading.
One measure of trading is “order flow”. Order flow is defined as net initiated purchases of foreign currency. If a customer calls a dealer and asks for
10 EUR in the SEK/EUR market, this implies an order flow of 10. If the
customer asks for 10 SEK, this implies an order flow of -10.
Order flow reflects “excess demand” in the market. What is “excess
demand”? Should not always demand equal supply? Well, the demand curve
might shift. Excess demand reflects the direction of shifts in the demand
curve.
How does this differ from the equilibrium models? In the monetary equilibrium model demand is determined by the current value of a number of
fundamental variables. The models assume that everyone has the same information, and that everyone uses the same model to interpret this information.
4
A ‘thick’ is a single trade.
182
However, “fundamental variables” are mostly reported only with a lag.
E.g. the inflation rate is reported only once a month, and with at least one
month lag. Real output is reported at a quarterly basis, with several months
lag. The numbers are often revised several times after that. At every given
point of time there exists no consensus of what real output is in exactly this
point. Further, it is no reason to believe that every investor uses the same
model to evaluate the information available.
It is however reasonable to assume that investors’ beliefs about current
fundamentals will be reflected in their trading. So if investors demands more
of a currency, this might imply that there are reasons for the exchange rate
to appreciate.
The main proponent of this approach, Richard Lyons, argues that actual
dealers hardly care about “news” when they are setting prices. He claims
that dealers mainly observe the amount of incoming trade, and adjust prices
as a result of this. If so, order flow will be the determinant of much of the
price fluctuations we can observe in the data.
Figure 6.12 depicts accumulated customer order flow in the Swedish market and the SEK/DEM exchange rate. As the order flow has a negative
number, we see that customers are net buying SEK. On the opposing side
must be either Sveriges Riksbank, or the reporting banks—the Riksbank or
the dealers must be accumulating DEM if customers shall be able to accumulate SEK. As we see there is a fairly strong correlation between the
customer order flow and the exchange rate. Table 6.3 reports regression results when we include order flow in regressions on the exchange rate. As we
see, including order flows in the regressions improve the R2 quite considerably compared with regression only including “fundamental variables”, like
interest rates and the stock exchange.
183
184
Note1: Estimated with OLS
Note2: * - 5 per cent, ** - 1 per cent
Note3: We include 5 lagged values of return in this regression. Only the
fourth lag is significant.
Table 6.3: Estimating daily returns—01.01.1998 to 06.30.1998
returns
(1)
t-stat
(2)
t-stat
(3)
Constant
0.000 0.576
0.000 0.984
0.001
Total customer OF
7.72E-07 3.987 **
Swedish customer OF
6.61E-07
Foreign customer OF
6.11E-07
Dealer-dealer flow
-1.94E-07
Change in for. reserves
-3.63E-06
Interest dif., d(rdif )
0.002 0.173
-0.002 -0.151
-0.006
Stock index return, d(lOM XC) -0.054 -2.472 *
-0.051 -2.437 *
-0.055
Lagged return (4)
Adjusted R2
0.03
0.14
0.18
DW
2.09
2.02
2.05
S.E. of regression
0.003
0.003
0.003
2.979
2.951
-0.637
-3.026
-0.507
-2.695
t-stat
2.776
2.880
3.442
-0.594
-3.194
-0.035
-2.689
2.445
t-stat
0.001 2.798
6.24E-07
7.06E-07
-1.76E-07
** -3.78E-06
0.000
**
-0.053
0.195
0.30
2.15
0.001
**
**
**
(4)
**
*
**
**
**
**
Chart1
Figure 6.12: Accumulated customer order
flow in the SEK/DEM market and
the SEK/DEM exchange rate, January 1, 1998, to June 30, 1998
0
2.19
1
log(SEK/DEM)
2.18
-5000
2.17
-10000
2.16
2.15
-15000
2.14
-20000
2.13
2.12
Customer order flow
-25000
2.11
-30000
6.9
2.1
Page 1
The uncovered interest rate parity (UIP)
In Lecture 5 we discussed the covered return to investing one krone in the
foreign money market. We argued that this return should equal the return
of investing one krone in the Norway. From this we derived the CIP, or
Ft
1 + it
=
.
t
1 + i∗t
(6.19)
ft − et = it − i∗t .
(6.20)
In log form this can be written
The uncovered return to investing one krone in the foreign money market
will be
(1 + i∗t )Et t+1
,
t
185
(6.21)
or in logs
i∗t + Et et+1 − et .
(6.22)
As described in Lecture 2 the UIP is the idea that if expectations are rational,
then the the expected uncovered return of this investment should equal the
return of investing one krone in Norway. Arbitrage should assure that the
uncovered excess return should be zero on average. We should expect
Et (i∗t + Et et+1 − et − it ) = 0.
(6.23)
There are three interpretations of this equation.
1. The expected depreciation rate equals the interest rate differential. Let
us define expected depreciation as Et dt+1 = Et et+1 − et . If we insert
this into (6.23) we obtain
Et dt+1 = it − i∗t .
(6.24)
2. Forward interest rates are unbiased predictors of future spot rates. If
we insert (6.20) into (6.23) we obtain
ft − et = Et et+1 − et ,
(6.25)
ft = Et et+1 .
(6.26)
or
3. The international Fisher relationship. From previous courses you should
be familiar with the term “real interest rate”, ir . The real interest rate
is defined by the Fisher equation that states that the real interest rate
is the differential between the nominal interest rate and expected in-
186
flation,
irt = it − Et π t+1 ⇒ it = Et π t+1 + irt
(6.27)
Similar, we must have
i∗t = Et π ∗t+1 + ir∗
t
(6.28)
If we substitute equations (6.27) and (6.28) into (6.24) we obtain
Et dt+1 = (Et π t+1 + irt ) − (Et π ∗t+1 + ir∗
t ).
(6.29)
The PPP states that
et = pt − p∗t .
(6.30)
Et et+1 = Et pt+1 − Et p∗t+1 .
(6.31)
We should also have that
So the PPP implies that
Et et+1 − et = Et pt+1 − Et p∗t+1 − (pt − p∗t ).
(6.32)
This can be rewritten as
Et dt+1 = Et π t+1 − Et π ∗t+1 .
(6.33)
So if the PPP holds we must have that
r
r∗
Et π t+1 − Et π ∗t+1 = (Et π t+1 + irt ) − (Et π ∗t+1 + ir∗
t ) ⇒ it = it . (6.34)
The real interest must be equal between countries.
187
6.9.1
Testing the UIP
The ‘expectations hypothesis’ or the ‘efficient market hypothesis’ is built
on the idea that if there are free capital flows and rational expectations we
should expect
ft = Et et+1
(6.35)
to hold if markets are efficient. It is reasonable to try to test whether this
hypothesis holds in empirical data. To do so we define a forecast error, u, as
et+1 = Et et+1 + ut+1 ⇒ Et et+1 = et+1 − ut+1 .
(6.36)
The forecast error is the difference between the realised exchange rate in
period t + 1 and the expected exchange rate.
If we substitute (6.36) and the CIP into the the UIP equation we obtain
et+1 − ut+1 − et = ft − et .
(6.37)
From (6.37) we can obtain the following testable equation
dt+1 = a + b(ft − et ) + vt+1 ,
(6.38)
where a is a constant and v is an error term. This is equivalent to testing
the equation
dt+1 = a + b(it − i∗t ) + vt+1 .
(6.39)
According to the UIP hypothesis we should expect a to be zero and b to be
1.
Figure 6.13 reports the finding of this regression for five different markets.
As we see b is not close to one in any of the five reported regressions. In fact
b is significant and negative. This implies that the interest rate differential
is negatively correlated with depreciation of the currency. An investor who
188
holds funds in a high yield currency not only benefits form higher yields, but
also tends to benefit from an appreciation in the long run. You simply get a
double dividend. But how can such excess returns exist?
We should notice that although the UIP does not seem like a good idea,
it is not certain that one can make money on doing the opposite of the UIP.
Even if the t-ratios of the b-parameters are significant, the R2 of the equations
are very low, indicating a poor fit of our model. It is reason to doubt whether
one can make money on trading against the UIP in the long run. However,
one certainly can make money trading against the UIP in the short run.
Figure 6.14 depicts the interest differential between Norwegian and German
three month interbank rates and the NOK/EUR exchange rate. In this case
Norway has over 3 per cent higher interest rates than Germany. According
to the UIP we should expect NOK to depreciate substantially vis-à-vis the
EUR. However, during the last months NOK has appreciated. Lending in
EUR, investing in NOK has given a double dividend—both a substantial
interest differential and an appreciation of NOK. Such cases are difficult to
explain using the UIP.
We are certainly missing out one something here. Notice that when we
set the expected future exchange rate equal to the forward rate we leave out
any discussion of risk. However, most investors are risk averse. We should
probably take this into regard in our calculations. Fama decomposed the
forward premium, ft − et into two parts:
ft − et = (ft − Et et+1 ) + (Et et+1 − et ).
| {z }
| {z }
rt
(6.40)
dt
where r = the risk premium and d as before is expected depreciation. One
implication of the above regression results is that r certainly must be different
from zero. However, here, as in many other parts of the asset pricing litera189
Forward and Eurocurrency Markets
4. UIP
Regression results
Figure 6.13: Regressions on the UIP
Currency
a
b
Standard
Error
R2
British Pound
-0.0067 -2.306
(0.0028) (0.862)
0.0322
0.0344
Canadian Dollar
-0.0027 -1.464
(0.0009) (0.581)
0.0120
0.0247
French Franc
-0.0026 -0.806
(0.0032) (0.928)
0.0326
0.0015
German Mark
0.0032 -3.542
(0.0043) (1.348)
0.0333
0.0287
Japanese Yen
0.0084 -1.813
(0.0032) (0.719)
0.0334
0.0201
Source: Backus, Foresi and Telmer (2001)
“Affine Models of Currency Pricing”
http://bertha.gsia.cmu.edu
18
190
Figure 6.14: The interest differential between Norwegian and German three
month interbank rates and the NOK/EUR exchange rate
4
3
2
1
0
10/26
11/30
1/04
2/08
3/15
NOK3-DEM3
2.09
2.08
2.07
2.06
2.05
2.04
2.03
10/26
11/30
1/04
2/08
LNOKEUR
191
3/15
ture, it is difficult to interpret the risk premium implicated by our findings. If
the risk premium was constant this should have been reflected in the finding
that a 6= 0, however that is not clear from the regressions in figure 6.13. If
the UIP shall match the data, the risk premium must fluctuate extensively.
This does not seem credible.5
Several explanations of the rejection of the UIP build on the presumption
that expectations are not perfectly rational. The peso problem is the idea
that investors expect a large correction of the exchange rate at some time,
they are however not certain when the correction will take place. If this
correction did not take place in the sample used to test the UIP, the UIP
will not hold.
In the regression (i−i∗ ) is known today while the actual value of e will first
be known in the future. The idea that expectations are an unbiased predictor
of future exchange rates will just hold if the environment is stable. If the
environment is unstable, one must expect investors to continuously update
their expectations. This ongoing learning process will create problems if we
try to test for the UIP.
Researchers have substituted actual data with expected depreciation rates,
as is reported in surveys from the financial markets. It shows up that if one
uses survey data instead of actual data, b tends to be close to one, and a is
significantly different from zero. This implies that on survey data the UIP
holds if one takes into regard a constant risk premium. People might indeed act according to the UIP, however their expectations are not the best
unbiased prediction of the future.
5
In the stock market one has attempted to use risk premiums as an explanation for the
high returns in equity compared with risk free assets. However, to make the model match
the data one must assume an incredible degree of risk aversion. The data simply does not
square at reasonable parameter assumptions.
192
Chapter 7
Portfolio choice, risk premia
and capital mobility
7.1
Introduction
The first six lectures have focused on how we should understand the exchange
rate from a macroeconomic point of view. If investors are rational and forward looking, we should expect the exchange rate to be determined by the
expectations of future values of certain economic variables, so-called fundamentals. We have discussed how the government would want to influence
the trade-off between an independent monetary policy and a stable exchange
rate, and investigated the limitations the government faces when it tries to
stabilise the exchange rate. Further we have looked at some institutional
factors of the exchange rate market. In the last lecture we discussed how
the equilibrium approach could be adjusted to better understand the actual
experience with floating exchange rates.
In this lecture we will turn to the investor. In the equilibrium model all
investors will be similar—everyone uses the same model, and has the same
expectations of the future. In Lecture 6 we made some attempts to modify
these assumptions. We looked at the possibility that agents might form their
193
expectations independently. In this lecture we will focus on the fact that
investors have different national affiliation. National affiliation must not be
understood as “citizenship”. Affiliation is decided by the the denomination
of costs and income. If your operating costs are paid in NOK, and your
sales are paid in NOK, how should you then adjust your currency holdings
to maximise your financial income?
7.1.1
Some notes on methodology
In economics one has tended to focus on utility maximisation when analysing
decisions under uncertainty. An economist is expected to work with as general specifications of the utility function as possible. The set up is as follows:
You control a number of variables, so-called choice variables. In addition
there is a number of factors you can not control, so-called state variables.
Let the choice variable be how much you will sow on a field. The state
variable will be the amount of rain that falls in the following months.
The payoff in the next period will depend on both factors. The more
you sow, the higher expected output. But output will be different for each
different state—it will depend on how much rain that falls. When you decide
how much to sow you must first make up your mind about the likelihood of
different states, e.g. the possibility of much rain, little rain or no rain. Then
you must calculate expected profits under each state. Having done this, you
can make a decision about how much to sow.1
This set up is of course also applicable to financial decisions. The statepreference framework concludes that the fundamental object of choice in
financial decisions are payoffs offered at different states of nature. However,
1
Just to point out how complicated this can get: assume that how much you can
sow next year depends on how much you do sow this year. In this case you must not
only calculate the possible outcomes for all states this year, you must also calculate the
outcomes for all possible states next year, and the year after that, and ... .
194
it is extremely difficult to list all payoffs offered at different states of nature.
As a result, the state-preference theory is almost without empirical content—
it is impossible to test it, as we can not characterise the objects of choice.
In finance this problem is solved by assuming that investors indifference
curves are defined in terms of the means and variance of asset return. It
is clear that this is only a very special case of the utility maximisation approach.2 However, in financial economics the possibility of empirical testing
is seen as more important than the generalisation of the theory.
In this lecture we will use the mean-variance analysis to derive demand
functions for foreign currency. The main idea behind the portfolio approach
to exchange rates is that assets in the home country and in the foreign country are not perfect substitutes. This is an important difference from the
monetary approach analysed in the previous lectures. In the monetary approach all assets are perfect substitutes, and the uncovered interest parity is
supposed to hold by assuming arbitrage. However, if similar assets at home
and abroad are not perfect substitutes the UIP will not hold—this leads to
the introduction of the concept of risk premium.
7.2
Demand for foreign currency
In the mean-variance analysis, the investor is assumed to maximise a utility
function, U , of the form
1
U = E(π) − Rvar(π),
2
(7.1)
where π is real rate of return on the portfolio, E is an expectation operator,
and R is the coefficient of relative risk aversion. We assume R > 0. The
higher R, the higher the risk aversion. High risk aversion implies that the
2
See appendix.
195
investor is willing to sacrifice more in the form of lower return if she can reduce
her risk. Risk is measured as the variance of return. In the currency market
risk is a factor because of uncertainty about depreciation and inflation.
The investor is assumed to hold two types of assets: domestic currency,
B, and foreign currency, F . Total real wealth, W , denominated in local
currency will be
W =
B F
+
,
P
P
(7.2)
where is the exchange rate. The share of total wealth the investor chooses
to hold in foreign currency is
F
.
PW
f=
(7.3)
The model treats f as the the choice variable. Given f , one can compute
F = f P W and B = (1 − f )P W .
Expected real return on the portfolio will be given by
·
·
·
·
·
π = (1 − f )(i − p) + f (i∗ + e − p) = (1 − f )i + f (i∗ + e) − p,
·
·
(7.4)
where i is the interest rate, p=rate of inflation, e=rate of depreciation and
∗
denotes foreign values.
·
We assume that p is a stochastic variable with the distribution
·
p ∼ N (µp , σ pp ).
(7.5)
µp is the expected mean of a change in inflation, and σ pp is the expected
standard deviation around the mean. Similar, we assume that
·
e ∼ N (µe , σ ee ).
·
·
(7.6)
The correlation between p and ee is σ ep . There is no uncertainty about the
196
interest rate, as it is observable today.
Given this, and using the rules for expectations and variances of linear
combinations of stochastic variables, we obtain
E(π) = (1 − f )i + f (i∗ + µe ) − µp ,
(7.7)
var(π) = f 2 σ ee + σ pp − 2f σ ep .
(7.8)
and3
If we substitute into equation (7.1) we obtain
1 U = (1 − f )i + f (i∗ + µe ) − µp − R f 2 σ ee + σ pp − 2f σ ep .
2
(7.9)
If we maximise with regard to f we obtain
δU
1
= −i + (i∗ + µe ) − R [2f σ ee − 2σ ep ] = 0.
δf
2
(7.10)
Solving (11.84) for f leaves us with
f=
σ ep
1
+
(i∗ + µe − i).
σ ee Rσ ee
(7.11)
We see that local investors demand for foreign currency increase as the
foreign interest rate increases, and decrease as the domestic interest rates
increases. Note that in the monetary model we assume the UIP to hold, which
implies that i∗ + µe − i = 0, as µe is just expected depreciation, Et (et−1 − et ).
In this model we assume that there is a risk premium on domestic currency,
r, that is given by
r = i − i∗ − µ e .
(7.12)
r is the extra return needed to hold domestic currency. Note that r can be
3
Remember that if z = αx + βz, and x and y is normally distributed, var(z) =
α σ xx + β 2 σ yy + 2 · αβσ xy .
2
197
negative—it might be that the risk is on the foreign currency.
Using the definition of r we can restate (11.48) as
f=
σ ep
r
−
.
σ ee Rσ ee
(7.13)
We see that the holdings of foreign currency can be divided in two terms.
The first term,
σ ep
,
σ ee
is called the minimum-variance portfolio, fM . This is
the share of foreign currency that minimises the variance of the return. The
second term, − Rσree , is the speculative portfolio, fS .
7.2.1
The minimum-variance portfolio
In this model we have no risk free asset, as the real rates of return in both
assets, i.e. domestic and foreign currency, are uncertain. It will only be
optimal to hold no foreign assets in the case when the correlation between
inflation and depreciation is zero. If the correlation is negative, one should
short-sell foreign currency. However, it is most reasonable to assume that
σ ep is positive. It would therefore be optimal to hold some foreign currency
in the minimum-variance portfolio.
One example can be to assume that PPP holds. Then we have that
·
·
·
e = p − p∗ . If domestic and foreign inflation is uncorrelated (σ pp∗ = 0), the
PPP implies that σ ee = σ pp + σ p∗ p∗ , and σ ep = σ pp . We can then write the
share of foreign currency in the minimum-variance portfolio as
fM =
σ pp
,
σ pp + σ p∗ p∗
(7.14)
and the share of domestic currency in the minimum-variance portfolio as
1 − fM =
σ p∗ p∗
.
σ pp + σ p∗ p∗
(7.15)
Note that if the variance of inflation in the home country goes to infinity,
198
e.g. because of hyperinflation, it would be optimal to hold only foreign
currency. If there is no inflation risk in one of the two countries, an investment
in that country would be equal to a risk-free investment. The investor would
minimise risk by only holding that currency. In general the investor should
divide her portfolio in inverse proportion to the variance in inflation in the
two countries.
An implication is that we should expect currency substitution in high
inflation countries. If inflation is spiraling out of control, domestic residents
should shift their holdings to foreign currency. This is actually what we
observe. In most high inflation currencies people tend to prefer to hold USD.
Domestic currency is only held in small amounts for transaction purposes.
In some hyperinflation countries people have actually substituted the local
currency with foreign currency as a means of payment.
If we instead assume that there is no correlation between prices and the
exchange rate we have σ ep = 0. In this case holding foreign currency would
only add risk, and the minimum-variance portfolio will only contain domestic
currency. In general deviations from PPP will create a preference for the
domestic currency in the minimum-variance portfolio.
7.2.2
The speculative portfolio
The speculative portfolio, − Rσree , depends on three parameters: the risk
premium, the risk aversion and the variance of the exchange rate.
First, observe that the sign is negative. This is due to the fact that
we define the risk premium as the risk premium of investing in domestic
currency. Remember that the risk premium is defined as i − i∗ − µe . If
this risk premium is positive one would optimise the speculative portfolio by
increasing the exposure in domestic currency. This can be done by borrowing
199
in foreign currency and investing at home. We see that the exposure to
foreign currency will decrease as the risk premium rises.
Second, the effect on the speculative portfolio of a change in R or σ ee
will depend on the sign of r. If risk aversion increases, the speculative portfolio will be reduced in size. If risk premium is negative, one will reduce
the exposure to foreign currency. However, if risk premium is positive one
will increase the exposure to foreign currency, as one reduces the speculative exposure to domestic currency. The same argument holds for increased
volatility in the exchange rate.
Capital mobility is the ability of capital to move freely across borders.
A high degree of capital mobility means that differences in expected return
have a strong effect on the supply of foreign currency. That should imply
that the share of foreign holdings in the investor’s portfolio should increase
if the risk premium decreases. The smaller the value of R and σ ee , the
more does a change in r affect the optimal currency portfolio. There will be
perfect capital mobility, fS → ∞, if risk aversion is zero, or it there is no
exchange rate risk (σ ee = 0). In this case all capital will flow to the country
with highest return. This should lead to the elimination of all risk premia,
implying a speculative portfolio of zero.
7.2.3
Empirical calculations
Let us take a look at Norwegian data for the period from January 1993
September 2001. Over this period we find
• σ ep = −1.85 ∗ 10− 5, and
• σ ee = 0.003850.
200
Note that these are results on monthly data. For the exchange rate we use
NOK/EUR (DEM before 1.1.99). This tells us that fM should be very small
in the Norwegian market—there is no reason to hold foreign currency to
hedge against inflation risk.
It is a general finding that the minimum-variance holdings of foreign
currency should be small for industrialised countries with stable inflation
rates. However, for countries with high inflation, this changes radically. Over
a high inflation period in Argentina it was found that the optimal holdings
of USD in the minimum-variance portfolio of an Argentinean investor was
86 per cent. As a comparison, the optimal holdings of USD for a German
investor was found to be 9 per cent.
Calculating the speculative portfolio is more difficult, not least because
we do not know the actual coefficient of the risk aversion. However, it is
usual to assume this to be around 2. Note that if the risk aversion is very
high, capital mobility becomes very low.
A simple estimate of the risk premium is to take realised interest rates
and return in the exchange market over the period we investigate. This is
obviously not the correct measure of the risk premium, as this depend on
expected values. However it should be reasonably close if we assume rational
expectations. I the case of Norway vs. Germany we find that over the period
from 1993 to 2001 we have
• i − i∗ = 0.0156
·
• e = −0.00034
The interest differential is the annualised value of the three month rates. We
·
use the mean of e as a measure of the expected depreciation.4 This leaves
·
4
One should however be aware that the distribution of e is severely skewed (it is not
normally distributed), so the mean might not be appropriate here. The median is as a
201
us with a risk premium, measured as an annual return, of r = 0.0156 ∗
−(−0.00034) ∗ 12 = .0198. Investing in NOK has over the last 9 years been
a purely win-win situation—you have got a higher interest rate than abroad,
and in addition the positive return from an appreciating currency.
The optimal speculative holdings of foreign currency by a Norwegian investor is found to be
fS =
−0.0198
= −0.214.
2 ∗ 0.00385 ∗ 12
(7.16)
Norwegian investors should have negative holdings of EUR. Norwegians should
borrow in foreign currency, and invest in Norway. In other words, they should
go short in foreign currency. In fact this is what we see—Norwegian banks
borrow extensively abroad to finance loans in NOK. And to a growing extent,
Norwegian households do the same. Note that foreigners should choose to
hold Norwegian currency.
7.2.4
Heterogenous agents
Capital mobility depends not just on the risk aversion, but also on how
much wealth, W , is actually invested. Assume e.g. that wealth is held
by two groups, households and professional investors. One would usually
expect that a household has a much higher coefficient of risk aversion than
a professional investor.
Assume only professional investors are active in the market, and that
these have a low R. Then even a small change in r or σ ee can lead to large
movements in the portfolio holdings of a currency. This can explain the
movements of currencies under speculative attacks. If a country has held a
high interest rate to attract foreign investors, we can expect these investors
comparison 0.00046—however both values are close to zero.
202
to hold mainly short term, liquid funds. If expected σ ee change, e.g. due to
a change in international circumstances, large funds might be extracted over
night.
One should also note that a the proportion of investors that take active
positions in the currency market might vary over time. If there is a cost of
obtaining information about the risk of investing in foreign currency, small
investors might prefer domestic currency. However, this will only be true up
to a certain point. If expected return in foreign currency increases beyond
the cost of investing, a large share of investors will shift from being “passive”
to being “active”. Such shift can be induced by dramatic movements in
interest rates, exchange rates or reserves. This might be one explanation for
contagion of currency crises, as we discussed in Lecture 4.
One should be aware that high R or high costs of information might not
be the only reason for not taking speculative positions in foreign currencies.
Many banks and insurance companies must fulfill regulations that often stipulate a limit for currency risk. That will regulate their ability to speculate
in the currency markets. An other factor might be credit constraints. If f
is outside the interval [0, 1] the investor must borrow money to obtain the
optimal portfolio.
7.2.5
Aggregate behaviour
Before we proceed we must understand the balance sheet of the economy.
Assume that we can divide the economy in three sectors,
• domestic government (superscript g),
• domestic private, and
• foreign (superscript *). Note that ‘foreign’ here will include both for203
eign private investors and the foreign government.
We retain the assumption of only two assets; domestic currency, B, and
foreign currency, F .
We are only looking at financial assets. Net financial holdings of an asset
summed over all sectors in the economy must be zero—investments made by
one group must be reflected as loans taken up by another group. In other
words: one agent’s assets are the liabilities of another agent.
A currency is the liability of the government. Net outstanding liabilities on the government must equal total holdings of domestic currency by
domestic private and foreign investors. We must have that
B g + B + B ∗ = 0.
(7.17)
This must also hold for foreign currency. We must have that
F g + F + F ∗ = 0.
(7.18)
Real financial wealth in for the private domestic sector, measured in domestic currency, will be
W =
B + F
.
P
(7.19)
Likewise, the real financial wealth of the foreign sector, measured in foreign
currency, will be
∗
W =
B∗
+ F∗
,
P∗
(7.20)
where P ∗ is the foreign price level.
If we use equation (11.53) and substitute that into (10.29) we obtain the
demand for foreign currency by domestic private investors,
PW
σ ep
r
PW
F =f
=
−
.
σ ee Rσ ee
204
(7.21)
Likewise we know that foreigner’s holdings of domestic currency, b∗ , which
from the point of view of the foreigner will be holdings of foreign currency,
will be
b∗ = −
r
σ ep∗
+
.
σ ee
Rσ ee
(7.22)
Note that we change signs, as the currency is defined as the price of foreign
currency in domestic currency. From the point of view of the foreigner a depreciation of the domestic currency becomes an appreciation of the currency
of his home currency, and vice versa.
The demand for foreign currency by foreign residents will then be
σ ep∗
r
F = (1 − b )P W = 1 +
−
P ∗W ∗.
σ ee
Rσ ee
∗
∗
∗
∗
(7.23)
Supply of currency to the central bank
If we insert equations (7.19-11.52) into (7.18), we obtain
σ ep
r
−
F =−
σ ee Rσ ee
g
B
+F
∗
σ ep∗
r
B
∗
− 1+
−
+ F . (7.24)
σ ee
Rσ ee
This can be restated as
σ ep
F =−
σ ee
g
∗
B
σ ep∗
B
r
B + B∗
∗
∗
+F − 1+
+F +
+F +F .
σ ee
Rσ ee
(7.25)
This gives us the supply of foreign currency to the domestic central bank. If
we e.g. think about the NOK/EUR market, this will be the supply of EUR
to Norges Bank.
How Norges Bank reacts to a change in supply of foreign currency depends on the exchange rate regime. In a floating rate regime F g is given
exogenously, and the right hand side of (7.25)) will determine the exchange
rate, as the exchange rate adjusts to clear the market. If the exchange rate
205
is fixed, F g must be adjusted to clear the market. This will be done through
interventions from the central bank.
If we draw a diagram with on the y-axis, and foreign reserves on the
x-axis, we tend to assume that supply of foreign currency to the central bank
will increase if the domestic currency fall in value,as we have done in figure
7.1.5 In other words, we expect
δF g
δ
> 0. This will hold if
∗
δF g
σ ep
B
σ ep∗
B
r
B + B∗
=
+ 1+
−
> 0.
δ
σ ee
2
σ ee
2
Rσ ee
2
(7.26)
This can be rewritten as
δF g
=f
δ
∗
B
B
∗
+ (1 − b )
> 0.
2
2
(7.27)
The condition will always be satisfied if both domestic and foreign investors
hold a positive amount of both currencies.
We can bring our understanding a little further. Let us make the convenient assumption that σ ep = σ ep∗ = 0. That is similar to a statement that the
PPP does not hold. We know that this implies that the minimum-variance
portfolio should contain no foreign currency. This is not unreasonable as a
short term description of a floating exchange rate.
Given this, we have that b∗ = −f . We also know that B = −B ∗ − B g . If
we substitute this into (11.59) we can solve for the condition of
δF g
δ
> 0 by
solving
f (−B ∗ − B g ) + (1 + f )B ∗ > 0.
(7.28)
B∗
> f.
Bg
(7.29)
We obtain
5
This is equivalent to assuming that demand for domestic currency rise as domestic
currency get cheaper, an assumption we used when drawing supply and demand for foreign
exchange in previous lectures.
206
We also know that B ∗ = −f P ∗ W ∗ , from which we obtain
P ∗W ∗
< −1.
Bg
(7.30)
B g is domestic currency issued by the central bank. As money is a liability
on the government, it must be assumed to be a negative number. (7.30) will
be equivalent to
P ∗W ∗
> 1.
−B g
(7.31)
P ∗ W ∗ is foreign wealth denominated in domestic currency. B g is domestic
currency issued by the domestic central bank. This will be a proxy for the
size of the domestic economy.
The implication is as follows: as long as foreign wealth is larger than the
domestic economy,
δF g
δ
> 0. In other words, if the foreign economy exceeds
the local economy, a reasonable assumption for most countries, the foreign
reserves will increase with a higher (weaker) exchange rate. However, note
that the slope of the line will depend on the ratio of foreign wealth to the
domestic economy. The smaller the domestic economy, the steeper the slope.
The intuition might be as follows: if the foreign currency reserves of the
domestic central bank increases, the holdings of domestic currency among
private domestic and foreign residents must increase. That follows from the
asset sheet of the central bank. Foreigners will hold more domestic currency if
this asset becomes cheaper—if it depreciates. Locals will retain more of their
earnings in domestic currency if it becomes more valuable—if it appreciates.
If both groups are equally large, the price of the currency need not adjust for
the market to absorb the increased supply of domestic currency. However, if
foreigners are the largest group, the price must depreciate. If locals are the
largest group, the price must appreciate, and the line will have downward
slope.
207
Figure 7.1: Supply of foreign currency to the central bank and the exchange
rate
e
Monetary policy,
fixed rate
Supply of foreign
currency to the
central bank
Monetary policy,
floating rate
Fg
208
What can we bring of this? A reasonable question is how the holdings of
F ∗ is affected by a shift in f . If we retain the assumption of σ ep = σ ep∗ = 0,
we can rewrite equation (11.57) as
F g = −f
PW
− (1 + f )P ∗ W ∗ .
(7.32)
Maximising with regard to f we then obtain that
δF g
PW
=−
− P ∗ W ∗ < 0.
δf
(7.33)
An increase in f will shift F g inwards in the diagram in figure 7.1. A fall in
f will shift F g out in the diagram in figure 7.1. If the central bank holds the
foreign currency reserves fixed, the central bank supply function is a vertical
line. Note that this gives an interesting application if we compare a small
country with a large country. In a small country the line is expected to be
steep. In a large country is almost horisontal. An implication will be that a
similar shift in f will cause quite different effects depending on whether we
are in a large country or a small country. In a small country the exchange
must adjust much more to balance the market than what is the case in a
large country. In previous lectures we have discussed the fact that small
countries and developing countries have tended to be sceptical to a freely
floating exchange rate. This might give an additional explanation of this
fact. In a country with a small economy small shifts in investor sentiment
might cause much larger impact on the exchange rate than what is the case
in rich and large countries.
A current account surplus
A current account surplus is the same as a shift in wealth from foreigners
to domestic private residents. A transfer of wealth shall not affect the spec209
Figure 7.2: Implications for how much the exchange rate much change to
clear the market if f change—small vs. large country
Small/poor country
e
Fall in ”f”
Effect, large/rich
country
Effect, small/poor
country
Large/rich country
Fg
ulative portfolio, only the minimum-variance portfolio. A positive current
account will increase the central banks holding of foreign currency if the
share of foreign currency is higher in the minimum variance portfolio of foreigners than of domestic residents, i.e. that there is home bias in currency
preferences. Mathematically speaking this can be expressed as
1+
σ ep∗
σ ep
>
.
σ ee
σ ee
(7.34)
This seems like a fairly reasonable assumption, not least given the empirical
numbers reported above. A country with a positive current account, like Norway, will accumulate foreign reserves. However, countries with substantial
negative current accounts shall, according to this rule, lose foreign reserves.
In our figure a current account surplus should lead to and outward shift
in F g . In a floating exchange rate regime a current account surplus should
lead to an appreciation of the domestic currency. However, as in the above
210
examples, the effect will depend on the relative size of the economy. A current
account surplus or deficit will presumably have less effect on the exchange
rate in a large countries like the US or Japan, than in small countries, like
Norway or Sweden.
One should note the following special case. If the PPP holds, we have
that σ ep∗ = −σ p∗ p∗ , σ ep = σ pp and σ ee = σ p∗ p∗ + σ pp . This would imply that
1+
σ ep
σ ep∗
=
,
σ ee
σ ee
(7.35)
as
σ p∗ p∗ + σ pp
σ p∗ p∗
σ pp
−
=
.
σ p∗ p∗ + σ pp σ p∗ p∗ + σ pp
σ p∗ p∗ + σ pp
(7.36)
When the PPP holds, the minimum-variance portfolio share should depend
only on the difference in inflation volatility between the two countries. Deviations from the PPP create a preference for the domestic currency. Current
account movements make no difference.
To understand the full effect on the government’s position one needs to
include government debt. If a country has a current account deficit there
will a drain of foreign reserves from the central bank. If it in addition has
a fiscal deficit it needs to finance this by issuing new debt. However, there
is no demand for domestic currency. So debt cannot be financed through
domestic currency bonds. The government has two choices:
• either it reduces foreign reserves, or
• it must borrow in foreign currency.
The first possibility is a short term solution. The second option might be
extremely expensive. A developing country with both substantial debts and
a current account deficit is not seen a especially creditworthy. If foreigners
211
doubt the long term prospects of the country, the demand for debt might
dry up.
Many developing countries are not able to finance their debt in long term
contracts. Much of the debt is short term. This implies that developing
countries are in the market for new loans not just to pay for a current deficit,
but also to refinance previous debts. If the borrowing possibilities in world
markets dry up, the country has to choose between depletion of the foreign
reserves or asking for a moratorium, i.e. a default on the foreign debt. This is
the story we see in countries like Russia in 1998, Brazil in 1999 and Argentina
in 2002.
Equilibrium risk premium
Let us restate equation (7.25) as
g
F = −fM
PW
− (1 −
b∗M ) (P ∗ W ∗ )
r
+
Rσ ee
PW
∗
∗
+ P W . (7.37)
If we solve for the risk premium, r, we obtain
r = Rσ ee
fM P W + (1 − b∗M )P ∗ W ∗
−F g
−
P W + P ∗ W ∗
P W + P ∗ W ∗
(7.38)
Note that as F g = −F − F ∗ , the last term can be written as
−F g
(F + F ∗
=
.
P W + P ∗ W ∗
P W + P ∗ W ∗
(7.39)
This is the share of foreign currency of total wealth held by private domestic
and foreign residents. Let us define this as f . As one can just hold two
assets, the share of total wealth held in domestic currency, b, must be
f = 1 − b.
212
(7.40)
The term
fM P W + (1 − b∗M )P ∗ W ∗
P W + P ∗ W ∗
(7.41)
gives the share of the minimum-variance portfolio of foreign currency of total
wealth. This tells us how much foreign currency investors will hold just to
minimise risk. Let us define this share as fM . Using the same argument as
above, we must have that
fM = 1 − bM .
(7.42)
This implies that we can simplify equation (7.38) to
r = Rσ ee b − bM .
(7.43)
We see that the risk premium is a product of three factors: R, σ ee and
fM − f . Risk premium will be high if risk aversion or exchange rate volatil
ity are high. This is a result of low capital mobility. b − bM tells us to which
extent investors are taking more exchange rate risk in the domestic currency
than the minimum that would optimise their portfolio. If “excessive risk”
goes up, the risk premium increases. b > bM implies that the market is “oversupplied” with domestic currency, so the risk premium must be positive to
make supply meet demand.
This is an equilibrium condition. We have previously defined r as
·
r = i − i∗ − e.
(7.44)
Interest rates and the expected depreciation must adjust to assure that equation (7.43) holds.
213
7.3
The collapse of a currency board
In previous lectures we have discussed the role of currency boards. A currency
board is an institution that guarantees to exchange the domestic currency in a
foreign currency at a given parity. The board is supposed to control an mount
of foreign currency that at least equals the amount of domestic currency in
circulation. On paper a currency board should be a fully credible institution
if the rules are followed. The risk of depreciation should be zero. If the UIP
holds there should be no risk premium on the country with the currency
board. However, when we discussed the case of Argentina in Lecture 3 we
found that (i − i∗ ) > 0 for the whole period since the currency board was
imposed in 1991.
7.3.1
Risk premium and the need for capital
In Argentina the trust of the government has been low for a long time. Even
with a currency board, it was reasonable to keep much of private holdings
in foreign currency. Foreigners would probably only place their money in
Argentina if it was for speculative purposes. So bM was probably low.
However, Argentina is a developing country with need for capital investments. There was need for b > bM to fulfill these needs. If this conditions
was to be satisfied, the equilibrium risk premium had to be positive. Both
Argentineans and foreigners would take advantage of this risk premium. As a
result Argentines held a negative speculative portfolio of foreign currency—
they borrowed money abroad and invested them in ARP assets.
7.3.2
Risk premium and expected depreciation
We need to give a short comment on the risk premium at this point. Expected
depreciation is not an easy term to handle. Even if domestic interest rates
214
are higher than foreign interest rates, the risk premium might be zero or
negative if expected depreciation exceeds the interest rate spread.
This makes it important to distinguish between risk premium at different time horizons. In most fixed exchange rate regimes it is only a small
probability that a devaluation will take place tomorrow. The probability of
a devaluation over the time frame of one week, or even one month is still relatively small. However, the longer the time span, the higher the probability
of an adjustment within that time span.6
In the case of Argentina, it was clear that the commitment to the currency
board was strong. The chance of a devaluation over night was considered
small. So if iARP > iU SD we should expect the short term risk premium in
Argentinean pesos to be positive. However, few believed the currency board
would exist for ever. So for long term investments the risk premium was
probably much smaller.
Note one implication for short term vs. long term capital flows: if we
believe the above argument, the risk premium tend to be higher in the short
run than in the long run in a fixed exchange rate regime. This encourages
the stream of short term capital over long term capital. A floating exchange
rate might increase the risk of adjustments in the exchange rate in the short
term. This will discourage short term flows.
One often assume that a country wants to attract long term capital. Long
term capital tends to be invested in firms with a long term horizon. This
might have give more utility for the home country than short term capital
flows. It is not clear whether expected depreciation over the long term will
be higher in a fixed or a floating exchange rate regime. If fundamentals are
important in the long run, it probably should make no difference. However,
6
This is the same argument as is applied in the “Peso problem” discussed in Lecture 6.
215
fixed exchange rate regimes often break down during periods of speculative
attacks. Speculative attacks tend to increase macroeconomic uncertainty for
some period of time. It might actually be that a fixed exchange rate regime
will discourage long term flows.
7.3.3
Effects of a fall in risk premiums
So what made the situation in Argentina unstable? Notice that if doubts are
created about the currency board, two things happen simultaneously:
·
1. Expected r will fall as expected depreciation, e rises.
2. σ ee rises as uncertainty rises.
It was clear that the competitiveness of Argentina had been eroded over a
long time. This was due to two factors:
• the USD was appreciating compared to other currencies. As a result
the ARP was appreciating compared to other currencies. In addition, a
Brazilian devaluation in 1999 had further worsened the competitiveness
of Argentine exporters.
• The fiscal deficit of Argentina created uncertainty about the long term
viability of the regime.
One option was to change the parity of the board. But the Argentine government repeatedly stated that the currency board would not be fiddled with.
However, in the middle of 2001 the Minister of Fiance, Domingo Cavallo,
openly suggested that leaving the currency board was an option.
Over night, the argument for taking speculative positions in the ARP
vanished. One held ARP because the risk premium was high. The risk
premium was high because one believed the currency board to be credible.
216
In the new situation everyone wanted to re-balance their portfolios with less
risk in ARP and more risk in USD.
Everyone went to the bank to exchange currency holdings of ARP into
USD. At the same time they wanted to close their ARP deposits. Remember
that people had loans denominated in USD and deposits denominated in
ARP.
According to the rules of a currency board, the board should be able to
redeem every currency note in circulation at parity. However, in this case
the currency in circulation was increasing fast, as everyone were withdrawing
deposits in exchange for currency. So possible demands on the currency board
far exceeded the amount of USD actually held by the board.
Further, the banking system was on the verge of collapse. The banks had
most of their assets in the form of long term USD loans. They did not have
sufficient reserves in ARP to cover all ARP deposits. The banks were not
able to redeem their holdings of ARP since they did not have the money in
their vaults. In this case the speculative attack on the currency was at the
same time a speculative attack on the banking system.
The government had two choices:
1. They could devalue over night. However, as most Argentineans had
loans in USD, and the cost of these loans would increase dramatically
if the currency collapsed, this option would certainly lead to immediate
social unrest. Indeed the government probably hoped they could retain
the currency board.
2. They could restrict the currency in circulation. The way of doing so was
to restrict the amount one could withdraw from the banks. The hope
was that this could give the government time to restore credibility. If
the amount of currency in circulation was restricted, it was possible to
217
redeem the currency that was in circulation into USD, thereby showing
that the system worked. At the same time one avoided a collapse of
the banking system. The problem was that this system was both unfair
and very problematic.
(a) It was unfair because they who had redeemed their money before
the restrictions now seemed to get a better deal—they could exchange their money at parity. Those who had trusted the system
got screwed.
(b) As we all know, most of us depend on the possibility to take
money out of our accounts every week if we shall be able to pay
our bills. Over night this possibility was restricted. Many middleclass Argentineans found themselves in grave liquidity problems.
On top of this the Argentinean government needed to borrow money.
Argentina had both a fiscal and a current account deficit. Foreigners were
of course doubtful about the long term prospects of Argentinean debt, not
least because the country was asking for a moratorium on existing debt. The
Argentinean government had to borrow at home. But nobody wanted to hold
domestic currency. The only way to solve the problem was to force people to
hold government debt. State wages were paid in government bonds. State
debts were paid in government bonds.
This further undermined the credibility of the system. On the one side the
government tried to reduce the amount of ARP in circulation to strengthen
the credibility of the currency board. On the other side they issued something
looking very much like new money in everything but the name. Argentina
became a country with many currencies. State bonds were used as means
of payment, although they were accepted to much under their face value.
218
Argentina was de facto experiencing inflation out of control.
The system could not work over time. People went on the streets demanding their money. The currency board was abolished, and the ARP
depreciated with about 50 per cent against the USD. To sweeten the pill
people were allowed to exchange their USD loans in Argentinean banks into
ARP loans at the old parity, at an unidentified cost to the government. Argentina declared that they were unable to repay foreign debts. The country
went into a state of total disarray from which it has yet, as of May 2002, to
emerge.
7.4
Empirical applications of the portfolio choice
model
There are two main problems if we want to test the above theory.
1. We have made very simplistic assumptions of monetary policy. The
most reasonable would be to assume a central bank reaction function
that was neither horisontal nor vertical, but downward sloping. The
actual slope is probably difficult to identify.
2. In practice we can observe the flow of private, government and domestic
holdings of foreign currency. However, we can not observe the stocks
involved. In the science of accounting it is by no means certain that
flows and stocks are compatible. However, one can perhaps argue that
observing flows might be sufficient if the focus of the analysis is on the
change in the exchange rate—not the level of the exchange rate.
One of the results above was that one should expect portfolio shifts to
have more impact in small than in large countries. One implication might
219
be that small floating currencies are more volatile than large floating currencies. That is not an obvious result from empirical data. Testing equality
of variance in daily returns on EUR/USD, SEK/USD and NOK/USD from
01/01-1999 to 04/01-2002 we find that there is no difference in the variance when we compare EUR/USD and SEK/USD. However, the variance in
NOK/USD is significantly lower than for the two other exchange rates.
It is very difficult to evaluate whether this is a result of our theory being
wrong, or if the Norwegian and Swedish governments make a stronger effort
to sterilise the effects of changes in currency flows on the currency than the
Federal Reserve does. This might be the case even though both Norway
and Sweden claim to have a freely floating exchange rate. Norway provides
an interesting example. Although there has been no “intervention” since
the beginning of 1999, Norges Bank is continuously active in the market,
accumulating foreign exchange that is invested in the government controlled
“Petroleum Fund”. It is hard to identify the actual effects on the exchange
rate from these activities. Likewise, we observe that Svenska Riksbanken is
de facto accumulating reserves in periods of current account surplus. Is this
just a random event, or the results of a conscious strategy?
7.5
Appendix
7.5.1
Mean-variance vs. state-preference
The mean-variance approach will match the state-preference utility maximisation if:
1. Preferences are time separable—the utility of consumption in the next
period does not depend on the current level of consumption.
2. The relative risk aversion is constant over time.
220
Figure 7.3: ARP/USD exchange rate 1998-2002
4
3.5
3
2.5
2
1.5
1
0.5
01.05.02
01.03.02
01.01.02
01.11.01
01.09.01
01.07.01
01.05.01
01.03.01
01.01.01
01.11.00
01.09.00
01.07.00
01.05.00
01.03.00
01.01.00
01.11.99
01.09.99
01.07.99
01.05.99
01.03.99
01.01.99
01.11.98
01.09.98
01.07.98
01.05.98
01.03.98
01.01.98
0
3. Both the price level, P , and the exchange rate, , follow Wiener processes, or Brownian motions. This implies that that level of return in
·
·
the two variables, p and e, are normally distributed and independent
over time.
4. Expectations, variances and covariances are constant over time.
7.5.2
The exchange rate
The most simplistic way to write equation (7.25) will be
g
F = −f
PW
− (1 − b∗ ) (P ∗ W ∗ ) .
(7.45)
If we solve this for the exchange rate we obtain
=
−f P W
.
F g + (1 − b∗ )P ∗ W ∗
221
(7.46)
In previous lectures we have stated that in a floating exchange rate regime
the central bank will hold no foreign reserves. We simplify by setting F g = 0.
We then obtain
=
−f W P
.
(1 − b∗ ) W ∗ P ∗
(7.47)
Remember that the PPP states that the exchange rate is given as
=
P
.
P∗
(7.48)
In this framework one ratio will differentiate the exchange rate from the PPP
rate: the ratio of nominal wealth held in the foreign currency unit. If this
fraction is shifting over time, we should expect to see the nominal exchange
rate changing, and we should also expect a correlation between the real and
the nominal exchange rate.
222
Chapter 8
The real exchange rate and
capital flows
8.1
Some notes on research strategy
Modern macroeconomics is built on analysing the maximising behavior of
agents in a general equilibrium multi period setting. Although this research
has been going on for some time—the book of Obstfeld and Rogoff from 1996
is probably the best summary of this kind of analysis in an open economy
framework—many questions remain unsolved. However, interesting questions can now be analysed in such a framework. Not least, this framework
allows to discuss questions in a more dynamic setting than what is possible
in the traditional models, like the Swan diagram or the Mundell-Fleming
model.
8.2
Some empirical observations
We remember that the real exchange rate, Q is defined as
Q=
P∗
.
P
223
(8.1)
Figure 8.1: The real exchange rate. DEM/USD
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
jul.98
jul.97
jul.96
jul.95
jul.94
jul.93
jul.92
jul.91
jul.90
jul.89
jul.88
jul.87
jul.86
jul.85
jul.84
jul.83
jul.82
jul.81
jul.80
jul.79
jul.78
jul.77
jul.76
jul.75
jul.74
jul.73
0
Real exchange rate calculated using CPI.
A central assumption in the monetary equilibrium model was the purchasing
power parity—the belief that arbitrage would assure that the real exchange
rate is constant over time. However, if we use the consumer price index as a
proxy for the price level, and calculate the real exchange rate, we find that
for most countries this is certainly not constant. Two examples are given in
figures 8.1 and 8.2.
Using the CPI for such measurement is not unproblematic. The weights
of goods in the CPI will differ between countries, and they will change over
time. Relative prices will change with changes in tariffs or taxes. However,
the findings illustrated in figures 8.1 and 8.2 are fairly representative for
the results reported in numerous empirical studies of the PPP. For countries
at about the same level of productivity, the PPP seems to hold over time,
although the real exchange rate tends to move in long swings, with a mean
reversion of about 3-6 years. The length of this cycle has been described
224
Figure 8.2: The real exchange rate. JPY/USD
1.2
1
0.8
0.6
0.4
0.2
jul.01
jul.00
jul.99
jul.98
jul.97
jul.96
jul.95
jul.94
jul.93
jul.92
jul.91
jul.90
jul.89
jul.88
jul.87
jul.86
jul.85
jul.84
jul.83
jul.82
jul.81
jul.80
jul.79
jul.78
jul.77
jul.76
jul.75
jul.74
jul.73
0
Real exchange rate calculated using CPI.
as a “puzzle”, given that the most reasonable explanation for swings in the
real exchange rate, sticky prices, should imply a mean reversion of about 1
year—in other words much faster than what is observed.
For countries with more marked differences in technical development the
PPP does not seem to hold. A general result is that countries with high
economic growth tend to experience real appreciation over time. This is
clearly illustrated in the case of Japan in figure 8.2.
8.2.1
Differences in the price level
Implicit in the assumption of purchasing power parity is the assumption that
over time the ratio of price levels will be one if measured in the same exchange
rate, i.e. =
P
.
P∗
The implication is that the price level should be the same
across countries.
Price levels are very difficult to measure. The standard measure of prices
225
published by statistical bureaus is the consumer price index, the CPI. However, the CPI does not measure the price level, only relative change in the
cost of a basket of consumption goods. The best measure of actual price levels is provided in the Penn World Tables, where prominent economists have
done empirical estimates of the relative price of comparable goods baskets
for a number of countries. These tables are only available with a lag of many
years—the most recent numbers are from the mid-1990’s.
However, what is clear from these data is that the price level is not the
same across countries. In general one finds that the price level is much higher
in countries with high income per capita. An interesting test of this result
can be found if we compare the numbers in the renown “Big Mac index”
published by The Economist in the end of April every year. The Economist
collects the price of a Big Mac sold by MacDonalds in a number of countries.
It calculates the price in USD at the current exchange rate. If absolute PPP
holds, the price of one Big Mac should be the same as in the US.
Of course, there are a number of problems using a Big Mac as an indicator
of the price level. This is one very specific good, not very representative of
“normal” consumption. One the other hand it is a very standardised good.
We are in fact pretty certain that we compare identical items across boarders.
The item contains both tradable parts, like beef and bread, and non-tradable
parts, like labour input.
Table 8.1 gives the price of a Big Mac measured in USD for seven different
countries. We can summarise some stylised facts from the table:
• The price is clearly much higher in the five industrialised countries than
in China and Russia.
• The prices are fluctuating over time.
226
• With the exception of Russia the price has moved towards the US price
from 1995 to 2002. This might be an indication that price levels over
time tend to converge.
Table 8.1 also illustrates how difficult it is to compare welfare when we
compare gross domestic product per capita using the nominal exchange rate.
If a Norwegian earn 30,000 USD a year, he can purchase 7,300 Big Macs...
However, in China, a wage of only USD 9300 will suffice to get the same
amount of food. To get a true picture of the purchasing power in Norway
and China income per capita must be adjusted for differences in price levels.
These are so-called PPP-adjusted per capita output numbers. Table 8.1 gives
a very simplified shoot at such estimates. Of course, one should be cautious
when interpreting such numbers.1 However, the table clearly illustrates that
output per capita measured in actual exchange rates is not a good measure
of the welfare of nations. Norway might be one of the richest countries in
the world. That does not necessarily imply that Norwegians are the people
best of—in fact purchasing power of Norwegians is (at best) in line with the
purchasing power of other Western European countries.
8.3
Accounting for what we do not know about
the real exchange rate
The data does not match with the assumptions used in previous lectures.
To understand what we do not understand, it can be useful to make a short
1
E.g. the GNI numbers and the Big Mac prices are not transferred into USD at the
same exchange rate. The GNI numbers use the World Bank method of the average rate
over three years (in this case 1999, 2000 and 2001), and adjust for inflation differences to
the the average of the inflation level in the G5 countries (USA, Japan, Germany, France
and Great Britain). The Big Mac price is calculated in USD at the spot exchange rate as
of April 2002. This probably leads to an overestimation of the “welfare” in Japan, and an
underestimation of the “welfare” in Europe compared to the US.
227
228
Sources: The Economist and The World Bank.
The first two columns give the the price of a Big Mac in seven different countries. Measured in USD at current
market exchange rate. Ratio is the country price price relative to the US. GNI per capita is numbers for 2000,
measured at the “Atlas method”, a three year average exchange rate. The PPP adjusted GNI per capita is the
GNI adjusted with the relative cost of BigMac in 2002.
Table 8.1: Price levels and welfare. Relative price level measured as price of a Big Mac in 1995 and 2002
1995 2002 Ratio GNI per capita Ratio to US PPP adj. GNI per capita Ratio to US
Norway
n.a. 4.09
0.61
33650
0.98
20486
0.60
Switzerland 5.20 3.81
0.65
38120
1.11
24913
0.73
USA
2.32 2.49
1.00
34260
1.00
34260
1.00
Germany
3.48 2.37
1.05
25050
0.73
26318
0.77
Japan
4.65 2.01
1.24
34210
1.00
42380
1.24
China
1.05 1.27
1.96
840
0.02
1647
0.05
Russia
1.62 1.25
1.99
1660
0.05
3307
0.10
summary.
First, let us restate the covered interest rate parity, a parity we know will
hold with certainty. The CIP can be written as
et = i∗t,T − it,T + ft,T .
(8.2)
when we it,T is the interest rate over the period from t to T . Further, we
can define the premium for bearing exchange rate risk—taking the chance on
buying the exchange rate spot at time T instead of securing the price today
by buying the exchange rate forward to ft,T —as the risk premium, r, which
can be defined as
rt,T = ft,T − Et (eT ).
(8.3)
If we substitute (8.2) into (8.3) we obtain
et = i∗t,T − it,T + rt,T + Et (eT ).
(8.4)
Let us define the real interest rate, ir , as
irt,T = it,T − (Et (pT ) − pt ).
(8.5)
If we substitute (8.5) into (8.4) we obtain
∗
∗
r
et = (ir∗
t,T + Et (pT ) − pt ) − (it,T + Et (pT ) − pt ) + rt,T + Et (eT ).
(8.6)
The real exchange rate, q, is defined as
qt = et + (p∗t − pt ).
(8.7)
Reordering, and using (8.7) we obtain
r
qt = ir∗
t,T − it,T + rt,T + Et (qT ).
229
(8.8)
The real exchange rate is given as the real interest differential, the expected
risk premium and the expected future real interest rate. In theory this should
be valid for any choice of T , but generally q is assumed to move towards some
equilibrium value over time, so the equation is probably most interesting
when analyzed over some time horizon.
But what does this actually tell us? Variability in the real exchange rate
can be transmitted through three channels:
• variability in the real interest differential,
• variability in the risk premium, and
• variability in the expected real exchange rate.
Empirical evidence suggests that the real interest rate does not explain much
of the variability in the real exchange rate. This leaves us with the risk
premium and the expected real exchange rate.
The effects of variability in the risk premium was discussed in lecture 8.
In general risk premiums will be of most interest if we assume that there are
some kind of imperfect substitution between holding domestic versus holding
foreign assets. As we saw, such differences might explain substantial swings
in capital flows.
In this lecture we will focus on the variability in the expected real exchange rate. Analysis of the expected real exchange rate must be seen together with the concept of “external balance” in the economy.
8.3.1
External balance
Defining external balance is not obvious. In more classic models, like the
Swan-diagram that analysis the relationship between “internal” and external balance, external balance is a balanced current account, and and internal
230
balance is an unemployment rate equal to the long term non-inflation accelerating rate of inflation (NAIRU). However, external balance need not mean
a balanced current account in a dynamic framework; at least not in the short
or medium term.
External balance will generally be achieved if the current account is consistent with “desired capital flows”. But what is “desired capital flows”?
First note that if the economy is in “equilibrium”—population is stable and capital intensity is according to the “golden rule” and there is no
unexpected changes, just to mention three requirements—then the current
account probably should be zero. These are not realistic assumptions. Different measures will affect long term prospects:
• If there is any sort of “consumption smoothing” in the economy, it will
be optimal to try to spread the effects of shocks between periods. If
there is a negative shock today, and we expect this to be temporary,
we would borrow today to smooth the consumption pattern. However,
on the national level borrowing is reflected as a current account deficit.
• “Structural shocks”: if a country finds e.g. natural resources, the structure of the economy must be expected to change to take advantage of
these opportunities. Very simplified such an economy can be expected
to venture through three periods:
1. An investment period, where income from production is low, and
costs are high.
2. A period of collecting rent from the resource.
3. A period of restructuring, as the fields are emptied.
From beginning to end the current account should accumulate to zero.
However, over the time from the source is found until it has been fully
231
extracted, we should expect the current account to be negative in the
initial period, positive in the producing period, and negative again as
saved income is used to build new industries.
• Imbalances in demographic developments should probably be reflected
in long periods with a current account different from zero, without this
reflecting an imbalance in the economy. E.g. the USA has a demographic profile very different from other developed nations, a fact that
can probably explain much of the US current account deficit. Most
developed countries must save to finance the increase of pensioners
relative to the working part of the population. The US will not experience this for many years, and can therefore for the time being focus
on investments instead of saving.
In fact, modern economics is still searching for models that can describe the
external balance over time. It is clear that our current knowledge does not
give a full description of how we should expect the current account to behave
in a dynamic framework. This also affects our ability to understand the real
exchange rate.
8.4
Explaining long term shifts in the real exchange rate
Note: section 4 is not required reading in GTA1333/6607. You should however be familiar with the main conclusions, as summarised in De Grauwe, ch.
5.3.
When we looked at figures 8.1 and 8.2 we saw that the behaviour of the
real exchange rate seemed to differ quite markedly in the case of DEM/USD
232
and JPY/USD. In the first case the real exchange rate was fluctuating around
1. In the second case, we clearly see a consistent downward trend.
The assumption of PPP builds on the law of one price, that states that
the price of a good that is traded between countries should be equal between
countries, give or take transportation costs between the two destinations. If
the law of one price, arbitrage should increase demand where the good is
expensive, and reduce supply where the good is cheap. However, empirical
analysis only find support for the law of one price in the case of storable,
highly traded goods, like corn, metals and oil. For most goods the law of one
price does not hold. Possible causes might be
• transportation costs,
• trade barriers, and
• non-competitive market structure.
For some goods transportation costs are so high that they are hardly
traded at all. These are non-tradable goods. One should not forget that
all goods sold will have contents that are not tradable across boarders, like
the cost of handling in the import country. The role of non-traded goods
is important if we want to understand structural shifts in the real exchange
rate.
8.4.1
The Balassa-Samuelson effect
The Balassa-Samuelson effect is an attempt to explain why poor countries
tend to experience real appreciation. The building block is that countries
with higher productivity in tradables compared with non-tradables tend to
have a higher price level. High growth is accomplished through high growth
in tradables. As productivity in the traded sector rise, the wage level in
233
this sector rises. However, if there are inter-sector labour mobility, this will
cause a rise in the wage level in the sector producing non-traded goods. To
compensate increased wage levels at a constant productivity, the price of
non-traded goods must rise. It follows that countries with high growth will
experience a rise in the price level, and thereby a real appreciation.
The price level in a two sector economy
The driving force in the following results will be our assumptions about the
movement of capital and labour. We assume that capital can move freely
between countries. We look at a small country. This assures that the real
interest rate, here denoted as i, will be the at home and abroad. The interest
rate is given exogenously. Labour is not mobile between countries. However,
it is assumed to be freely mobile between sectors in the economy. As a result
the average wage level, w, will be the same in all sectors.2 This is only
a realistic assumption if we look at the economy over time—this must be
perceived as a description of long term price adjustments.
The exogenous interest rate and the equalisation of the wage level between
sectors give the domestic economy a certain flexibility to meet shocks to
demand and supply. An increase in domestic demand should increase the
price level of non-traded goods. However, at the same time, an increase in
demand should lead to more capital and labour employed in the non-traded
sector. It can be shown that our assumptions of capital and labour mobility
is enough to assure shocks to domestic demand will not affect the relative
price of non-traded goods in this economy.
Note that we focus on the real effects to the real exchange rate. This
implies that we disregard money. All prices will be measured relative to the
2
The way to think about this is that two persons with the same education and background will receive the same wage in both sectors.
234
price of a traded industrial good, Pi , a price we set equal to 1. This implies
that in the following analysis we assume
• no nominal rigidities,
• no feedback from money, and
• no risk premium.
These assumptions are not credible in the short term. This implies that the
models are best fitted to explain medium or long term movements in the real
exchange rate.
The economy has two sectors. The traded sector is producing two goods,
industrial goods and a natural resource, e.g. oil. The price of industrial
goods is set to 1. We assume that extraction of oil returns a rent of τ in
excess to the price of industrial goods. The amount of oil produced make
up a share γ of total production of industrial goods. We then have that the
average income from one good sold in the traded sector must be
(1 − γ) · 1 + γ(1 + τ ) = 1 + γτ .
(8.9)
The price of non traded goods is measured in quantities of industrial goods.
The price is set to Pd .
The production function of the traded sector is given as At F (Kt , Lt ),
where At is the level of productivity in the traded sector, Kt is the level of
capital stock, and Lt is the labour employed in this sector. The production
function in the non-traded sector is Ad G(Kd , Ld ), where
d
denotes the non-
traded sector. Both production functions have constant returns to scale.
Total supply of labour, L, must be the labour employed in the traded and
non-traded sector combined, L = Lt + Ld . There is no unemployment in this
economy, and prices are fully flexible.
235
Over time excess profit must be zero in both sectors. This gives us two
equilibrium conditions. For the traded sector we must have that
∞ X
s=t
1
1 + is
[(1 + γ s τ s )At,s F (Kt,s , Lt,s ) − ws Lt,s − is Kt,s ] = 0.
(8.10)
For the non-traded sector we must have that
∞ X
s=t
1
1 + is
[(Pd,s Ad,s G(Kd,s , Ld,s ) − ws Ld,s − is Kd,s ] = 0.
(8.11)
If there are no unexpected shocks, these conditions are expected to hold
in every period. Under this assumption we can remove the time notation,
and state that
(1 + γτ )At F (Kt , Lt ) − wLt − iKt = 0,
(8.12)
Pd Ad G(Kd , Ld ) − wLd − iKd = 0.
(8.13)
and
In macroeconomics we often state output as a fraction of employment.
Let us define capital per employee in the traded sector as
kt =
Kt
.
Lt
(8.14)
As the production function has constant returns to scale, we have that
F (Kt , Lt ) = Lt F
Kt L t
,
Lt Lt
= Lt f (kt ).
(8.15)
Likewise, we have that
kd =
Kd
,
Ld
(8.16)
and
G(Kd , Ld ) = Ld G
Kd L d
,
Ld Ld
236
= Ld g(kd ).
(8.17)
We can no restate equations (8.12) and (8.13) as
(1 + γτ )At f (kt ) − w − ikt = 0,
(8.18)
Pd Ad g(kd ) − w − ikd = 0.
(8.19)
and
These are equilibrium conditions. But what happens if there is a marginal
change in one of the variables? If we take the total differential of equation
(8.18) we obtain
τ At f (kt )dγ + (1 + γτ )f (kt )dAt + (1 + γτ )At f 0 (kt )dkt − dw − idkt = 0, (8.20)
As i and τ are given exogenously, so we hold them constant. Note that if you
take the differential of equation (8.10) with regard to Kt you obtain that
(1 + γτ )At FK (Kt , Lt ) = i,
(8.21)
δF (Kt , Lt )
.
δKt
(8.22)
where
FK (Kt , Lt ) =
From this we know that
(1 + γτ )At f 0 (kt ) = i,
(8.23)
as
FK (Kt , Lt ) = Lt
1 0
f (kt ) = f 0 (kt ).
Lt
(8.24)
We can then restate equations (8.20) as
τ At f (kt )dγ + (1 + γτ )f (kt )dAt + idkt − dw − idkt = 0.
(8.25)
It is easier to interpret this equation if we look at percentage changes. If dx
237
is the change in x, then
dx
x
is the percentage change in x. Further we want
to look at percent of total output in the traded sector, (1 + γτ )At f (kt ). If
we divide (8.25) by (1 + γτ )At f (kt ) and rearrange we obtain
w
γτ
dγ dAt
dw
+
−
= 0.
(1 + γτ ) γ
At
(1 + γτ )At f (kt ) w
(8.26)
Let us define labour’s share of total output in the traded sector as
µLt =
wLt
.
(1 + γτ )At F (Kt , Lt )
(8.27)
As (1 + γτ )At Lt f (kt ) = (1 + γτ )At F (Kt , Lt ) we can restate equation (8.26)
as
dγ dAt
wLt
dw
γτ
+
−
= 0.
(1 + γτ ) γ
At
(1 + γτ )At F (Kt , Lt ) w
(8.28)
Rearranging, we obtain
µLt
dw
γτ
dγ dAt
=
+
.
w
(1 + γτ ) γ
At
(8.29)
If we turn to the non-traded sector, we find that the total differential of
equation (8.19) as
Ad g(kd )dPd + Pd g(kd )dAd + Pd Ad g 0 (kd )dkd − dw − idkd = 0.
(8.30)
We know that
Pd Ad g 0 (kd ) = i,
(8.31)
Ad g(kd )dPd + Pd g(kd )dAd − dw = 0.
(8.32)
so (8.30) can be simplified as
As above, we can define labour’s share of output in the non-traded sector as
µLd =
wLd
.
Pd Ad F (Kd , Ld )
238
(8.33)
Dividing by total output in the non-traded sector, and rearranging, we obtain
dw dAd
dPd
= µLd
−
.
Pd
w
Ad
(8.34)
We have obtained an expression for the price level of non-traded goods.
However, the wage level must be the same in both the traded and the nontraded sectors. This implies that there must be a relationship between the
two sectors. From equation (8.29) we can obtain an equation for
dw
.
w
If we
subsitute this into (8.35) we obtain
dPd
µLd
γτ
dγ dAt
dAd
=
+
−
.
Pd
µLt (1 + γτ ) γ
At
Ad
(8.35)
The fraction of labour’s share of output in the non-traded over the traded
sector,
µLd
,
µLt
can be assumed to be bigger than one. In general the non-traded
sector is more labour intensive than the traded sector.
If productivity in traded goods rise while productivity in non-traded
goods remains constant, the price of non-traded goods will rise. We also
see that a higher share of “high rent” products in the traded sector will rise
the price of non-traded goods. The intuition is simple: more high rent products lead to a rise in the wage level in the traded sector. This puts pressure
on the wage level in the non-traded sector, and forces up the price of nontraded goods. Norway, a country that has experienced a substantial change
in the composition of traded goods over the last 30 years, is a good example.
The increase in the share of high rent products in Norwegian exports have
put pressure on wages in other sectors in the Norwegian economy, raising
Norwegian prices. This is one explanation for the high Norwegian price level
documented in table 8.1.
3
3
As noted above, the price level in non-traded goods does not depend on domestic
demand for non-traded goods in this model.
239
In general one assumes that productivity growth is higher in the traded
than in the non-traded sector. This is the so-called Baumol-Bowen Paradox.
The reasoning is that the non-traded sector is dominated by services. These
are labour intensive, with low capital input per worker. Many examples of
services, like hair cutting, health care or cultural activities, depend on high
input of manual labour. Quality of such services can be made better by
machines, but only to a limited degree.
It is a general assumption that rich countries are rich because of their high
productivity in traded goods. An implication is that rich countries should
be expected to have a higher price level than poor countries. Again, this is
in line with the empirical facts stated above.
The price index and the real exchange rate
The real exchange rate is the ratio of national price levels. In this case the
price level will be the cost of some representative basket of consumption
good. The terms of trade is the ratio of relative prices of exports to the
relative prices of imports. The terms of trade tells us something about the
competitiveness of the national economy.
Let us assume that the price index is made up of traded and non-traded
goods. For simplicity, let us assume that the price of non traded goods is Pd ,
and the price of traded goods in local prices is Pt . The weight of non traded
goods is σ, and the weight of traded goods is (1 − σ). If we assume that the
price index, P , is made up as geometric average, P is given as
P = Pdσ Pt1−σ .
(8.36)
For simplicity we assume the relative consumption of traded and non-traded
good to be the same between countries. The foreign price index, P ∗ , is then
240
given as
∗(1−σ)
P ∗ = Pd∗σ Pt
.
(8.37)
We assume the exchange rate between the two countries to be fixed at 1:1.
The ratio of home-to-foreign prices become
Pdσ Pt1−σ
P
=
.
P∗
Pd∗σ Pt∗(1−σ)
(8.38)
However, it is reasonable to assume that the price of traded goods will be the
same—eventual price differences will just be traded away. So we can simplify
equation (8.38) to
P
=
P∗
Pd
Pd∗
σ
.
(8.39)
This has an important implication for the real exchange rate. If we ignore
shocks to the nominal exchange rate, changes in the real exchange rate will
depend on the relative prices of non-traded goods.
If we take the total derivative of equation (8.39) we obtain
1
−Pd
σ
dPd + ∗2 dPd∗
∗
Pd
Pd
σ−1
= 0.
(8.40)
= 0.
(8.41)
If we rearrange, we obtain
Pd dPd
Pd dPd∗
σ
−
Pd∗ Pd
Pd∗ Pd∗
σ−1
This can be rewritten as
dPd dPd∗
− ∗
Pd
Pd
σ−1
= 0.
We have already obtained an expression for
241
dPd
.
Pd
(8.42)
If we substitute in from
equation (8.35) we obtain
∗ σ∗ −1
γτ
dγ dAt
dAd
µLd
γ∗τ
dγ ∗ dA∗t
dA∗d
µLd
+
−
−
+ ∗ − ∗
= 0.
µLt (1 + γτ ) γ
At
Ad
µ∗Lt (1 + γ ∗ τ ) γ ∗
At
Ad
(8.43)
We make two simplifying assumptions. We focus on differences in productivity, and assume that γ = 0 for both countries. Further, we assume that
µLt and µLn is the same in both countries. We can then rewrite (8.44) as
σ∗ −1
dAd dA∗d
µLd dAt dA∗t
− ∗ −
− ∗
= 0.
µLt At
At
Ad
Ad
(8.44)
Changes in the real exchange rate will depend on the relative changes in
the traded and non-traded sectors. Countries with relatively higher growth
in the traded sector will experience a real appreciation as the price level of
non-traded goods in these countries increase relative to the price level of
non-traded goods in the other countries.
8.5
Fluctuations in the real exchange rate and
capital flows
The following model is an example of an intertemporal approach to modelling
the real exchange rate. This is a two country-two goods model, assuming that
each country are producing separate goods, and that all goods are traded.
Even in this “simple” framework we can achieve some interesting implications about how shocks to the economy should be expected to affect the real
exchange rate, and how capital flows and trade patterns might influence the
the movement in the real exchange rate.
242
8.5.1
Model of two countries and terms of trade shocks
We are in a two-country world, where each country produce a single good.
The home country produces good H, and the foreign country good F . Each
good has the price of unity measured in the local currency. The relative
price of the two goods, which is the same as the real exchange rate, Q, will
be measured as the price of one unit of foreign good denominated in home
currency,
Q=
PF
.
PH
(8.45)
This is in line with the definition of the exchange rate used in this course.
A higher Q implies a real depreciation, a lower Q a real appreciation, when
seen from the home country.
Total consumption in the home country of good H is CH , and total con∗
sumption of good F is CF . Foreign consumption is CH
and CF∗ . Consumption
∗
of good H, CH and CH
, is denominated in home currency, and consumption
of good F , CF and CF∗ , is denominated in foreign currency. Total production
of the home country is Y = H, and total production of the foreign country
is Y ∗ = F .
The net capital inflow of the home country is B. B will equal the negative
of the current account,
B = −CA,
(8.46)
as we have that the capital account=the current account, and a current
account surplus must give a capital outflow. B reflects capital mobility. If
B is zero, there is no capital mobility. Note that there might still be trade.
However, the trade balance must always be zero.
The rate of absorption, A, is the total consumption and investment in
243
the home country. In standard terms we have that
Y = C + I + G + CA,
(8.47)
where C is total consumption, I is investment, and G is government consumption. Absorption is then given by
A = C + I + G.
(8.48)
For convenience we set I and G equal to zero. We then see that
A = Y − CA = Y + B.
(8.49)
A∗ = Y ∗ + B ∗ .
(8.50)
Similarly, we have that
Notice that
B∗ =
−B
,
Q
(8.51)
as B ∗ is measured in foreign currency, and capital inflow in one country
by definition must equal capital outflow in the other, as we have only two
countries.
We make the convenient assumption of Cobb-Douglas utility functions.
That implies that the utility function are given by
U=
1−m
(QCF )m ,
CH
∗
U =
∗
CH
Q
m∗
∗
(CF∗ )1−m .
(8.52)
where m reflects the share of foreign goods in home consumption, and m∗
is the share of home goods in foreign consumption. Further, it is natural to
assume that
1 − m > m∗ ,
244
(8.53)
which implies that foreigners have a weaker preference for good H than the
residents of the home country themselves.
We now have the two maximisation problems. For the home country we
have
1−m
(QCF )m s.t. A = Y + B = CH + QCF ,
M ax U = CH
(8.54)
and for the foreign country
∗
M ax U =
∗
CH
Q
1−m∗
∗
(CF∗ )m
s.t. A∗ = Y ∗ −
B
C∗
= H + CF∗ .
Q
Q
(8.55)
To solve these equations, we use a standard Lagrange function:
1−m
L = CH
(QCF )m + λ (Y + B − CH − QCF ) .
(8.56)
The choice variables are CH and CF . We obtain
δL
−m
= (1 − m)CH
(QCF )m + λ = 0,
δCH
(8.57)
δL
1−m
= mQm (CF )m−1 CH
+ Qλ = 0,
δCF
(8.58)
δL
= Y + B − CH − QCF = 0.
δλ
(8.59)
and
Equation (11.81) can be reformulated as
1−m
m(QCF )m−1 CH
+ λ = 0.
(8.60)
Setting (8.57) equal to (8.60) we obtain
−m
1−m
(1 − m)CH
(QCF )m = −λ = m(QCF )m−1 CH
,
245
(8.61)
which implies that
(1 − m)
QCF = CH .
m
(8.62)
If we insert (8.62) into (8.59) we obtain that
(1 − m)
QCF = Y + B − QCF
m
⇒ CF = m
Y +B
.
Q
(8.63)
This gives us a function for home country consumption of the foreign good,
CF . Inserting (11.62) in (8.62) we obtain the function for consumption of
the home produced good,
CH = (1 − m)(Y + B).
(8.64)
The similar procedure can be applied to the the consumption problem of the
foreign country. We will then find that
∗
CH
= Qm∗ (Y ∗ −
B
),
Q
CF = (1 − m∗ )(Y ∗ −
B
).
Q
(8.65)
We have now identified the optimal consumption structure for both countries.
Market clearing demands that
∗
CH + CH
= Y,
CF + CF∗ = Y ∗ ,
(8.66)
as total consumption by definition must equal total production. If we insert
(8.64) and (11.66) into (11.70) we get
(1 − m)(Y + B) + Qm∗ (Y ∗ −
B
) = Y.
Q
(8.67)
Here Y , Y ∗ , m and m∗ are assumed to be given exogenously. However, Q
and B must adjust to clear markets. Our main focus is on the real exchange
rate. Taking B as given, we can use (8.67) to calculate the market-clearing
246
level of the exchange rate as
Q=
(1 − m − m∗ )B
mY
−
.
m∗ Y ∗
m∗ Y ∗
(8.68)
The real exchange rate has two parts: one is the result of the relative preference for the demand of good H as a share of output in the two countries,
and the other is a result of capital flows between the two countries. If capital flows are zero, the real exchange rate will only be a product of relative
demand for home and foreign goods in the two countries.
It is interesting to look at how Q is affected by changes in Y , Y ∗ and B.
We find that
δQ
m
= ∗ ∗ > 0.
δY
mY
(8.69)
This implies that if there is a positive supply shock to the domestic economy,
the exchange rate will depreciate. A positive supply shock implies that there
is an increase of domestic goods offered in the market—a supply shock here is
by definition an increase in production. The real exchange rate must weaken
to induce increased demand for domestic goods in the foreign country.
We also find that
δQ
mY − (1 − m − m∗ )B 1
Q
=
−
= − ∗ < 0.
∗
∗
∗
∗
δY
mY
Y
Y
(8.70)
A positive supply shock in the foreign country will lead to a real appreciation.
This time the exchange rate must adjust to increase demand for foreign goods
in the home country. A real appreciation will increase the purchasing power
of domestic residents.
Last, we have that
δQ
(1 − m − m∗ )
=−
< 0.
δB
m∗ Y ∗
247
(8.71)
The result follows from equation (11.68), as we know that (1 − m − m∗ ) > 0.
The real exchange rate appreciates if there is increased capital inflow to the
home country. An example of such inflows might be increased lending due
to a positive demand shock. Increased lending increases the total amount
available for purchases in the home country. As more of this is used to
purchase domestic goods than foreign goods, the price of domestic goods rise
more than the price of foreign goods, leading to a real appreciation.
However, there will normally be a relationship between a shock to Y or Y ∗
and B. Let us assume that there is a shock θ that affects all three variables.
To analyse the effect of θ we can take the total differential of Q.4 Assume
that Y = Y (θ), Y ∗ = Y ∗ (θ) and B = B(θ). The total differential of Q with
regard to θ will then be given by
δQ dY
δQ dY ∗ δQ dB
dQ
=
+
+
.
dθ
δY dθ
δY dθ
δY dθ
(8.73)
Inserting the results from equations (8.69-8.71) we obtain
dQ
m dY
Q dY ∗ (1 − m − m∗ ) dB
= ∗ ∗
− ∗
−
.
dθ
m Y dθ
Y dθ
m∗ Y ∗
dθ
We can simplify the notation be setting
and
dB
dθ
dQ
dθ
= ∆Q,
dY
dθ
= ∆Y ,
(8.74)
dY ∗
dθ
= ∆Y ∗
= ∆B. Further, we assume that the initial trade balance is zero. This
implies that
m∗ Y ∗ =
mY
,
Q
(8.75)
as m∗ Y ∗ is the fraction of foreign output denominated in foreign currency
4
What is the total differential? Assume that we have a function F = (X(θ), Y (θ)).
The differential of X with regard to θ, X 0 (θ) = dX
dθ . From the product rule we know that
dF
δF dX
δF dY
=
+
.
dθ
δX dθ
δY dθ
This gives the total differential of F with regard to θ.
248
(8.72)
that foreigners use to purchase good H. If there is a trade balance this must
equal the fraction of home output used to purchase good F , denominated in
foreign currency, namely
mY
Q
. Also note that if we assume a trade balance,
we implicitly assume that B = 0 in the initial period.
If we insert (11.69) into (8.74) we obtain
∆Q =
Qm
Q
Q(1 − m − m∗ )
∆Y − ∗ ∆Y ∗ −
∆B.
mY
Y
mY
It is easier to interpret changes in
∆Q
Q
than in ∆Q, as
∆Q
Q
(8.76)
represent the
percentage change in Q. If we divide (8.76) by Q, we get
∆Y
∆Y ∗ (1 − m − m∗ ) ∆B
∆Q
=
−
−
.
Q
Y
Y∗
m
Y
(8.77)
We here have expressed the percentage change in the real exchange rate as a
function of the effect of a relative change in home output, the relative change
in foreign output and the relative change in capital inflow as a percentage of
home output.
Analysing the effect of shocks
Let us discuss some specific cases.
• Assume a symmetric shock to the two countries, and that B is zero.
We see that in this case the real exchange rate will be unaffected.
• Assume that there is a negative shock to home output only, and that
there is no capital mobility. Then the real exchange rate will appreciate
equiproportionate to the change in home output:
∆Q
∆Y
=
.
Q
Y
(8.78)
• Assume that there is full capital mobility, but that the shock to home
249
output, Y , is perceived to be permanent. It would not be rational to
borrow in the international markets to compensate for a permanent
shock. Optimal behavior would suggest that the most effective way to
behave if the shock is permanent is to adjust absorption immediately
to the new long term sustainable level. This implies a change in the
real exchange rate of
∆Q
∆Y
=
.
Q
Y
(8.79)
If there is capital mobility and shocks are perceived to be temporary,
there will be a relationship between ∆B and ∆Y that depends on the rate of
capital mobility and the cost of borrowing abroad. Let us assume that that
people care about future generations just like they care about themselves.
If there is a temporary negative shock to Y the effect on current absorption
can be limited if one borrows in the international markets. The possibility
to borrow will be given by x and the cost of borrowing will be set to the
international real interest rate, r.
Assume that we can repay the loan over an infinite number of periods, so
we can disregard repayments. The cost of the loan in each period will be the
interest paid on the loan, rB. We postulate that the economy in this case
will choose to borrow according to the rule
∆B = −∆Y · x − r∆B,
x ≥ 0.
(8.80)
This implies that if borrowing is possible (x > 0) how much one will borrow
will depend on both the opportunity to borrow, x and the cost of borrowing,
r. Inflow will be positive is the shock to output is negative, therefore we have
a negative sign on ∆Y . The loan will be repayed by all future generations at
250
the cost of rB. From this we can derive the optimal ∆B, which is given by
∆B =
−∆Y x
.
1+r
(8.81)
If the shock is temporary and we assume consumption smoothing, it would
not be optimal to let the present generation bear the whole cost of the shock.
To alleviate the negative shock the country will borrow in the international
markets and let ∆B =
−∆Y x
.
1+r
If so we have
∆Y
(1 − m − m∗ ) x ∆Y
∆Q
=
+
.
Q
Y
m
1+r Y
where we know that
(1−m−m∗ )
m
(8.82)
∈ [0, 1i .
The effect under a temporary shock will depend on four variables: x, r,
m and m∗ . We can show that
δ( ∆Q
)
Q
δx
δ( ∆Q
)
Q
δr
and
=
=−
δ( ∆Q
)
Q
δm
1 (1 − m − m∗ ) ∆Y
> 0,
1+r
m
Y
(8.83)
x
(1 − m − m∗ ) ∆Y
< 0,
(1 + r)2
m
Y
(8.84)
x
(1 − m∗ ) ∆Y
=
> 0.
1+r
m2
Y
(8.85)
The effect of a supply shock on the real exchange rate will be higher the
higher the capital mobility and the more international trade. However, the
effect will decrease with the cost of borrowing.
Note one important implication: freer capital flows will enhance the effects of a real supply shock on the real exchange rate. What is the intuition
behind such a result? If there is no capital flows, the real exchange rate
must adjust to clear the markets. A negative supply shock will lead to a fall
in supply of good H, and a relative in the price of H, thereby leading to a
251
real appreciation. If the shock is alleviated by capital inflow, such inflow will
increase the relative demand for good H over good F , as we assume the consumers of the home country to have a higher share of H in their consumption
than the share of F . This will put further pressure on the price of H, leading
to an even stronger real appreciation.
Assume output is back to its long term value in the next period. Even
if the shock only lasts for one period, the country is now left with a net
debt. This debt must be repaid. There is a capital inflow of ∆B =
∆Y x
1+r
in
the period of the shock, and a capital outflow of ∆B = −rB for all future
periods. Absorption must fall to a new level in the period of the shock, and
remain at this level for all future—or at least to the next shock.
The capital outflow, giving a negative value of ∆B, must affect the real
exchange rate as well. The real exchange rate will no depreciate to a level
above its value before the shock, as absorption now will be below absorption
before the shock. Capital flow will not only enhance the effect on the real
exchange rate in the period of the shock, it will enhance the change in the
following periods as well.
The case of a negative supply shock is illustrated in figures 8.4 and 8.3.
Figure 8.4 show the effect on Y and Q. Figure 8.4 is a more complex diagram.
If there are no capital flows A = Y and the economy must be at the 45 degree
line all the time. However, in every point we can adjust absorption through
capital flows. This will lead to an adjustment of Q according to the rule
∆Q
(1 − m − m∗ ) ∆B
=−
.
Q
m
Y
(8.86)
This is the downward sloping line in the diagram. Note that with our “rule”
absorption will settle at a new long term value in the period of the shock.
252
Figure 8.3: The effect on the real exchange rate of a temporary negative
supply shock (a)
Y
time
Q
Free capital flow
No capital flow
time
253
Figure 8.4: The effect on the real exchange rate of a temporary negative
supply shock (b)
dQ/Q =(dY/Y)+-[1/(1+r)]*[(1-m-m*)/m]*(dY/Y)
Full capital mobility (x=1). All future periods.
Q
Y1
Y0 , Y2
45 degree line. Defines B=0
In Y=45 degree line, Y=A
Absorption=output, before
shock
dQ/Q =(dY/Y)+-[1/(1+r)]*[(1-m-m*)/m]*(dY/Y)
Full capital mobility (x=1).Period of shock
dQ/Q=dY/Y
No capital mobility.
r*B, current account surplus for all future
Y
Current account deficit in
period of shock, optimal
policy.
A 1,1 :
Absorption in
period of shock if
no capital mobility.
A 0 : Absorption before shock
A 1,2 : Absorption in all
future periods if full
capital mobility and
”optimal policy”
Lines given by:
dQ/Q -[(1-m-m*)/m]*(d B/Y)
254
This policy is only one of many policy options available. The actual lending in response to a negative supply shock might not follow the rule described
above. If actual lending is less than described in this rule, absorption will
fall more in the period of the shock. However, it will bounce back to a level
higher than under the described policy for all future periods, as repayment
costs are less. The real exchange rate will appreciate less in the period of the
shock. It will however also depreciate less in the following periods.
A demand shock will not affect the levels of Y or Y ∗ . If there is no
capital mobility, the demand shock must be compensated through an adjustment of the national price level, and a similar adjustment of the nominal
exchange rate, leaving the real exchange rate unaffected. However, if there
is capital mobility, a positive demand shock will lead to capital inflow, and
an appreciation of the real exchange rate, given by
(1 − m − m∗ ) ∆B
∆Q
=−
.
Q
m
Y
8.6
(8.87)
The importance of capital flows for consumption smoothing
There are short term and long term capital flows. Short term flows will
be in the form of interbank flows, i.e. flows between banks, and purchases
of money market instruments, such as Treasury bills, i.e. government bonds
with less than one year from issuance to maturity, or other commercial paper.
Long term flows will be in the form of purchases of bonds or equity, either
as portfolio investment or for the purpose of direct control.
For consumption smoothing long term flows are of most importance.
Given our discussion above, it is of some interest to measure the degree
of mobility of long term capital.
255
Feldstein and Horioka, in a paper published in 1980, argued that if capital
mobility is high one should expect zero or low correlation between national
saving and investment, as countries would use the current account to smooth
consumption. They tested this proposition by estimating the equation
I
S
=α+β
+ ui,t ,
Y i,t
Y i,t
(8.88)
where I/Y is the investment rate and S/Y is the savings rate. If capital
mobility is high, β is expected to be close to zero. However, on data from
1961 to 1980, what they found was
I
S
= 0.035 + 0.89
(0.018)
(0.074)
Y
Y
R2 = 0.91,
(8.89)
where numbers in parenthesis are standard errors. Instead of β close to zero,
they were not able to reject β = 1 at a 95 per cent level. This results is now
known as the “Feldstein-Horioka puzzle”.
8.6.1
Explaining the Feldstein-Horioka puzzle
There are two ways to react to this result. Either you try to explain why
capital mobility is so low, or you argue that the estimation does not really
estimate capital mobility. After all, our intuition on this question is not
really clear. One the one hand we do see substantial flows of capital between
countries. One the other hand, one finds that many types of investment,
and especially high risk investments like venture capital, tend to be national
more than international.
There is a good argument for why we should not expect β = 0 even if
capital is mobile. In the model in section 8.5 we argued that if shocks were
permanent, it would be optimal to adjust absorption immediately. In the
life-cycle theory of consumption, sustained shocks to e.g. productivity or
256
demographics that will affect investments should also be expected to affect
savings. So if shocks are mainly perceived as permanent we would expect
a high correlation between savings and investments even with full capital
mobility.
However, there are also good reasons to assume that capital mobility is,
or has been limited:
1. Currency risk. Financial firms usually state their liabilities, i.e. deposits, in the national currency. Investing abroad means taking a currency risk. For long term investments such risk is difficult and/or expensive to hedge.
An indication of how importance currency risk is can be found be comparing capital flows between countries and capital flows between regions
within countries. Generally, one finds little or no correlation between
savings and investment in studies of inter-country data. The implementation of the euro will in a few years provide a very strong test of
the importance of currency risk.
2. Until recently, government regulations on capital flows were widespread,
even in developed countries. Only in the last ten to twenty years have
restrictions on capital flows been fully removed. The Feldstein-Horioka
result might therefore just reflect that capital restrictions were in fact
effective. More recent studies tend to find that the estimate of β is
getting smaller as new observations are added. β is however still significantly larger than zero.
In line with the Feldstein-Horioka puzzle, it is generally found that countries do not tend to smooth consumption as much as the theory would expect.
Why this is so, and whether this impression will change as (or if) we see more
257
Figure8.5:
1: Conjecture?
Stylized
View of mobility
Capital Mobility
in Modern
History
Figure
Stylized A
view
of capital
in modern
history
High
2000
Gold Standard
1880–1914
1914
1900
Float
1971–2000
1929
1880
Bretton Woods
1945–71
1860
1925
1918
1971
1960
Interwar
1914–45
1945
Low
1860
1880
1900
1920
1980
1940
1960
1980
2000
Source: Obstfeld and Taylor, 2002
Source: Introspection.
for exchange-rate
flexibility
inflation targeting.
global integration
in the
comingcoupled
years,with
is uncertain.
One should however note
In the 1990s, the term “globalization” has became a catch-all to describe the
that international
mobility
of factors
is aand
rather
recent world
feature
of theone
postphenomenon of
an increasingly
integrated
interdependent
economy,
that exhibits supposedly free flows of goods, services, and capital, albeit not of
war world.
andhype,
Taylor
(2002)
argue
thatthat
as we
late
in cautious
1980 capital
labor.Obstfeld
Yet for all the
economic
history
suggests
be aaslittle
in
how amazing this development really is. We will show that a period of
mobilityassessing
was still
lower than in the early years of the Gold Standard. Only
impressive global integration has been witnessed before, at least for capital markets,
the turn
of the twentieth
about ashift
hundred
years ago.mobility
Of course,between
that
over theatlast
20 years
have wecentury,
seen ajust
radical
in capital
earlier epoch of globalization did not endure. As the above discussion suggests,
countries.
According
to to
Obstfeld
we did notinreach
if we
were roughly
sketch outand
the Taylor
implied movements
capitalpre-World
mobility, weWar
would chart an upswing from 1880 to 1914; this would be followed by a collapse
1 levels to
of1945,
capital
mobility
yearrecovery
2000. during
Their the
“introspective”
view is
though
perhapsbefore
with a in
minor
brief reconstruction
of the gold standard in the 1920s, between the autarky of World War One and the
given in figure 8.5. Two conclusions from this illustration might be that
Depression; we would then think of a gradual rise in mobility after 1945, becoming
faster after the demise of Bretton Woods in the early 1970s.
Formobility
illustrative is
purposes,
let us
make
the tenuous assumption that international
1. capital
nothing
new,
and
capital mobility or global capital market integration could be measured in a single
parameter. Suppose we could plot that parameter over time for the last century or so.
2. making assumptions of high capital mobility in data from the period
6
1945-1990 is probably not reasonable.
258
Chapter 9
International capital flows, the
IMF and monetary reform
9.1
Topics
• History of capital mobility
• The Eurodollar market
• International debt
• Interbank lending and bank regulation
• International bonds and national defaults
• The IMF
• Taxation of capital flows
9.2
Capital flows
• International bank lending
– lending to customer
259
Figure 1: Conjecture?
A Stylized
Capital
Mobility
in Modern History
Figure 9.1: Stylized
view of View
capital of
mobility
in modern
history
High
2000
Gold Standard
1880–1914
1914
1900
Float
1971–2000
1929
1880
Bretton Woods
1945–71
1860
1925
1918
1971
1960
Interwar
1914–45
1945
Low
1860
1880
1900
1920
1980
1940
1960
1980
2000
Source: Obstfeld and Taylor, 2002
Source: Introspection.
for exchange-rate flexibility coupled with inflation targeting.
In the 1990s, the term “globalization” has became a catch-all to describe the
phenomenon of an increasingly integrated and interdependent world economy, one
that exhibits supposedly free flows of goods, services, and capital, albeit not of
labor. Yet for all the hype, economic history suggests that we be a little cautious in
assessing how amazing this development really is. We will show that a period of
impressive global integration has been260
witnessed before, at least for capital markets,
at the turn of the twentieth century, just about a hundred years ago. Of course, that
earlier epoch of globalization did not endure. As the above discussion suggests,
if we were roughly to sketch out the implied movements in capital mobility, we
would chart an upswing from 1880 to 1914; this would be followed by a collapse
Table 9.1: International capital
In billion USD
Total stocks, 1997 % of
Lend. to final user:
from bank
5285
bonds and notes
3358
money market
184
Total:
8827
Interbank dep.
5098
FX-reserves
1732
Direct for. invest.
3000
FX-trading per day
1600
flows
total
0.60
0.38
0.02
1.00
– interbank
• Securities
– money market instruments
– bonds and notes
• Portfolio investments
• Direct investments
“Eurobanking”—banking services provided in a currency that is not the
currency of country where the bank is located
“Eurodollars”—USD deposited in banks outside US. There exists “Euro
markets” for most currencies.
Note:
• Commercial banks: hold their reserves as cash or deposits with a central
bank.
• Eurobanks hold all reserves as deposits with commercial banks. In
the end every dollar in the Eurobank system will be a liability on a
commercial bank in the US.
261
Figure 10:
Did9.2:
Capital
Flowflows—poor
to Poor Countries?
Versus 1997
Figure
Capital
vs. rich1913
countries
Share of world stock of foreign capital
50%
1913, gross stocks
1997, gross stocks
40%
30%
20%
10%
0%
<20
20–40
40–60
60–80
>80
Per capita income range of receiving region (U.S.=100)
Sources: The 1913 stock data are from Woodruff (1967) and Royal Institute for International Affairs (1937), incomes
from Maddison (1995). The 1997 data are from Lane and Milesi-Ferreti (2001), based on the stocks of inward direct
investment and portfolio equity liabilities.
Source: Obstfeld and Taylor, 2002
they are today, so it is all the more remarkable that so much capital was directed
to countries
below theHalf
20 percent
and 40inpercent
EvolvedatinorLondon.
the market
Europe,income
rest inlevels
Asia(relative
and taxto
the U.S.). Today, a much larger fraction of the world’s output and population is
havens.
located in such low productivity regions, but a much smaller share of global foreign
History:
investment
reaches them.69
As we have noted, capital is discouraged from entering poorer countries by a
host1.of avoid
factors,
and some of
wereflows,
less relevant a century ago. Capital controls
restrictions
onthese
capital
persist in many regions. The risks of investment may be perceived differently
after2.a century
exchange
risks,
expropriations,
and defaults. Domestic policies
invest inofUSD
without
investing
in the US.
that distort prices, especially of investment goods, may result in returns too low to
attract
any capital.
conditions
makeina difficult
much
worse.
1957:
capital These
restrictions
imposed
UK. UKsituation
residents
wanted
to Poorer
avoid
countries must draw on foreign capital to a greater extent than they do at present if
restrictions
by investing
in USD.
1958:
several
European
currencies
made
they
are to achieve
an acceptable
growth
in living
standards.
That
is a fundamental
reason
why reform
andUSD
liberalization
in the
developing world, despite the setbacks
convertible,
making
investments
possible.
of the late 1990s, are likely to continue, albeit hopefully with due regard to the
Russia
in need
of in
USD,
did however
painful
lessons
learned
the recent
past. not want deposits in US in fear of
69 See Clemens and Williamson (2001) for a detailed analysis of the determinants of British
retaliation.
capital export before 1914.
New growth in the 1970’s: OPEC got income in USD, did however not
want to invest in US.
60
262
Easy access for third world countries. Main market for international debt.
Eurodollar market generally offers lower spreads than domestic commercial banks—Eurobanks have higher deposit rates and lower loan rates.
How?
• Little or no regulation in the Euro market. Until recently the US
banking market was heavily regulated.
– Regulation Q—maximum deposit rates
– Interest Equalisation Tax and Voluntary Foreign Credit Restraint
Guidelines: imposed to reduce US lending to foreigners.
However, today little regulations in the US market.
– No minimum reserve requirements.
– Economics of scale—used to deal in large loans.
Credit multiplier: do the existence of Eurobanks affect the liquidity in
the USD market?
Supply of USD, M :
M = Mp + ME ,
(9.1)
Mp = dollars held by private sector excluding Eurobanks, ME = USD
held by Eurobanks with domestic US banks as reserves.
Liquid assets held by the private sector, L:
L = Mp + E,
E = the public’s holding of Eurodollar (deposits in Eurobanks).
263
(9.2)
How does the existence of Eurobanks affect L? We see that
L
Mp + E
=
.
M
Mp + ME
(9.3)
L can be expressed as
L
=
M
ME
:
E
Mp
+1
E
Mp
+ MEE
E
.
(9.4)
Reserve to deposit ratio in the Eurobank system. Expect to be
low.
Mp
:
E
Ratio of holdings of dollars outside the Eurobanks to the holdings
in the Eurobanks. Expect to be high.
⇒ should probably expect that
L
M
≈ 1.
Eurobanks have only a marginal effect on liquidity in the USD-market.
9.3
The international debt market
Makes it possible to finance current account deficits over long periods
of time without any automatic stabilisation effects
⇒ same countries remain deficit countries over long periods of time.
⇒ “ballooning” of debt for some countries.
Assume three regions: US, Latin America and Europe. Only trade
between Latin America and US, between US and Europe, not trade
between Europe and Latin America.
US trade surplus of 100 with Latin America, deficit of 100 with Europe.
US: trade balance.
Europe: surplus of 100.
Latin America: Deficit of 100.
264
Latin America finance deficit by borrowing 100 in Eurodollar market.
Europe accumulates assets of 100 as deposits in Eurobanks. If pattern
continues, Latin America will accumulate debt, Europe accumulate assets.
Eurodollar market continue to grow as long as balance of payments
deficit persists.
Why no automatic stabilisation?
– Growth of euro-dollar market is non-inflationary as for each amount
borrowed there is an equal amount saved. Money base does not
change here.
– Balance-of-payments surpluses “recycled”, world aggregate demand remains unchanged.
– Note that the ballooning of USD debt is created although the US
have a balanced current account.
What is driving this?
Europe willing to hold USD. Latin America needs USD, not EUR.
If Europe not willing to hold USD, US would have to use foreign reserves
to finance deficit with Europe. The US money base would be reduced.
US competitiveness would grow, US imports fall.
At the same time, Latin America would not get USD to finance US
imports—would have to improve own competitiveness.
Result: more US exports to Europe, more Latin American exports to
US.
With Eurobanks: Latin America can postpone reform of exporting
sector. Imbalances not corrected.
265
Latin America is the debtor of the Eurobanks. Eurobanks are the
debtors of Europe.
So Latin America owes its debt to Europe? No—and yes. Europe
has deposits in banks—seemingly a safe investment. However, if Latin
America defaults the bank will default, and Europe will not get any
money.
Why is this a problem:
– In many cases the creditors of banks believe banks to be “safe”,
because they believe banks will not be allowed to default. So bank
deposits are sometimes made with a “wrong” perception of risk.
– Assume “Europe” is a number of smaller investors. If Latin America defaults on its debt this will lead to losses for a potentially large
group of people.
– As pointed out above, debt allows Latin America to postpone
reform. However, if they can just default and get rid of debt, do
they ever have incentive to reform?
Inter-bank market: loans and transactions between banks
– To satisfy (short-term) needs to fulfill regulation criteria in resident country.
– Banks obtain deals at different times—continually need to balance
their accounts.
– Utilise opportunities for niche specialisation—banks specialise in
lending, and obtain financing through the interbank market.
– Arbitrage trades.
266
Bank interdependence
Because of the interbank lending, there is interdependence in the capital
markets: if one bank defaults other banks might default as well.
Some problems associated with banks:
– Information asymmetries. Depositors know little about the bank,
the bank has little knowledge of its debtors. Both the bank and
the final borrower might have incentive to take excess risk.
– Risk asymmetries. Depositors believe their deposits to be covered by deposit insurance or a central bank lender of last resort
function. Have little incentive to reduce risk taking in the bank.
– “Lender’s trap”. If you have borrowed a firm a large sum of money,
and the firm is on the edge of default, should you borrow it a little
more to let this firm avoid default?
– “Race to the bottom”. To increase profits banks can reduce the
bank capital. However, this makes them more vulnerable for loan
losses.
– If lending and borrowing is international, but regulations of capital
requirements is national ⇒ potential instability.
The structure of the banking business seems to imply that aggressive
banks get the upper hand. However, this seems to be the result of a
market failure where banks not fully internalises the cost of default in
the banking industry.
If we accept this reasoning, there is an argument for regulation of the
banking industry.
267
If the industry has a global scope, and the costs of failure are of an
international character, then regulation should be international.
⇒ The Basel Capital Accord. Agreement on capital adequacy measurement and standards. Defines
1. eligible capital elements,
2. variable risk weights applicable to several main categorises of onand off-balance sheet exposure,
3. set overall minimum capital ratio to 8 per cent of risk weighted
assets, and
4. set overall “core capital” to at least 4 per cent.
Agreement implemented in 1992. It imposed a substantial increase
in capital requirements for some banks. However, many problems remained unsolved:
– Interbank lending was seen as low risk. However, as discussed
above interbank lending is not risk free.
– Many banks were able to take considerable risk within this accord,
e.g. as seen under the Asian crisis in 1997.
Currently discussions about “Basel 2”. Main changes from “Basel 1”:
– Risk will be measured with “value-at-risk” models. As banks often
have the best models of this kind, risk will be measured by the
banks own models.
– Ratings from rating agencies—like Moody’s or S&P—may be used
to assess the riskiness of the bank’s entire portfolio.
268
New accord to be implemented in 2006. However, already much discussion of how this will work in practice.
The international bond market
– Foreign bonds: bonds issued by foreign corporations or countries
in the domestic capital market of another country. Normally sold
by a host-country investment bank, and traded in the host financial market. Subject to host country laws.
– Eurobonds: bond issued in a country that does not use the currency as domestic currency, e.g. USD denominated bond issued
in London. Usually issued by a syndicate of underwriters, and
issued in a number of countries simultaneously.
Annual new eurobonds run about twice the rate as new foreign bonds.
Why direct finance instead of finance through banks?
– Potential asymmetry problems in direct finance. Banks are supposed to be able to generate superior information, and therefore
have an information advantage.
– However, for large companies this is less the case. Should expect
more direct finance.
– The easier to collect information, the more direct finance.
Information problems might be a problem for small and/or developing
countries when obtaining loans. International agencies, like the World
Bank, work as intermediaries in the bond market. People will rather
buy a World Bank bond than say, an Indian government bond.
Use of the international bond market. Why borrow in a currency different form the domestic currency?
269
– Profit on risk premiums.
– Diversify risk. International business cycles are not perfectly correlated. Return is less correlated between countries than within
countries.
– Hedge currency risk, especially if costs and incomes are denominated in different currencies.
– Finance current account deficits. If state companies finance new
investments aborad, they reduce demand for capital at home. Implicitly this takes pressure away from the foreign reserves.
– If local markets are illiquid, international borrowing might be the
only option.
– The foreign banking industry might be more efficient, and therefore offer better rates than the domestic industry.
– Tax adjustments and use of tax havens.
Government vs. national debt
(1) Balance of payment (BOP)= current account surplus + capital
account surplus = ∆F g (increase in foreign reserves)
(2) Capital account surplus = net long term private capital inflow +
government foreign borrowing - gross short-term capital outflow
Combine (1) and (2):
(3) Government foreign borrowing = current account deficit + ∆F g +
gross short-term capital outflow - net long term private capital inflow
Note: net national indebtness is determined only by current account
deficit.
270
Government indebtness will increase even if current account is zero if
large short term outflow of capital. What determines short-term capital
outflow? This was discussed in Lecture 8—the speculative portfolio.
Lender’s trap
Why do international banks continue to make loans to countries on the
verge of default?
Problem for the banks: either make new loans so the country can service
payments on old debt, or declare the borrower insolvent, and write off
the loan.
Expected benefit from lending:
E(B) = (P0 − P1 )D.
(9.5)
P0 = probability of default before new loan is made.
P1 = probability of default after new loan is made.
D = debt outstanding before new loan.
Expected cost of new loan:
E(C) = P1 L.
(9.6)
L = value of new loan.
Net benefit of new loan as percentage of outstanding debt:
L
E(B) − E(C)
N (B) =
= P0 − P 1 1 +
.
D
D
Give new loan if N (B) > 0.
271
(9.7)
9.4
Can a country default?
Many poor countries heavily indebted.
– African countries: mostly debt to foreign governments.
– Latin America: mostly debt to foreign banks.
1982: Debt crisis. Mainly caused by the rising cost of imports due to
OPEC 2 rise in oil prices. Many debtors de facto insolvent—debt forgiveness necessary. Important ratio: debt payment to export earnings.
What happens if a country can not service its debts?
Problem: as a creditor your debt becomes more worth if other creditors
are willing to reduce their claims.
⇒ tragedy of the commons. No one has incentive to move first.
Search for agreement that is binding across different asset classes and
jurisdictions.
Possible solutions:
– International bankruptcy court
– Majority action clauses in debt contracts: allows a majority of the
creditors to agree on changes in the debt contract that affects all
creditors.
– Increase IMF power.
Current discussion:
– IMF: proposes to allow majority voting, overseen by the IMF.
60-70 per cent of creditors should be enough to determine restructuring.
272
– US Treasury: borrowing countries should add clauses to debt contracts that describe what happen if the country gets into trouble,
like how a default will be initiated et.c. Introducing such clauses
should be condition for receiving IMF loans.
9.5 The role of the International Monetary Fund (IMF)
When confronted with a member with a balance of payment deficit:
restore equilibrium. But how?
Role:
– “to promote the adjustment process”,
– “restore viability of balance of payment in the context of price stability and sustained economic growth, without resort to measures
that impair the freedom of trade and payments.”
Earlier: much emphasis on fiscal deficit.
Later years: take more country specific considerations, look more at
long term prospects and structural reform process.
Policy choices
– Monetary policy; usually setting ceiling on the rate of domestic
credit growth.
– Devaluation of fixed exchange rate.
– Reduce price distortions, e.g.
∗ by reducing subsidies,
273
∗ eliminate interest rate ceilings, or
∗ by trade liberalisation.
– Freeze wages.
– Target the growth of net foreign indebtness.
“Demand management”. Important IMF policy:
Domestic absorption must be constrained to a level consistent with the
level of domestic production plus any sustainable net capital inflows,
otherwise the balance of payments deficit is unsustainable.
To assure a permanent solution to balance of payment problems:
– Improve resource allocation to lessen the constraint on the level
of domestic demand imposed by a given availability of resources.
Policies include:
∗ exchange rate adjustments,
∗ interest rate adjustments,
∗ reducing subsidies.
– Structural reform. If problem is high imports of expensive oil,
increase domestic energy production, reduce energy vast.
As pointed our above, there is a close connection between domestic
banks and international capital flows. This has been important factors
in recent financial crises, like in Asia 1997.
Should international financial stability be on the agenda of IMF?
IMF: much focus on the importance of reducing asymmetric information. Elements:
274
– Increased disclosure of information. Arrange common reporting
standards.
– Requirements for bank capital.
– Modification of creditor rights (as discussed above), so as to stop
“grab-races”, attempts to cash in, and therefore force insolvency
on an illiquid, but solvent debtor.
– Reduce short-term capital flows if such flows have negative externalities.
IMF can force compliance to international standards by conditioning
lending on such compliance.
Does the IMF create moral hazard?
IMF works like a lender of last resort for countries.
Reduce incentive to balance your own books, as the IMF will rescue
the government if balance of payment deficit becomes unsustainable.
Is the economy better of without a lender of last resort? Might be less
irresponsible behaviour. However, crisis will still exist. How large will
the cost of such crisis be without a lender of last resort?
For countries of strategic importance: Someone will step in anyway (?)
By setting conditions for loans, phase out payments, and have close
surveillance of results, the IMF seeks to reduce moral hazard.
The monetary approach
IMF:
– Balance of payments deficits tend to have a common cause.
275
– The policies mentioned above are mostly sufficient to correct such
imbalances.
Argument: in developing countries money used to finance public deficits.
No “wall” between the government asset sheet and the central bank asset sheet
Budget deficit
⇒ increase in money supply
⇒ inflation
⇒ the public want to increase holdings of foreign currency, dishoard
domestic currency (as in lecture on portfolio choice)
⇒ foreign reserves fall, country must finance deficit by borrowing abroad.
The country experience a real appreciation because of the increase in
the domestic price level. To retain domestic production tariffs introduced. Frequent devaluations might alleviate the problem for short
periods of time. However, if government deficit persists, the spiral continues.
When debt level no longer sustainable, IMF called in. Situation:
– Not able to service debt.
– Domestic economy distorted by trade restrictions.
– Financial markets distorted by “financial repression”, means used
to make domestic markets accept domestic government debt.
The IMF’s approach: adjustment requires a fundamental change in
economic and financial conditions. Budget deficit reduced, distortions
reversed. Main target: stop dishoarding of local currency.
276
Question: should change be gradual or rapid? Historically IMF has
favoured rapid reform. Has taken more flexible approach in later years.
The New Structuralist debate
Critique: IMF approach should be expected to work well in developed
countries. However, developing countries have different structure, need
different approach. There exists no “common cause”, and no singular
solution.
Examples:
– Reducing money supply could increase inflation if “interest cost
push” strong—lower money supply would push up interest rates,
higher interest rates might push up prices.
– Devaluation might be negative if
∗ the cost of necessary imports so much that domestic supply
will fall.
∗ the fall in the spending power of wages fall so much that
aggregate demand falls, leading to lower growth.
∗ if much of domestic debt is denominated in foreign currency,
leading to higher cost of debt servicing.
∗ if tariffs are measured in per cent, a devaluation, leading to
higher import prices, will at the same time mean higher taxes,
i.e. contractionary fiscal policy.
– Reduction of subsidies might decrease local demand, leading to
slower growth.
– If deficits have non-monetary causes, like recession in export markets, IMF strategy will be counterproductive.
277
These arguments depend on assumptions of import dependence and
resource immobility.
Example: Asian crisis in 1997
IMF advice: increase interest rates to stop dishoarding of domestic
currency. Balance public deficits.
Problem: these countries were in recession. Increased interest rates
made could make this recession even deeper. Reducing fiscal deficits in
periods of recession is pro-cyclical, not counter cyclical policy.
Empirical evidence: not much support for one nor the other. IMF
policies stabilise the situation, but “sustainability” is not guaranteed.
However, most countries do not fully implement IMF policies. New
structuralist’s claims about devaluation not supported.
IMF and Argentina
IMF sceptical to currency board from the start. However: IMF focus
on “national adoption of policies”—the country must be presented with
alternatives and get to make a choice.
IMF tried to make Argentina leave the board in 1997-98. At this time
Argentina was doing well. Probably only small effects if board had
been changed. However, the board was very important as a symbol of
new brooms in Argentinean politics.
August 2001: IMF still supported Argentina.
Damned if you do,
damned if you don’t...
Now IMF is stating requirements:
– Restore the confidence in the banking system. (But how?)
278
– Change legal structure to protect creditors—current system favours
debtors.
– Reign in spending by the provinces.
9.6
Capital controls in Chile
History: Introduced in June 1991.
Initially: 20 per cent reserve requirement on portfolio investments to
be deposited in central bank at no interest. For maturities under one
year it applied for the whole period, for maturities over one year, it
applied for one year.
In July 1992: changed to requirement of 30 per cent for ne year, independent of maturity of investment. Extended to trade credits and
loans to FDI.
In June 1998 reduced to 10 per cent, and abolished in September 1998.
Intentions:
– Slow down volume of capital flowing into the country.
– change composition of flows to longer maturities.
– Allow the Central Bank to maintain a higher interest differential
between domestic and foreign interest rates.
– Reduce vulnerability to international financial instability.
Effects:
– Ratio of long term flows to short term flows increased.
– However, so did “residual flows”—there is some evidence of evasion.
279
– Some evidence of increased “independence” in monetary policy.
– However, measures of international vulnerability shows mixed results:
∗ Almost no reaction to the Mexican crisis in 1994,
∗ however, a more marked reaction to the Asian crisis than what
was felt in the rest of Latin America.
∗ Further, financial stability was restored in 1999, after the reserve requirements were abolished altogether.
In the end however, Chile probably remained stable because economic
policy as a whole was stable during the 1990’s.
Potential problems:
– Increases the cost of capital, especially for small and mid-sized
firms.
– Always the temptation to turn such measures into permanent policies.
– Policymakers might become overconfident, neglecting the needs
for more general reform.
280
50
Table 2 : Capital
(gross)inflows
to Chile:
Millions of US$
Figure Inflows
9.3: Capital
to Chile
Year
Short term Percentage Long term Percentage
flows
of total
flows
Total
Deposits*
of total
1988
916,564
96.3
34,838
3.7
951,402
--
1989
1,452,595
95.0
77,122
5.0
1,529,717
--
1990
1,683,149
90.3
181,419
9.7
1,864,568
--
1991
521,198
72.7
196,115
27.3
717,313
587
1992
225,197
28.9
554,072
71.1
779,269
11,424
1993
159,462
23.6
515,147
76.4
674,609
41,280
1994
161,575
16.5
819,699
83.5
981,274
87,039
1995
69,675
6.2
1,051,829
93.8
1,121,504
38,752
1996
67,254
3.2
2,042,456
96.8
2,109,710
172,320
1997
81,131
2.8
2,805,882
97.2
2,887,013
331,572
* Deposits in the Banco Chile due to reserve requirements.
Source: Edwards, 2000
281
59
Figure 9.4: The tax equivalent of the Chilean reserve requirement
0.06
0.05
0.04
0.03
0.02
0.01
0.00
90
91
92
TAX180
93
94
95
TAX1YR
96
97
98
TAX3YRS
Stay of 3 months, 1 year and 3 years. Source: Edwards, 2000
Figure 2: Tax Equivalent of Capital Controls:
Stay of 180 days, 1 year and 3 years
282
Chapter 10
Exercises
Lecture 1
1. Gresham’s law
(a) Gresham’s law states that bad money always will drive good
money out of circulation. People will choose to use the bad
money for transactions, and store the good money. Explain
why.
(b) Assume a system where two types of coins circulate in the
economy. Some coins are of silver, and some coins are of gold.
Discuss possible problems that can arise in such a system if
there is discovered a huge deposit of silver. Will silver or gold
coins dominate circulation? Will silver or gold dominate as a
store of value?
(c) Assume that one has a currency that is backed by a two-metal
standard. Assume that for 35 units of currency one can claim
1 ounce of gold or 35 ounces of silver at the central bank.
Assume gold supply increases three-fold, while supply of sil-
283
ver remains constant. How will this affect the central banks
holdings of gold and silver? Will this currency be “stable”?
2. Fiat money and free banking...
(a) Assume that the Norwegian government allows everyone to
print Norwegian kroner on their own colour printers. What
would do you think would happen to the Norwegian money
supply? What will happen to the Norwegian price level?
(b) At the islands Yap in the Pacific Ocean people used large,
heavy round stones with a hole in the middle as currency. One
stone took two men approximately one week to make. These
stones worked as both unit of account, means of payment and
store of value. However, as they were difficult to carry, the
islanders did not care to carry them around. Instead they
issued legal titles to the stones. These legal titles were used
for trading.
Note that the stones only had value as currency. They had
no value as a commodity.
i. What is the difference between the stones on Yap and the
ability to print your own money?
ii. Explain the fact that inflation on Yap was stable.
iii. What would happen to the price level on Yap if the islanders got a new technology that would reduce the time
to make a new stone from one week to one day? Should
this have any effects for the real economy on Yap?
3. Seignorage
284
(a) Seignorage is given by
Seignoraget =
Mt − Mt−1
.
Pt
(10.1)
We know that real money demand can be written as
Mt
= Et
Pt
Pt+1
Pt
−η
.
(10.2)
Assume perfect foresight. Further, assume that the central
bank can commit to a fixed rate of money growth for all future, µ, so that
Mt
= 1 + µ.
Mt−1
(10.3)
Use this information to show that the rate of money growth,
µopt , that will maximise seignorage revenue is equal to η1 .
(b) Average growth in Norwegian M1 over the period from December 1992 to January 2002 has been 9.48 per cent on a
yearly basis. Assume that Norges Bank behaves according to
the rule of optimal seignorage. Find η.
(c) Assuming constant money growth, the formula for seignorage
can be written
Seignoraget = µ(1 + µ)−η−1 .
(10.4)
Calculate seignorage for Norway.
(d) We want to find seignorage as a percentage of public expenditure. Note that in equation (11.4) seignorage is measured as
a fraction of the price level. For our purposes it is reasonable
to approximate the price level with the money stock in the
last period. In January 2002 Norwegian M1 was 382.6 billion
285
NOK. The public expenditure for 2001 was expected to be
487.9 billion NOK. Calculate seignorage as a percentage of
government expenditure for Norway. Compare your number
with the numbers in Box 8.1 in Obstfeld and Rogoff, ch. 8.2.
Lecture 2
In its simplest form, a currency board is a money printing rule. We
will consider Argentina, where the domestic currency is the Argentinean peso (ARP). The currency board arrangement says that (a) the
ARP/USD exchange rate is 1.00, and (b) for every peso in circulation
the currency board must hold USD 1.00 in reserve.
Figure 10.1 gives a simple example. Mark that all units are ARP.
The financial system are characterised by two key ratios:
1. The public’s deposit-to-cash ratio. Here that ratio is 12 (9000/750).
This reflects the optimal amount of ‘liquidity’ which the public demands, relative to the size of their bank deposits. What ‘liquidity’
means here is ‘cash required to facilitate purchases of goods and
services.’ The ratio of 12 reflects a tradeoff. On the one hand, the
more cash held, the easier it is to transact. One the other hand,
the more cash held, the more is given up in foregone interest income.
2. The banking system’s deposit-to-reserve ratio. Here that ratio is 60
(9000/150). This reflects a tradeoff which underlies good banking
practice. The banker needs some cash in the vault in order to
satisfy customer withdrawal demands (and prevent a bank run).
286
287
8,850
900
900
150
8,850
Pesos
Net Worth
Deposits
Net Worth
900
0
Liabilities
Pesos
Loans
Currency Board
Assets
Loans
Net Worth
USD (cash or securities)
9,000
750
Liabilities
(i) The public’s deposit-to-cash ratio is 12. This reflects the optimal amount of
‘liquidity’ which the public demands, relative to the size of their bank deposits. What ‘liquidity’ means (here) is ‘cash required to facilitate purchases
of goods and services.’ The ratio of 12 reflects a tradeoff. On the one hand,
the more cash held, the easier it is to transact. On the other hand, the more
cash held, the more given up in foregone interest income.
9,000
0
Commercial Bank
Assets
Liabilities
What characterizes this simple financial system are two key ratios:
Deposits
Pesos
Assets
Public
Figure 10.1: Example of a currency board
In its simplest form, a currency board is a money printing rule. We’ll consider Argentina, where the domestic currency is the Argentinean peso (ARP). The currency
board arrangement says that (a) the ARP/USD exchange rate is 1.00, and (b) for
every peso in circulation the currency board must hold USD 1.00 in reserve. Here
is a simple example. All units are ARP except the assets of the currency board.
PART A
However, the more cash in the vault the fewer loans made, which
in turn reduces interest income.
The balance sheets in figure 10.1 represents ‘equilibrium’ in that the
amount of deposits, cash and reserves are consistent with the two above
ratios—i.e. we assume by definition that these two ratios characterise
equilibrium. For more on a monetary equilibrium, see the appendix.
1. Here are two definitions:
– Money supply=currency held by the public plus deposits held
by the public.
– Monetary base=total currency in circulation plus commercial
bank reserve deposits held at the central bank (the latter are
zero here). This is called high powered money. It is also called
the liabilities of the central bank.
Note that the monetary base is what is exogenous in the above
system of balance sheets. That is, given the monetary base
and the two above ratios, everything else is determinate. This
will be clearer as we go along.
Given the data in figure 10.1, compute the values of the money
supply and the monetary base.
2. Next, assume that the Argentinean real exchange rate appreciates vis-a-vis USD. Provide one or two sentences to say what this
means. This question should be answered abstractly, without references to the above data. Your answer should be expressed in
intuitive terms, using plain, jargon-free language.
3. Now suppose that, because of the ARP real appreciation, an Argentinean importer wants to import some U.S. goods. Specifically,
288
she wants to import 18 dollars worth of machines. This means that
she needs to obtain USD 18.
(a) First, suppose the importer goes to her commercial bank and
asks for USD 18. The commercial bank turns to a trader in an
American bank, and asks him to sell it USD 18 in return for
ARP 18. Assume the trade goes through, and the importer
receives USD 18 from its bank in return for ARP 18. What
is the effect on the Argentinean monetary base?
(b) Second, suppose that, because of the overvaluation, the trader
at the American bank will not sell USD for ARP at 1:1. He
might sell each USD for 1.2 ARP, but if he did then the fixed
exchange rate would have de facto collapsed. The good news
for the Argentinean importer is that the currency board is
obliged to sell her USD at 1:1. The commercial bank will
trade ARP 18 for USD 18 by sending a request to the currency
board.
What is the currency board supposed to do with the pesos it
receives for these USD? If the currency board does this, what
is the effect on the Argentinean monetary base?
(c) According to the quantity theory of money, money (M ) times
the number of transactions conducted with money (velocity,
V ) should equal the price level, P , times the number of transactions in the economy, T , or
M · V = P · T.
(10.5)
We can simplify by assuming that velocity is constant, and
that T can be set equal to to total production in the economy,
289
Y.
Do you think the actions by the currency board described
above will alleviate the overvaluation of the Argentinean peso?
Why?
(d) What will happen if, for some reason, this process continues?
That is, what will happen if Argentineans try to convert all
their ARP-denominated bank deposits into USD?
4. Given the transaction by the Argentinean importer, what will happen to the Argentinean current account once this transaction occurs? Will there be change in the direction of trade flows? How
will capital flows be affected?
5. Once the Argentinean importer has obtained the USD 18, you
should find that the system of balance sheets are no longer ‘in
equilibrium’. That is, the two ratios discussed above are no longer
12 and 60. Use the four linear equations described in the appendix
to compute the new equilibrium. What is the new money supply?
Is this new value for the money supply consistent with alleviating
the overvaluation problem?
6. The money multiplier is defined as the ratio of the reduction in the
money supply to the reduction in the monetary base. The money
multiplier tells us how fast the supply of money grows if another
unit of monetary base is created. What is the money multiplier
here? If the central bank prints one more piece of currency, how
much will the total money supply grow, and therefore how much
will the price level increase (if V and Y is constant)?
The important point in the example above is to show that a currency
290
board has a ‘self-correcting’ aspect to it. Excessive inflation (relative
to the reserve country) and/or real exchange rate overvaluation should
be corrected if the currency board does what it is supposed to do. In
addition, the example points out that a county with a currency board
has effectively given up any sort of active monetary policy. Monetary
policy becomes a currency printing/burning robot.
Policy questions:
1. Look at attached reading and what you have learned above and
in class, and make a table which briefly outlines the pros and cons
of a currency board for a country like Argentina.
2. Pretend that you are an economic advisor to the Argentinean president Carols Menem and his Minister of Finance, Domingo Cavallo, in 1991. With the befits of knowing what has happened up
to today (April 2002), make a recommendation to them regarding the type of exchange rate mechanism which Argentina should
adopt.
Appendix
The essence of a ‘monetary equilibrium’ is that the the public’s depositto-cash ratio must equal 12 and the banking system’s deposit-to reserve
ratio must equal 60. This, in addition to the accounting definitions
inherent in the balance sheets, imply the following system of linear
equations must hold:
291
H = R+C
60 =
R+L
R
12 =
D
C
D + C = L + H,
where
– H≡the monetary base (number of pesos in circulation).
– R≡reserves of the banking system (cash in the vault).
– L≡loans.
– C≡currency held by the public.
– D≡deposits held by the public at commercial banks.
In a currency board H is given from outside the system, by market
forces. Given H, the above four equations are linear in 4 unknowns,
D, C, L and R.
Attached readings
(Included in separate file)
– Kurt Sculer: “Introduction to currency boards”,
(http://users.erols,com/kurrency/intro.htm)
292
– “The ABC of currency boards”, The Economist, October 1997
– “Dollar mad?”, The Economist, October 2001
– “A decline without parallel”, The Economist, March 2002
Lecture 3
1. What do we mean with the n-1 problem in a multilateral exchange
rate system?
2. In the European Monetary System (EMS) a number of European
countries had agreed to fix their currencies to the European Currency Unit (ECU). ECU was defined as the value of a basket that
contained a weighted average of the currencies of the member
countries.
In the early 1980’s the EMS was a fairly flexible system, with
frequent adjustments. However, as a first step on the road towards
a common currency in the EU, it was in 1987 decided to let the
currencies be fixed to ECU, and to avoid adjustments.
After the opening of Eastern Germany in 1989, and the introduction of DEM in the eastern territories in the summer of 1990,
Germany experienced an economic boom. To avoid inflation, the
Bundesbank responded to this growth by tightening money supply. A result was that German interest rates rose.
At the same time a number of other members of the EMS, including France and Great Britain, experienced an economic slowdown.
These countries wanted a loser money supply to reduce interest
rates.
293
Assume that the UIP holds. Use the n-1 problem to illustrate
the strains put on the EMS-system. If possible, use diagrams to
illustrate the problem.
3. In a meeting in 1991 Germany suggested to revalue the DEM
inside the EMS system (increase the value of DEM relative to the
other currencies in the system). Could this have alleviated the
strains on the system?
4. France vetoed the German suggestion. Discuss why.
Lecture 4
From your former lessons in macro, you know the concept of a Phillips
curve. The Phillips curve implies a relationship between unemployment and inflation. In “modern macroeconomics” one thinks about the
Phillips curve as a fluctuations around a “non-accelerating-inflationrate-of-unemployment” (the NAIRU). The NAIRU is seen as the longrun rate of unemployment. In the short term unemployment can be
higher or lower than the NAIRU, depending on whether inflation is
higher or lower than expected inflation. If we call unemployment for
u, the NAIRU for un and inflation for π, and we let π e be expected
inflation, we can express the Phillips curve as
u = un + a(π e − π).
(10.6)
If inflation exceeds expected inflation, the unemployment rate can for
be less than the NAIRU. However, one can not expect inflation to
exceed expected inflation over time.
We assume that the government has two policy goals: to keep inflation
294
stable, and to keep unemployment low. In fact, the government has as a
goal to keep unemployment at a level u∗ < un . This can be rationalised
if one think there are some sort of inefficiencies in the labour market
that lead to an increase in the NAIRU rate. As a second best policy
the government target an unemployment rate below the NAIRU. We
specifically assume that
u∗ = σun ,
(10.7)
where 0 < σ < 1.
The government minimises a loss function, L, that contain these two
elements:
L = π 2 + b[u − u∗ ]2 ,
(10.8)
where b (assumed to be > 0) is the weight on holding unemployment at
u∗ . If we substitute in for the equations (11.85) and (11.86), we obtain
L = π 2 + b[(1 − σ)un + a(π e − π)]2 .
(10.9)
1. Assume the PPP to hold, i.e.
et = pt − p∗t ,
(10.10)
where et is the exchange rate in period t, and p∗ is the foreign price
level. Assume that the foreign price level is fixed at p∗ = 0, and
that foreign inflation, π ∗ , is zero. Discuss the relationship between
domestic inflation, π, and the depreciation of the exchange rate,
·
e, under these assumptions.
2. We assume that the government focuses on the exchange rate instead of the price level. Give some arguments for why a government could choose to focus monetary policy on a stable exchange
295
rate instead of controlling the money supply.
3. Assume that the exchange rate is fixed, so that et = e. This
·
implies that e = 0. If the government adjusts the fixed rate this
will have the cost of C. As long as the regime is fixed at et = e,
C = 0. If the rate is adjusted, C > 0. The loss function can now
be written as
·2
·e
·
·
L = e + b[(1 − σ)un + a(e − e)]2 + C e,
(10.11)
·e
where e is expected depreciation. Explain why C might be positive.
4. Assume that the fixed exchange rate is credible and the government does not adjust the exchange rate. Calculate the loss of the
government.
5. Assume that the fixed exchange rate is credible. Discuss under which circumstances the government might have incentive to
change the exchange rate. What is the role of C?
6. Assume that the fixed exchange rate is not credible. Assume the
market expects the government to devalue the exchange rate, i.e.
·e
assume e > 0. How would this affect optimal government policy?
7. In the light of the above results, discuss the term “self-fulfilling
speculative attacks”.
Lecture 5
1. The Krugman model
Country A is a developing country with a long history of high
296
inflation. The money demand is given by
mt − pt = −η(Et pt+1 − pt ).
(10.12)
Assume that PPP holds, so that the exchange rate on log-form,
e, is given by
et = pt − p∗t .
(10.13)
For simplicity we set p∗ = 0, and assume that foreign inflation
is zero. If we assume perfect foresight, and use continuous time
notation, so that
·
et+1 − et = e,
(10.14)
we can write the money demand function as
·
mt − et = −η e.
(10.15)
Money supply, M (remember that m = log(M )) reflects the central bank asset sheet. We remember that the central bank has
two main types of assets, foreign reserves and domestic government bonds. We can therefore write M as
M = D + R,
(10.16)
where D is domestic bonds, and R is foreign reserves. The central
bank only hold foreign reserves when the exchange rate is fixed.
The exchange rate is fixed at a level e = e. This implies that the
money supply is fixed at a level m = m. However, assume that
the central banks holdings of domestic bonds grow at a rate µ.
297
The size of domestic credit at time t will be given by
dt = d0 + µt.
(10.17)
(a) If domestic credit grows at a speed µ and the exchange rate
shall remain fixed, what must happen to the money supply?
Which implication will this have for the level of foreign reserves, R?
Assume that domestic credit grows by 20 per cent a year, so
that µ = 0.2. Assume that initial domestic credit is D0 = 10
and initial foreign reserves are R0 = 90. At what time will
R = 0 if this policy is not changes?
(b) If we use the above model, and assume money supply growth
at a fixed rate µ, we find the following expression for the
exchange rate:
et = mt + µη.
(10.18)
The “shadow exchange rate”, ee, is defined as the exchange rate
that would have been the actual exchange rate if a speculative
attack had already happened. Assume that the government
continues the policy of fixed growth in domestic credit forever.
Identify the shadow exchange rate given our definition of M .
(c) According to the Krugman model a speculative attack will
happen in the point T , when the fixed exchange rate equals
the shadow exchange rate, or e = ee. Illustrate the paths of e
and ee. Explain why a speculative attack must happen at T .
(d) Assume that η = 2. Find T .
2. Tobin tax
298
Assume that we have a fixed exchange rate. The rate is fixed at
1:1.
The economy fluctuates between three ‘states’—high output, intermediate output and low output. Assume that the government
believes the costs of a devaluation will be high. However, if there
is a speculative attack, the government will devalue the currency.
How much will depend on the state of the economy. In the low
output state the new exchange rate will be 1.5:1. In the intermediate state the exchange rate will be 1.25:1. In the good state the
government will not make a shift.
The central bank has committed 10 million domestic currency
units to defend the exchange rate. There are two traders in the
market. Each controls 5 million domestic currency units. If the
trader sells his domestic currency to the central bank he obtains
foreign currency at the rate 1:1. If there is a devaluation, he can
exchange back at the new rate. If there is no cost of speculation his
profit will be the amount of foreign currency times the change in
the exchange rate. Example: sell 4 million, exchange rate devalue
to 1.5:1. Profit: (1.5-1)*4=2.
(a) Assume that the cost of speculation is 1. Calculate the profit
of each trader if he sells and the other holds, and if he holds
and the other sells, and if both hold and both sell for all three
states of the economy. Organise your findings in three two by
two matrixes. Identify Nash equilibria for all three cases.
(b) Let the cost of speculation increase from 1 to 1.5. Will any
of the above Nash equilibria change? How? Discuss the consequences.
299
(c) Discuss whether or not this is a good argument for introducing
a Tobin tax.
Lecture 6
1. Assuming no transaction costs, suppose GBP=USD 2.4110 in New
York, USD=FRF 3.997 in Paris, and FRF=GBP 0.1088 in London. How could you take advantage of these rates?
2. The media frequently report that ”the dollar’s value strengthened
against many currencies in response to the Federal Reserve’s plan
to increase interest rates.” Explain why the dollar’s value is expected to appreciate, and why the rate may change even before
the Fed affects interest rates.
3. The following quotations are available to you. (You may either
buy or sell at the stated rates.)
Hong Kong Shanghai Bank: FRF/USD=4.8600
Dredsner Bank: DEM/USD=1.4200
Banque National de Paris: FRF/DEM=3.4400
Assume that you have an initial USD 1,000,000. Is triangular
arbitrage possible? If so, explain the steps and compute your
profit.
4. You plan to spend one month at the luxurious Nusa Dua Hotel
in Bali, Indonesia, a year from now. The present charge for a
suitable suite plus meals is Rps 28,800 per night or USD 800 at
the present exchange rate of INR/USD 36.
(a) The Nusa Dua Hotel tells you that next year’s charges will
increase with Indonesian inflation, which you expect to be 16
300
per cent. U.S. inflation is currently 4 per cent per annum. You
believe implicitly in the theory of purchasing power parity.
How many U.S. dollars will you need one year hence to pay
for your 30-day vacation?
(b) The forward rate on a one year contract is INR/USD=40.
How many dollars do you need one year hence if you enter
into a forward contract today?
(c) On a one year instrument, the US rate of interest is 8 per
cent. What is the rate of interest on a similar instrument in
Indonesia?
5. The United States and France both produce Cabernet Sauvignon
wine. A bottle of Cabernet Sauvignon sell in the United States
for USD 18. An equivalent bottle sells in France for FRF 100.
(a) According to purchasing power parity, what should be the
U.S. dollar/French franc spot rate of exchange?
(b) Suppose the price of Cabernet Sauvignon in the US is expected to rise to USD 20 over the next year, while the price
of a comparable bottle of French wine is expected to rise to
FRF 118. What should be the one-year forward U.S. dollar/French franc exchange rate?
(c) Given your answers to (a) and (b) above, and given that the
current interest rate in the United States is 6 per cent for
notes of one-year maturity, what would you expect current
French interest rates to be?
6. Suppose today’s spot exchange rate is USD/DEM=0.51. The
six-month interest rates on dollars and DM are 13 per cent and
301
6 per cent respectively (these are annualised rates). The sixmonth forward rate is USD/DEM=0.5273. A foreign exchange
advisory service has predicted that the DEM will appreciate to
USD/DEM=0.54 within six months.
(a) How would you use forward contracts to profit in the above
situation?
(b) How would you use borrowing and lending transactions to
profit?
7. In the 1950s and 1960s many influential economists like Milton
Friedman and Harry Johnson were in favour of floating exchange
rates. Johnson argued that floating exchange rates normally would
”move only slowly and fairly predictably.”
(a) Explain the reasoning behind such a statement.
(b) With the benefit of hindsight we know that exchange rate
fluctuations have been anything but slow and predictable, at
least in the short run. Explain.
Lecture 7
The starting point of the monetary equilibrium model is the real money
demand function, given as
mt − pt = −ηit+1 + φyt .
(10.19)
From this we can derive an expression for the price level, given as
s−t
T
∞ 1 X
η
η
pt =
(ms − φys + ηis+1 ) + lim
pt+T .
T →∞
1 + η s=t 1 + η
1+η
(10.20)
302
If we assume PPP and UIP to hold at all times, and we assume perfect
foresight, we can obtain an expression for the the exchange rate:
s−t
T
∞ η
η
1 X
∗
∗
et =
(ms −φys +ηis+1 −ps )+ lim
et+T .
T →∞
1 + η s=t 1 + η
1+η
(10.21)
1. Define the real exchange rate, Q. What assumption do we make
about the real exchange rate when we assume PPP to hold?
2. Write the assumptions of the uncovered interest rate parity in
mathematical terms. Explain the intuitive argument behind the
UIP. If the PPP holds at all times, and expected depreciation
is zero, what are the implications for the relationship between
domestic and foreign interest rates?
3. Both equation (11.42) and (11.43) contain two elements. The last
element is on the form
lim
T →∞
η
1+η
T
et+T .
(10.22)
et+T 6= 0?
(10.23)
(a) What is the implication if
lim
T →∞
η
1+η
T
(b) Explain the term “rational bubbles”.
(c) One often assumes that
lim
T →∞
η
1+η
T
et+T = 0.
Explain why this is reasonable. Discuss.
303
(10.24)
4. Assume that the price level is given by
s−t
∞ 1 X
η
pt =
(ms − φys + ηis+1 ),
1 + η s=t 1 + η
(10.25)
and that the exchange rate is given by
s−t
∞ 1 X
η
et =
(ms − φys + ηi∗s+1 − p∗s ).
1 + η s=t 1 + η
(10.26)
Hold i∗ , p∗ and y constant. Assume that m is fixed at m until
time t. At time t therei s an unexpected, permanent contraction
in the money supply. m falls to m0 .
(a) What will be the effect to e and p? Illustrate.
(b) What is the effect to inflation? Illustrate.
(c) What is the effect to the interest rate? Illustrate.
5. In the Dornbusch model one assumes that prices are sticky. The
PPP does no longer hold at every point of time, although it does
hold in the long run. However, the UIP still holds.
(a) Making the assumptions of the Dornbusch model, illustrate
the effects to e, p and i of a contractionary shock to money
supply.
(b) Explain the term overshooting. Why does overshooting arise
in this model?
6. What is a chartist? How does the behaviour of a chartist differ
from the behaviour assumed in the monetary equilibrium model?
7. Read the enclosed article by J. Frankel and K. Froot. Explain the
possible role of chartist during the appreciation of the USD from
1980 to 1985.
304
Lecture 8
Domestic investors are assumed to hold two types of assets: domestic
currency, B, and foreign currency, F . Total real wealth, W , denominated in local currency will be
B F
+
,
P
P
W =
(10.27)
where is the exchange rate. The share of total wealth the investor
chooses to hold in foreign currency is
f=
F
.
PW
(10.28)
We treat f as the the choice variable of the domestic investor. Given
f , one can compute F = f P W and B = (1 − f )P W .
Similar, foreign investors hold currency of the home country1 , B ∗ , and
foreign currency, F ∗ . Total real wealth held by foreigners, W ∗ , denominated in foreign currency will be
W∗ =
B∗
F∗
+
.
P ∗ P ∗
(10.29)
The share of total wealth the foreign investor chooses to hold in domestic currency is
B∗
b =
.
P ∗ W ∗
∗
(10.30)
We treat b∗ as the the choice variable of foreign investors. Given b∗ ,
one can compute B ∗ = b∗ P ∗ W ∗ and F ∗ = (1 − b∗ )P ∗ W ∗ .
Expected real return on the portfolio of a domestic investor will be
1
The home country is the same throughout the exercise—it is the country of the domestic investor, not the foreign investor.
305
given by
·
·
·
·
·
π = (1 − f )(i − p) + f (i∗ + e − p) = (1 − f )i + f (i∗ + e) − p, (10.31)
·
·
where i is the interest rate, p=rate of inflation, e=rate of depreciation
and
∗
denotes foreign values. Expected real return on the portfolio of
a foreign investor will be given by
·
·
·
·
·
π = (1 − b∗ )(i∗ − p∗ ) + b∗ (i − e − p∗ ) = (1 − b∗ )i∗ + b∗ (i − e) − p∗ . (10.32)
·
We assume that p is a stochastic variable with the distribution
·
p ∼ N (µp , σ pp ).
(10.33)
µp is the expected mean of a change in inflation, and σ pp is the expected
standard deviation around the mean. Similar, we assume that
·
p∗ ∼ N (µp∗ , σ p∗ p∗ ),
(10.34)
and
·
e ∼ N (µe , σ ee ).
·
(10.35)
·
The correlation between p and ee is σ ep , and the correlation between
·
·
p∗ and ee is σ ep∗ . There is no uncertainty about the interest rate, as it
is observable today.
Last, define the risk premium, r as
r = i − i∗ − µ e .
306
(10.36)
1. Investors maximise function of the form
1
U = E(π) − Rvar(π).
2
(10.37)
We assume R to be the same for all investors. Find the optimal
f and b∗ .
2. Explain the risks of holding a currency in this model.
As you have found, f and b∗ can both be written as two terms:
one that depends on r and one that does not depend on r. Give an
interpretation of these two terms. Explain how a fall in r affects
f and b∗ . What is the effect for currency flows?
3. In addition to domestic investors and foreigners there is a domestic
central bank. The holdings of the central bank is denoted as B g
and F g for domestic currency and foreign currency respectively.
Explain why we must have that
B g + B + B ∗ = 0,
(10.38)
F g + F + F ∗ = 0.
(10.39)
and
4. Start with the condition F g + F + F ∗ = 0. Insert your findings
for F and F ∗ . Show that
δF g
>0
δ
(10.40)
if all investors have positive holdings of both currencies.
5. Draw a diagram with on the y-axis, and F g on the x-axis. Insert the equilibrium condition of F g using the assumption above.
Explain how F g will change with a change in f , assuming
307
(a) a fixed exchange rate, and
(b) a floating exchange rate.
6. Illustrate the effect of fall in r. Use three graphs:
(a) first assume a fixed exchange rate,
(b) second assume a floating exchange rate,
(c) then assume that the rate is fixed until the foreign reserves
reach a certain level F g . At this point the rate is allowed to
float.
Lecture 9
We are in a two-country world, where each country produce a single
good. The home country produces good H, and the foreign country
good F . Each good has the price of unity measured in the local currency. The relative price of the two goods, which is the same as the real
exchange rate, Q, will be measured as the price of one unit of foreign
good denominated in home currency,
Q=
PF
.
PH
(10.41)
A higher Q implies a real depreciation, a lower Q a real appreciation,
seen from the home country.
Total consumption in the home country of good H is CH , and total
∗
consumption of good F is CF . Foreign consumption is CH
and CF∗ .
Total production of the home country is Y = H, and total production
of the foreign country is Y ∗ = F .
The net capital inflow of the home country is B. B will equal the
308
negative of the current account,
B = −CA,
(10.42)
as we have that the capital account=the current account, and a current
account surplus must give a capital outflow. B reflects capital mobility.
If B is zero, there is no capital mobility. Note that there might still be
trade. However, the trade balance must always be zero.
The rate of absorption, A, is the total consumption and investment
in the home country. We assume no investment and no public sector.
Absorption will then be given as
A = C = Y − CA = Y + B.
(10.43)
Similarly, we have that
A∗ = Y ∗ + B ∗ .
(10.44)
Notice that
B∗ =
−B
,
Q
(10.45)
as B ∗ is measured in foreign currency, and capital inflow in one country
by definition must equal capital outflow in the other, as we have only
two countries.
There were some sources of confusion in the lecture held May 28. The
questions bellow should help you to resolve these...
1. The following was stated in the Lecture on May 28:
“We have two maximisation problems. For the home
309
country we have
1−m
M ax U = CH
(QCF )m s.t. A = Y + B = CH + QCF ,
(10.46)
and for the foreign country
∗
M ax U =
∗
CH
Q
1−m∗
∗
(CF∗ )m s.t. A∗ = Y ∗ −
B
C∗
= H +CF∗ .00
Q
Q
(10.47)
From these two maximisation problems we derived consumption
functions. For the home country we found
CH = (1 − m)(Y + B),
CF = m
Y +B
,
Q
(10.48)
and for the foreign country
∗
CH
= Qm∗ (Y ∗ −
B
),
Q
CF = (1 − m∗ )(Y ∗ −
B
).
Q
(10.49)
The four consumption functions are correct. However, the maximisation problem for the foreign consumers is not. Given the
four consumption functions, make the necessary adjustment of
the maximisation problem.
2. Given what you find above, is it reasonable to assume that
1 − m > m∗ ?
(10.50)
3. Explain why
m∗ Y ∗ =
mY
Q
(10.51)
will imply a trade balance of zero.
4. Using the consumption functions above, and the market clearing
310
clearing condition of
∗
CH + CH
= Y,
(10.52)
and inserting the consumption functions, we derive the market
clearing real exchange rate as
Q=
mY
(1 − m − m∗ )B
−
.
m∗ Y ∗
m∗ Y ∗
(10.53)
Find the effect on Q of a change in Y ∗ . What does this imply
for the welfare of the home country? Is a positive supply shock
abroad good or bad for the home country?
5. We want to illustrate the effect of a temporary shock in Y , and
how different capital flows affect Q differently.
Use the equation for Q stated above. Assume Y ∗ = 20, m = 1/3
and m∗ = 1/3 in all periods. Ignore the existence of interest on
debt.
We look at 4 periods. In period 0 Y is 20, debt is zero, and the
current account is zero. In period 1 output fall from 20 to 10.
In period 2 output bounces back to 20, and remains constant in
period 3 and 4.
Note that the results are not in line with what was presented
during the lecture...
(a) Assume no capital flows. Illustrate the paths of Y , Q, A, B
and total debt.
(b) Assume that the country does not allow A to change in period
1. However debt accumulated in period 1 is to be repaid with
equal amounts in period 2, 3 and 4. Illustrate the paths of Y ,
Q, A, B and total debt.
311
(c) Assume that the country adjusts absorption in period 1, but
with the goal of having the same absorption in period 1, 2,
3 and 4. In the end of period 4 total debt should be zero.
Illustrate the paths of Y , Q, A, B and total debt.
Lecture 10
Solve the following problems:
1. Given
Seignoraget = (1 −
1
)(1 + µ)−η = µ(1 + µ)−η−1 ,
1+µ
(10.54)
find
δSeignoraget
.
δµ
(10.55)
L = π 2 + b[(1 − σ)un + a(π e − π)]2 ,
(10.56)
δL
.
δπ
(10.57)
2. Given
find
3. Given
1−m
L = CH
(QCF )m + λ (Y + B − CH − QCF ) ,
(10.58)
find
δL
.
δCF
(10.59)
4. Given
1 U = (1−f )i+f (i∗ +µe )−µp − R f 2 σ ee + σ pp − 2f σ ep , (10.60)
2
312
find
δU
.
δf
(10.61)
Other questions
1. The Barro-Gordon model (45 %)
We can express the Phillips curve as
u = un + a(π e − π).
(10.62)
Here u is the unemployment rate, un is the “non-accelerating inflation rate of unemployment”, or NAIRU. π is the observed rate
of inflation, and π e is the expected rate of inflation. If inflation
exceeds expected inflation, the unemployment rate can for a short
period be less than the NAIRU. However, one can not expect inflation to exceed expected inflation over time.
We assume that the government has two policy goals: to keep
inflation stable, and to keep unemployment low. In fact, the government has as a goal to keep unemployment at a level u∗ < un .
We specifically assume that
u∗ = σun ,
(10.63)
where 0 < σ < 1.
The government minimises a loss function, L, that contain these
two elements:
L = π 2 + b[u − u∗ ]2 ,
(10.64)
where b (assumed to be > 0) is the weight on holding unemployment at u∗ . If we substitute in for the equations (11.85) and
313
(11.86), we obtain
L = π 2 + b[(1 − σ)un + a(π e − π)]2 .
(10.65)
(a) Assume that the government set π = 0, and that this is fully
credible—the public believes the government, so that π e = 0
as well. Show the loss of the government.
(b) Assume that all agents are rational and have perfect foresight.
Why can the government not achieve the loss in (1a)? What
will be the actual rate of inflation in this economy?
(c) Assume two countries have different values for b in their loss
functions. Why would this create a credibility problem if
the two countries tried to establish a fixed currency between
them?
2. The Krugman model (45 %)
Country A is a developing country with a long history of high
inflation. The money demand is given on logarithmic form as
mt − pt = −η(Et pt+1 − pt ),
(10.66)
where m is the log of the money supply, m = ln(M ), p is the log
of the price level, and η is a parameter.
Assume that PPP holds, so that the exchange rate on log-form,
e, is given by
et = pt − p∗t .
(10.67)
p∗ is the foreign price level. For simplicity we set p∗ = 0, and assume that foreign inflation is zero. If we assume perfect foresight,
314
and use continuous time notation, so that
·
et+1 − et = e,
(10.68)
we can write the money demand function as
·
mt − et = −η e.
(10.69)
Money supply, M , reflects the central bank asset sheet. The central bank has two main types of assets, foreign reserves and domestic government bonds. We can therefore write M as
M = D + R,
(10.70)
where D is domestic bonds, and R is foreign reserves. The central
bank will support a fixed exchange rate as long as R > 0.
Three results:
·
– If the exchange rate is fixed at a level e = e, then e = 0, so
we must have
e = mt .
(10.71)
This implies that the money supply is fixed at a level mt = m.
– If the money supply, M , grows at a fixed rate µ, the exchange
rate is given as:
et = mt + µη.
(10.72)
– Note that if a variable X grows at a given rate µ, the value
of ln(Xt ) = xt can be stated as a function of the growth rate
and the initial value of x:
xt = x0 + µt.
315
(10.73)
In the following we assume that the exchange rate is initially fixed.
The exchange rate is fixed at e = e = m. We have that
M = D0 + R0 .
(10.74)
(a) Assume that the central bank’s holdings of domestic government bonds, D, grows at a speed µ. If the exchange rate shall
remain fixed, what must happen to the money supply? Which
implication will this have for the level of foreign reserves, R?
Why can this policy be described as “inconsistent”?
(b) The “shadow exchange rate”, ee, is given as
eet = dt + µη.
(10.75)
Explain the term “shadow exchange rate”.
(c) According to the Krugman model a speculative attack will
happen in the point T , when the fixed exchange rate equals
the shadow exchange rate, or e = ee. Illustrate the paths of e
and ee. Explain why a speculative attack must happen at T .
(d) At p. 74 in “International Money”, in the discussion of the
Krugman model, De Grauwe states:
“The timing of the attack is independent of the
stock of international reserves the authorities start
with.”
Find the expression for T . Comment on this statement. What
is independent of the initial stock of reserves?
(e) Illustrate the path of foreign reserves and the money supply.
What happens to money supply at time T ? How much does
316
it change? Give an intuitive understanding of this result.
(f) If the central bank increases its holdings of domestic bonds
at a given rate, what might that tell you about fiscal policy
in this country?
Assume that the government is following the policy described
above. However, the central bank is not increasing its holdings of domestic bonds. Instead the government is borrowing
money abroad. Would this make a difference for the results in
our model? Discuss consequences of the different strategies.
3. High volume—Is it a puzzle? (10 %)
The daily volume in the FX spot market in April 1998 was 600
billion USD. As a comparison, the daily volume in the New York
Stock Exchange in this period was 30 billion USD, and average
daily world trade in goods and services was about 15 billion USD.
Given your knowledge of how the FX-market works, discuss these
fact. What features of the FX market might explain the high
volume of the FX-market compared to other markets?
317
Chapter 11
Solutions
Lecture 1
1. Gresham’s law
(a) Question Gresham’s law states that bad money always will
drive good money out of circulation. People will choose to use
the bad money for transactions, and store the good money.
Explain why.
Solution The point here is that one asset (here currency) has
different value depending on how it is used. Assume that the
currency is in the form of gold coins. When this currency is
used for transactions one unit has a value set by the price
level. However, at the same time the coins has a commodity
value equal to its weight in gold.
The value of a coin as a commodity depends on the gold content of the coin. The value of a coin as a means of transaction
only depends on the denomination of the coin. If you have
two coins with the same denomination, but different gold contents, you will store the one with more gold. The one with
318
less gold you will use for transactions. If more bad coins are
introduced, these will be used for transactions, and the good
coins will be stored—bad money drive out good money.
(b) Question Assume a system where two types of coins circulate
in the economy. Some coins are of silver, and some coins are
of gold. Discuss possible problems that can arise in such a
system if there is discovered a huge deposit of silver. Will
silver or gold coins dominate circulation? Will silver or gold
dominate as a store of value?
Solution If supply of silver rise, the value of silver must be
expected to fall. If the relationship between the transaction
value of a silver and a gold coin is fixed, silver is now the bad
coin and gold is the good coin. Silver will drive gold out of
circulation, as people store gold and use silver. Over time the
relationship between the value of a silver and gold coin must
be readjusted if a two metal standard is to be reintroduced.
(c) Question Assume that one has a currency that is backed by
a two-metal standard. Assume that for 35 units of currency
one can claim 1 ounce of gold or 35 ounces of silver at the
central bank. Assume gold supply increases three-fold, while
supply of silver remains constant. How will this affect the
central banks holdings of gold and silver? Will this currency
be “stable”?
Solution In the short-term the exchange ratio in the central
bank remains fixed. However, an increase in the supply of
gold would lead to fall in the relative price of gold to silver
in the commodity markets. So people will bring their paper
319
money to the central bank to get silver in return, take this
silver abroad and exchange it to gold, and return home and
exchange gold into currency at the central bank. This form
of arbitrage could return a handsome profit.
This is in effect a “silver-run” on the central bank. One should
expect the central bank to lose all its silver within a relatively
short period of time. At this point the central bank must
either change the exchange ratios, or convert to a unilateral
gold standard.
Bilateral currency standards was introduced because central
banks did not have enough gold, and needed a wider basis
for backing of a sufficient money supply. However, as long as
there is a risk of large swings in the relative value of the two
metals, such an arrangement must either be flexible—i.e. the
exchange ratios must be frequently adjusted, or the system
will be prone to currency runs.
2. Fiat money and free banking...
(a) Question Assume that the Norwegian government allows everyone to print Norwegian kroner on their own colour printers.
What would do you think would happen to the Norwegian
money supply? What will happen to the Norwegian price
level?
Solution The cost of printing notes on a printer is close to
zero. Everyone would expect that everyone else prints as much
as he or she can, so everyone will print as much as he or she
can as well. This can be illustrated by a simple game theoretic
approach (try to use the prisoners dilemma). The solution is
320
evidently not welfare improving.
(b) At the islands Yap in the Pacific Ocean people used large,
heavy round stones with a hole in the middle as currency. One
stone took two men approximately one week to make. These
stones worked as both unit of account, means of payment and
store of value. However, as they were difficult to carry, the
islanders did not care to carry them around. Instead they
issued legal titles to the stones. These legal titles were used
for trading.
Note that the stones only had value as currency. They had
no value as a commodity.
i. Question What is the difference between the stones on
Yap and the ability to print your own money?
Solution At Yap it took one week of labour to get the new
note finished. There was real cost of producing currency.
ii. Question Explain the fact that inflation on Yap was stable.
Solution People would produce “currency stones” to the
point where the marginal return of producing one was
equal to the alternative value of labour. If the productivity growth in the rest of the economy is the same as the
increase in the ability to produce stones, people would
continue to produce the same ratio of stones to the economy as a whole.
iii. Question What would happen to the price level on Yap
if the islanders got a new technology that would reduce
the time to make a new stone from one week to one day?
321
Should this have any effects for the real economy on Yap?
Solution If productivity in producing stones increased
dramatically, it would be reasonable to produce a lot
more stones. This would induce inflation. The value of
all stones would fall. People who had all their assets in
“stones” would no longer be so rich, while people who had
“stone debts” could no repay these debts with a fraction
of the labour. If contracts are stated in nominal terms
(contracts are stated as the number of stones owed, not
as the number of stones owed as a fraction of the price
level) money will not be neutral in this system.
3. Seignorage
(a) Question Seignorage is given by
Seignoraget =
Mt − Mt−1
.
Pt
(11.1)
We know that real money demand can be written as
Mt
= Et
Pt
Pt+1
Pt
−η
.
(11.2)
Assume perfect foresight. Further, assume that the central
bank can commit to a fixed rate of money growth for all future, µ, so that
Mt
= 1 + µ.
Mt−1
(11.3)
Use this information to show that the rate of money growth,
µopt , that will maximise seignorage revenue is equal to η1 .
Solution The following list of equations go through the whole
322
derivation:
St =
Mt − Mt−1
Pt
Mt − Mt−1 Mt
Mt
Pt
−η
Mt
Pt+1
=
Pt
Pt
−η
Mt − Mt−1 Pt+1
St =
Mt
Pt
−η
Mt−1
Pt+1
St = 1 −
Mt
Pt
St =
Mt
Pt
=1+µ=
Mt−1
Pt−1
1
St = 1 −
(1 + µ)−η
1+µ
µ
St =
(1 + µ)−η
1+µ
St = µ (1 + µ)−1 (1 + µ)−η
St = µ (1 + µ)−η−1
∂St
= (1 + µ)−η−1 + µ (−η − 1) (1 + µ)−η−2 = 0
∂µ
µ (η + 1) (1 + µ)−η−2
=0
1−
(1 + µ)−η−1
1 − µ (η + 1) (1 + µ)−1 = 0
(1 + µ) − (µη + µ) = 0
1 − µη = 0
µ=
1
η
(b) Question Average growth in Norwegian M1 over the period
from December 1992 to January 2002 has been 9.48 per cent
323
on a yearly basis. Assume that Norges Bank behaves according to the rule of optimal seignorage. Find η.
Solution η =
1
µ
⇒η=
1
0.0948
= 10.55
(c) Question Assuming constant money growth, the formula for
seignorage can be written
Seignoraget = µ(1 + µ)−η−1 .
(11.4)
Calculate seignorage for Norway.
Solution Seignoraget = µ(1+µ)−η−1 = 0.0948(1+0.0948)−10.55−1 =
0.0333
(d) Question We want to find seignorage as a percentage of public expenditure. Note that in equation (11.4) seignorage is
measured as a fraction of the price level. For our purposes it
is reasonable to approximate the price level with the money
stock in the last period. In January 2002 Norwegian M1 was
382.6 billion NOK. The public expenditure for 2001 was expected to be 487.9 billion NOK. Calculate seignorage as a
percentage of government expenditure for Norway. Compare
your number with the numbers in Box 8.1 in Obstfeld and
Rogoff, ch. 8.2.
Solution Seigniorage as per cent of public expenditure:
St · M 1t
0.0333 · 382.6
=
= 0.0261.
P ublic expenditure
487.9
(11.5)
Our estimate is that seignorage amounts to 2.61 per cent of
public expenditure in Norway. As one can see from Box 8.1
in Obstfeld and Rogoff this is in line with estimates for other
industrialised countries.
324
Lecture 2
1. Given the data given in the exercise, compute the values of the
money supply and the monetary base.
Solution: Money supply: 9750, money base: 900
2. Next, assume that the Argentinean real exchange rate appreciates vis-a-vis USD. Provide one or two sentences to say what this
means. This question should be answered abstractly, without references to the above data. Your answer should be expressed in
intuitive terms, using plain, jargon-free language.
3. Now suppose that, because of the ARP real appreciation, an Argentinean importer wants to import some U.S. goods. Specifically,
she wants to import 18 dollars worth of machines. This means that
she needs to obtain USD 18.
(a) First, suppose the importer goes to her commercial bank and
asks for USD 18. The commercial bank turns to a trader in an
American bank, and asks him to sell it USD 18 in return for
ARP 18. Assume the trade goes through, and the importer
receives USD 18 from its bank in return for ARP 18. What
is the effect on the Argentinean monetary base?
Solution: This transactions does not involve the currency
board. The money base is not affected.
(b) Second, suppose that, because of the overvaluation, the trader
at the American bank will not sell USD for ARP at 1:1. He
might sell each USD for 1.2 ARP, but if he did then the fixed
exchange rate would have de facto collapsed. The good news
for the Argentinean importer is that the currency board is
325
obliged to sell her USD at 1:1. The commercial bank will
trade ARP 18 for USD 18 by sending a request to the currency
board.
What is the currency board supposed to do with the pesos it
receives for these USD? If the currency board does this, what
is the effect on the Argentinean monetary base?
Solution: The currency board is supposed to burn the ARPs
it receive. To keep the balance sheet in balance, the amount
of ARP issued must match the reserve holdings of USD. If
reserves are reduced with 18, the amount of money issued
must be reduced by 18.
(c) According to the quantity theory of money, money (M ) times
the number of transactions conducted with money (velocity,
V ) should equal the price level, P , times the number of transactions in the economy, T , or
M · V = P · T.
(11.6)
We can simplify by assuming that velocity is constant, and
that T can be set equal to to total production in the economy,
Y.
Do you think the actions by the currency board described
above will alleviate the overvaluation of the Argentinean peso?
Why?
Solution: According to the QTM a contraction of the money
base should lead to lower prices. It the Argentinean price level
falls, the real exchange rate of Argentina devalues. This will
alleviate the overvaluation.
326
(d) What will happen if, for some reason, this process continues?
That is, what will happen if Argentineans try to convert all
their ARP-denominated bank deposits into USD?
Solution: If the process continues, the currency board will
run out of USD. At this point Argentina must either float
the peso or impose capital controls. If the process continues
further the banks will collapse. The reason is that the holdings of the currency board only back-up the currency, not the
entire monetary supply.
4. Given the transaction by the Argentinean importer, what will happen to the Argentinean current account once this transaction occurs? Will there be change in the direction of trade flows? How
will capital flows be affected?
Solution: If the overvaluation in Argentina is alleviated, Argentine goods become more attractive in foreign markets, and foreign
goods less attractive in Argentina. The Argentinean trade deficit
will be reduced. Capital flows that are necessary to finance the
trade deficit will abate.
5. Once the Argentinean importer has obtained the USD 18, you
should find that the system of balance sheets are no longer ‘in
equilibrium’. That is, the two ratios discussed above are no longer
12 and 60. Use the four linear equations described in the appendix
to compute the new equilibrium. What is the new money supply?
Is this new value for the money supply consistent with alleviating
the overvaluation problem?
327
Solution: The four equations can be expressed as:
C =
60H
12 + 60
R = H −C
L = (60 − 1)R
D = 12C.
H is given as 900 − 18 = 882. We then find that
C = 735
R = 147
L = 8673
D = 8820.
The new money supply will be 9555, which is less than 9750. This
is consistent with alleviating the overvaluation. The money supply
has decreased, which will decrease prices and make the real value
of ARP fall.
The economics behind this might go as follows. Upon seeing reserves fall below a safe level, commercial banks start to call in
loans. This causes interest rates to rise. The increase in interest
328
rates induces a fall in the level of economic activity and a drop in
national income. The latter reduces the demand for goods, as well
as money, thereby pushing the domestic price level down. The reduction in domestic demand, in addition to the depreciation of
the real exchange rate, tends to push the current account balance
toward surplus.
6. The money multiplier is defined as the ratio of the reduction in the
money supply to the reduction in the monetary base. The money
multiplier tells us how fast the supply of money grows if another
unit of monetary base is created. What is the money multiplier
here? If the central bank prints one more piece of currency, how
much will the total money supply grow, and therefore how much
will the price level increase (if V and Y is constant)?
Solution: The money multiplier is
9750 − 9555
= 10.83
18
(11.7)
The important point in the example above is to show that a currency
board has a ‘self-correcting’ aspect to it. Excessive inflation (relative
to the reserve country) and/or real exchange rate overvaluation should
be corrected if the currency board does what it is supposed to do. In
addition, the example points out that a county with a currency board
has effectively given up any sort of active monetary policy. Monetary
policy becomes a currency printing/burning robot.
329
Lecture 3
1. Question What do we mean with the n-1 problem in a multilateral exchange rate system?
Solution The n-1 problem relates to the fact that when two currencies have a fixed exchange rate, the ratio of the money supplies
in the two countries is fixed. Two currencies and one exchange
rate implies one monetary policy. If the money supply of one country changes, the money supply of the other country must change
as well. In a multilateral exchange rate agreements all countries
must agree on changes in the money supply. If two countries disagree about the optimal money supply, the system can not survive
unless one of the parties is willing to compromise.
2. Question Assume that the UIP holds. Use the n-1 problem to
illustrate the strains put on the EMS-system by the German unification.
Solution See De Grauwe, ch. 2.2.
The German contraction of the money supply lead to a reduced
demand for e.g. the French franc. The “market rate” of DEM
appreciated, and the “market rate” of the FRF depreciated. To
assure that the system was held within the established target zone
either Germany had to increase its money supply or France had
to reduce its money supply.
In the early 1990’s the Bundesbank’s policy clearly did not fit several of the other countries in the EMS. The system got a credibility
problem. The countries with a weak commitment to fix their rates
within the EMS left the system in 1992. However, France never
330
Figure 11.1: Money supply shock in Germany...
DEM/ECU
DDEM
So DEM
S1 DEM
M DEM
The Bundesbank contracted the German money supply to contain inflationary
pressure.
331
Figure 11.2: And the consequences for France
FRF/ECU
D1 FRF
D0 FRF
SFRF
M FRF
A money supply shock in Germany decreased demand for FRF. To hold the
exchange rate within the target zone France needed to contract their money
supply as well.
332
Figure 11.3: A change in the target zone
DEM/ECU
DDEM
New zone
So DEM
S1 DEM
M DEM
A change in the target zone would have allowed the Bundesbank to contract
the German money supply without putting strains on the fixed exchange rate.
devalued its exchange rate. It was forced to widen the target zone
of exchange rate fluctuations in 1993, however.
3. Question In a meeting in 1991 Germany suggested to revalue the
DEM inside the EMS system (increase the value of DEM relative
to the other currencies in the system). Could this have alleviated
the strains on the system?
Solution A German appreciation would have shifted the target
zone up in the case of France, and down in the case of Germany.
This would have allowed Germany to decrease its money supply
without affecting the money supply of France.
4. Question France vetoed the German suggestion. Why would the
French do this?
333
Solution Some possible arguments:
– France believed that the fixed exchange rate was an important
symbol for European integration. Changing the rate could
endanger the credibility of the system.
– France probably wanted to put pressure on Germany to compromise. After all the EMS was a multilateral agreement, and
it was problematic that the Bundesbank acted without regard
to common European goals.
– It was not clear that the FRF was overvalued. In fact the FRF
remained relatively stable against the DEM over the period
from 1990 to 1998. A de facto devaluation of the FRF could
have lead to increased inflation in France.
Lecture 4
1. Assume the PPP to hold, i.e.
et = pt − p∗t ,
(11.8)
where et is the exchange rate in period t, and p∗ is the foreign price
level. Assume that the foreign price level is fixed at p∗ = 0, and
that foreign inflation, π ∗ , is zero. Discuss the relationship between
domestic inflation, π, and the depreciation of the exchange rate,
·
e, under these assumptions.
·
Solution If p∗ = 0 ⇒ et = pt , so we must have that e = π.
2. We assume that the government focuses on the exchange rate instead of the price level. Give some arguments for why a government could choose to focus monetary policy on a stable exchange
334
rate instead of controlling the money supply.
Solution By focusing on the exchange rate the government can
achieve a number of things:
– In a fixed exchange rate regime money growth will be determined by factors outside the central bank. This might
increase credibility in monetary policy.
– Unlike e.g. an inflation target, where the results of current
monetary policy can first be observed after some time, an
exchange rate is immediately observable in the market.
– A stable exchange rate might have positive implications for
trade.
3. Assume that the exchange rate is fixed, so that et = e. This
·
implies that e = 0. If the government adjusts the fixed rate this
will have the cost of C. As long as the regime is fixed at et = e,
C = 0. If the rate is adjusted, C > 0. The loss function can now
be written as
·2
·e
·
·
L = e + b[(1 − σ)un + a(e − e)]2 + C e,
(11.9)
·e
where e is expected depreciation. Explain why C might be positive.
Solution By adjusting the exchange rate the government might
indicate that it is not really committed to a fixed rate. There
might arise doubts about future monetary policy—i.e. the government loose credibility. One result might be higher interest rates
in the future, as the markets no longer trust the fixed exchange
rate.
335
4. Assume that the fixed exchange rate is credible and the government does not adjust the exchange rate. Calculate the loss of the
government.
·e
·
Solution Here we have that e = 0 and e = 0. So
L = b[(1 − σ)un ]2 .
(11.10)
5. Assume that the fixed exchange rate is credible. Discuss under which circumstances the government might have incentive to
change the exchange rate. What is the role of C?
Solution The rate of depreciation that minimises the government
loss will be given by
δL
·
δe
·e
·
·
= 2e − 2ab[(1 − σ)un + a(e − e)] + C = 0.
(11.11)
This gives us an optimal policy of
·e
· opt
ab(1 − σ)un
ba2 e
C
=
+
−
.
2
2
1 + ba
1 + ba
1 + ba2
·e
·
e
(11.12)
I this case e = 0. It will only be optimal to set e > 0 if
ab(1 − σ)un > C.
(11.13)
The cost of adjusting the rate increases the credibility of the
regime.
6. Assume that the fixed exchange rate is not credible. Assume the
market expects the government to devalue the exchange rate, i.e.
·e
assume e > 0. How would this affect optimal government policy?
Solution In this case it would be optimal to change the exchange
336
rate if
·e
ab(1 − σ)un + ba2 e > C.
(11.14)
Notice that in this case the left hand side is notably larger, as
·e
ab(1 − σ)un + ba2 e > ab(1 − σ)un .
(11.15)
In words: the probability of devaluation being the optimal policy
has increased.
7. In the light of the above results, discuss the term “self-fulfilling”
speculative attacks.
Solution (Very short) The implication of the above results is
that the cost of devaluing depends on market expectations. If
the market expects a devaluation, this makes a devaluation a less
costly policy option.
Lecture 5
1. The Krugman model
(a) If domestic credit grows at a speed µ and the exchange rate
shall remain fixed, what must happen to the money supply?
Which implication will this have for the level of foreign reserves, R?
Assume that domestic credit grows by 20 per cent a year, so
that µ = 0.2. Assume that initial domestic credit is D0 = 10
and initial foreign reserves are R0 = 90. At what time will
R = 0 if this policy is not changes?
Solution If the exchange rate shall remain fixed, the money
supply must remain equal to M . This implies that an absolute
337
increase in domestic credit must be reflected by an absolute
fall in foreign reserves. We have that M0 = 90 + 10 = 100.
So when D = 100, R must by definition be zero. When is
D = 100?
ln(100) = ln(10) + 0.2 · t ⇒ t = 11.5.
(11.16)
With this policy foreign reserves will be zero in 11.5 years.
(b) If we use the above model, and assume money supply growth
at a fixed rate µ, we find the following expression for the
exchange rate:
et = mt + µη.
(11.17)
The “shadow exchange rate”, ee, is defined as the exchange rate
that would have been the actual exchange rate if a speculative
attack had already happened. Assume that the government
continues the policy of fixed growth in domestic credit forever.
Identify the shadow exchange rate given our definition of M .
Solution After a speculative attack foreign reserves goes to
zero. So the money supply will only consist of domestic credit.
We obtain
eet = dt + µη = d0 + µt + µη.
(11.18)
(c) According to the Krugman model a speculative attack will
happen in the point T , when the fixed exchange rate equals
the shadow exchange rate, or e = ee. Illustrate the paths of e
and ee. Explain why a speculative attack must happen at T .
Solution Assume that the fixed exchange rate equals the
shadow rate at time T . Let the fixed exchange rate collapses
338
Figure 11.4: Fixed vs. shadow rate
log exchange rate
T
Shadow floating rate
Fixed rate
log money supply
time
at a T + 2. In this case the shadow rate will exceed the fixed
rate. The fixed rate is terminated at this point, the exchange
rate must make a jump from e to ee. A discrete jump in the
exchange rate will imply infinite profit opportunities for rational speculators. As everyone have perfect foresight, everyone
will try to sell the domestic currency at time T + 1. Hence,
the speculative attack will take place at T + 1. However, at
T + 1 the jump will still be discrete. So everyone will sell at
T . Why not sell at T − 1? Simply because one would lose
money by doing so. If everyone sell at T − 1 the exchange
rate actually will appreciate, as the shadow rate at this time
is lower than the fixed rate.
time
log foreign reserves
(d) Assume that η = 2. Find T .
339
Level of foreign reserves at
time of attack
Solution We have that by definition e = ln(M ) = ln(D0 +
R0 ). At T we have that
e = ln(D0 + R0 ) = d0 + µT + µη.
(11.19)
We insert the information above to obtain
ln(10 + 90) = ln(10) + 0.2 · T + 0.2 · 2.
(11.20)
We can then find T as
T =
ln(D0 + R0 ) − d0 − µη
ln(10 + 90) − ln(10) − 0.2 · 2
=
= 9.5.
µ
0.2
(11.21)
The fixed exchange rate will collapse after 9.5 years of this
policy, 2 years before the foreign reserves would have been
empty without a speculative attack.
2. Tobin tax
(a) Assume that the cost of speculation is 1. Calculate the profit
of each trader if he sells and the other holds, and if he holds
and the other sells, and if both hold and both sell for all three
states of the economy. Organise your findings in three two by
two matrixes. Identify Nash equilibria for all three cases.
Solution The following three illustration give the results in
the three cases. We have one Nash equilibrium (hold, hold)
in the case if output is high, and two equilibria [(hold, hold)
and (sell, sell)] in the case if output is low or intermediate.
(b) Discuss the consequence of an increase in the cost of speculation from 1 to 1.5. Will any of the above Nash equilibria
change?
340
Figure 11.5: High output
Trader 1
Hold
Sell
Hold
0,0
0,-1
Sell
-1,0
-1,-1
Trader 2
341
Figure 11.6: Intermediate output
Trader 1
Hold
Sell
Hold
0,0
0,-1
Sell
-1,0
1/4,1/4
Trader 2
342
Figure 11.7: Low output
Trader 1
Hold
Sell
Hold
0,0
0,-1
Sell
-1,0
3/2,3/2
Trader 2
343
Solution The Nash equilibrium will change in the intermediate case. We move from two equilibria to one equilibrium with
(hold, hold). This increases the ability of the government to
hold the exchange rate stable over the business cycle.
(c) Discuss whether or not this is a good argument for introducing
a Tobin tax.
Solution Increasing the cost of speculation might reduce the
willingness of speculators to take speculative positions. However, there are some problems:
– To avoid speculation when investors expect a substantial
change in the exchange rate would imply that one needs
a very high tax. The higher the tax, the more stability
the tax will provide. However, the higher the tax, the
higher the potential problems of such a tax. It is not
certain that the cost of high tax can justify the potential
stability introduced by such a tax.
– A tax in only one country could lead to capital flight from
this country.
– With the use of financial derivatives speculators can use
other financial markets to do much of the same as they do
in the FX market. It is very difficult to have such control
over the financial markets that “tax avoidance” can be
efficiently stopped.
344
Lecture 6
1. Assuming no transaction costs, suppose GBP=USD 2.4110 in New
York, USD=FRF 3.997 in Paris, and FRF=GBP 0.1088 in London. How could you take advantage of these rates?
Solution Assume the two dollar rates to be “correct”. Then the
GBP/FRF rate should be
1
GBP/U SD
2.4110
GBP/F RF =
=
= 0.10377 6= 0.01088.
F RF/U SD
3.997
(11.22)
⇒ The FRF is expensive in London. Triangular arbitrage does
not hold. Strategy: use FRF 1,000,000 to buy GBP in London.
⇒ obtain GBP 108,800.
sell GBP 108,800 in New York
⇒ obtain USD 262319.
sell USD 262319 in Paris
⇒ obtain FRF 1048480.
⇒ Profit=FRF 48480.
2. The media frequently report that ”the dollar’s value strengthened
against many currencies in response to the Federal Reserve’s plan
to increase interest rates.” Explain why the dollar’s value is expected to appreciate, and why the rate may change even before
the Fed affects interest rates.
Solution Higher interest rates means a monetary contraction.
According to the monetary equilibrium model a monetary contraction should lead to an appreciation of the exchange rate, as
money supply, m, fall. According to the Dornbusch model we
should expect a monetary contraction to lead to an immediate
345
appreciation, followed by a depreciation.
If the Federal Reserve signals a change in interest rates, investors
will update their expectations. As we have seen in the monetary
equilibrium model, the exchange rate depends on expectations
of the future values of fundamental variables. new information
should immediately be incorporated in the exchange rate, even
before the change has come into effect.
3. The following quotations are available to you. (You may either
buy or sell at the stated rates.)
Hong Kong Shanghai Bank: FRF/USD=4.8600
Dredsner Bank: DEM/USD=1.4200
Banque National de Paris: FRF/DEM=3.4400
Assume that you have an initial USD 1,000,000. Is triangular
arbitrage possible? If so, explain the steps and compute your
profit.
Solution The cross rates from Dresdner and BNP implies a FRF/USD
of
F RF/U SD =
F RF/U SD
4.8600
=
= 4.8848 6= 4.8600.
1
U SD/DEM
1.4200
(11.23)
You should find that by investing FRF 100 you can make a profit
of FRF 0.51029.
4. You plan to spend one month at the luxurious Nusa Dua Hotel
in Bali, Indonesia, a year from now. The present charge for a
suitable suite plus meals is Rps 28,800 per night or USD 800 at
the present exchange rate of INR/USD 36.
(a) The Nusa Dua Hotel tells you that next year’s charges will
346
increase with Indonesian inflation, which you expect to be 16
per cent. U.S. inflation is currently 4 per cent per annum. You
believe implicitly in the theory of purchasing power parity.
How many U.S. dollars will you need one year hence to pay
for your 30-day vacation?
Solution
800U SD · (1 + 1.04) · 30 = 24, 960U SD
(11.24)
(b) The forward rate on a one year contract is INR/USD=40.
How many dollars do you need one year hence if you enter
into a forward contract today?
Solution In one year you need
28, 800 · (1 + 0.16) · 30 = 1, 002, 240IN R
(11.25)
If the forward contract is at 40 INR= 1 USD, you need
1, 002, 240
= 25, 056U SD
40
(11.26)
in one year.
(c) On a one year instrument, the US rate of interest is 8 per
cent. What is the rate of interest on a similar instrument in
Indonesia?
Solution If you use numbers from (b):
F =
1+i
1 + i∗
⇒i=1−
40 · 1 + 0.08
= 0.2.
36
(11.27)
5. The United States and France both produce Cabernet Sauvignon
wine. A bottle of Cabernet Sauvignon sell in the United States
347
for USD 18. An equivalent bottle sells in France for FRF 100.
(a) According to purchasing power parity, what should be the
U.S. dollar/French franc spot rate of exchange?
Solution
=
100F RF
18U SD
⇒ 1U SD = 5.5556F RF.
(11.28)
(b) Suppose the price of Cabernet Sauvignon in the US is expected to rise to USD 20 over the next year, while the price
of a comparable bottle of French wine is expected to rise to
FRF 118. What should be the one-year forward U.S. dollar/French franc exchange rate?
Solution
F =
118F RF
20U SD
⇒ 1U SD = 5.90F RF.
(11.29)
(c) Given your answers to (a) and (b) above, and given that the
current interest rate in the United States is 6 per cent for
notes of one-year maturity, what would you expect current
French interest rates to be?
Solution
5.90 = 5.5556
1+i
1 + 0.06
⇒ i = 0.1257.
(11.30)
6. Suppose today’s spot exchange rate is USD/DEM=0.51. The sixmonth interest rates on dollars and DM are 13 per cent and 6 per
cent respectively. The six-month forward rate is USD/DEM=0.5273.
A foreign exchange advisory service has predicted that the DEM
will appreciate to USD/DEM=0.54 within six months.
348
(a) How would you use forward contracts to profit in the above
situation?
Solution A forward contract implies that you get a certain
amount of currency at some time in the future. You will pay
the contract at delivery.
If you buy 100 DEM at the current forward rate, you will have
to have to pay out 100 · 0.5273 = 52.73 U SD in 6 months.
However, if the advisory is correct, in 6 months 100 DEM will
give 54.00 USD. How to make a profit? Assume that the spot
rate in 6 months really will be 0.54. Contract to sell 52.73
USD in 6 months. You get 100 DEM. Exchange these back to
USD at the spot rate. You will now hold 54.00 USD. Profit
equals 54.00-52.73=1.27 USD.
(b) How would you use borrowing and lending transactions to
profit?
Solution Assume the spot rate in 6 moths will actually be
0.54. Borrow 51 USD at 13 per cent today. In six months you
will have to repay 54.32 USD. Exchange to DEM at current
rate, obtain 100 DEM. Invest in Germany at 6 percent for 6
months, in 6 months you obtain 103. Exchange back at the
rate USD/DEM=0.54. You will get 103 ∗ 0.54 = 55.62. Profit
will be 55.62 − 54.32 = 1.30 U SD.
7. In the 1950s and 1960s many influential economists like Milton
Friedman and Harry Johnson were in favour of floating exchange
rates. Johnson argued that floating exchange rates normally would
”move only slowly and fairly predictably.”
(a) Explain the reasoning behind such a statement.
349
Solution The market knows better than governments what
is the true value of the currency. Speculation would be stabilising rather than destabilising. A speculator who increased
the magnitude of exchange rate fluctuations could only do so
by buying high and selling low, which is a recipe for going out
of business rather quickly.
(b) With the benefit of hindsight we know that exchange rate
fluctuations have been anything but slow and predictable, at
least in the short run. Explain.
Solution Lecture 6 discusses a number of avenues to understanding this “puzzle”. In fact, there is no good answer.
Lecture 7
The starting point of the monetary equilibrium model is the real money
demand function, given as
mt − pt = −ηit+1 + φyt .
(11.31)
From this we can derive an expression for the price level, given as
s−t
T
∞ η
η
1 X
(ms − φys + ηis+1 ) + lim
pt+T .
pt =
T →∞
1 + η s=t 1 + η
1+η
(11.32)
If we assume PPP and UIP to hold at all times, and we assume perfect
foresight, we can obtain an expression for the the exchange rate:
s−t
T
∞ 1 X
η
η
∗
∗
et =
(ms −φys +ηis+1 −ps )+ lim
et+T .
T →∞
1 + η s=t 1 + η
1+η
(11.33)
350
1. Define the real exchange rate, Q. What assumption do we make
about the real exchange rate when we assume PPP to hold?
Solution
P∗
Q= .
P
(11.34)
where is the actual level of the exchange rate, P is the domestic price level and P ∗ is the foreign price level. On logs this is
equivalent to
q = e + p∗ − p.
(11.35)
In the PPP we assume that
=
P
.
P∗
(11.36)
To exact, this is the absolute PPP. The implication of the absolute
PPP must be that Q = 1, or that the log of Q, q, equal 0.
2. Write the assumptions of the uncovered interest rate parity in
mathematical terms. Explain the intuitive argument behind the
UIP. If the PPP holds at all times, and expected depreciation
is zero, what are the implications for the relationship between
domestic and foreign interest rates?
Solution
Et t+1
1 + it
=
,
t
1 + i∗t
(11.37)
Et et+1 − et = it − i∗t .
(11.38)
or on log form as
The argument behind the UIP is that expected returns in two
similar assets should be the same. The expected uncovered return
of investing in foreign assets should equal the return of investing
351
in a similar domestic asset.
If expected depreciation is zero, we must have i = i∗ at all times.
3. Both equation (11.42) and (11.43) contain two elements. The last
element is on the form
lim
T →∞
η
1+η
T
et+T .
(11.39)
et+T 6= 0?
(11.40)
(a) What is the implication if
lim
T →∞
η
1+η
T
Solution If the term is not zero, the value of (in this case e)
will diverge from the value implied by “fundamentals”, y, i∗ ,
p∗ and m.
(b) Explain the term “rational bubbles”.
Solution If the timing of the crash of the bubble is uncertain,
a bubble can exist even if everyone knows it is a bubble. If
we expect prices to rise in this period, and the next period,
and the period after that, we can make money by buying the
asset today. But doing so, we just fuel the bubble—the more
people who buy the asset, the more do prices rise. In fact
everyone find it profitable to let the bubble exist—although
everyone knows that a some time in the future the prices need
to revert to a lower level. “Rational bubbles” are models
where the there is much uncertainty about when the bubble
will collapse.
352
(c) One often assumes that
lim
T →∞
η
1+η
T
et+T = 0.
(11.41)
Explain why this is reasonable. Discuss.
Solution If we assume perfect foresight, as we have done
above, it does seem unreasonable to think that we do not
know when a bubble will end. In other words a bubble can not
exist. However, under less strict assumptions about foresight,
it is less certain whether the assumption of no bubbles will
hold. In the end this is a question about how we believe
expectations to be formed.
4. Assume that the price level is given by
s−t
∞ η
1 X
(ms − φys + ηis+1 ),
pt =
1 + η s=t 1 + η
(11.42)
and that the exchange rate is given by
s−t
∞ 1 X
η
(ms − φys + ηi∗s+1 − p∗s ).
et =
1 + η s=t 1 + η
(11.43)
Hold i∗ , p∗ and y constant. Assume that m is fixed at m until
time t. At time t therei s an unexpected, permanent contraction
in the money supply. m falls to m0 .
(a) What will be the effect to e and p? Illustrate.
Solution See figure 11.8.
(b) What is the effect to inflation? Illustrate.
Solution There is of course no inflation before and after the
event—m is supposed to be stable in both periods. There will
be deflationary blip in period t.
353
Figure 11.8: The equilibrium model vs. the disequilibrium model
e
t
time
p
t
time
i
t
time
The whole lines give the solution to an unexpected negative monetary shock
in the monetary equilibrium model. This is as discussed in lecture 1 and
2. The dashed lines give the movements of e, p and i as is expected in the
354
Dornbusch model.
(c) What is the effect to the interest rate? Illustrate.
Solution See figure 11.8.
5. In the Dornbusch model one assumes that prices are sticky. The
PPP does no longer hold at every point of time, although it does
hold in the long run. However, the UIP still holds.
(a) Making the assumptions of the Dornbusch model, illustrate
the effects to e, p and i of a contractionary shock to money
supply.
Solution See figure 11.8.
(b) Explain the term overshooting. Why does overshooting arise
in this model?
Solution The UIP states that
1 + it
Et t+1
=
.
t
1 + i∗t
(11.44)
We know the long term value of e. We know that i will rise
above i∗ in the period of the contractionary shock, and move
back to i∗ over time. We further know that e will fall in the
period of the shock. If e falls to the long term value of e, there
will be no appreciation over time, and UIP will not hold. So
must fall bellow the long term value of e. This is overshooting.
6. What is a chartist? How does the behaviour of a chartist differ
from the behaviour assumed in the monetary equilibrium model?
Solution A chartist is an investor who bases his investment strategy on historic movements in the asset price. In the equilibrium
model we assume that all historic information is incorporated in
the current price, and that only new information can change this
355
price. In the equilibrium model past prices should tell nothing
about future price movements.
7. Read the enclosed article by J. Frankel and K. Froot. Explain the
possible role of chartist during the appreciation of the USD from
1980 to 1985.
Lecture 8
1. Investors maximise function of the form
1
U = E(π) − Rvar(π).
2
(11.45)
We assume R to be the same for all investors. Find the optimal
f and b∗ .
Solution Domestic investors will maximise a function on the form
1 U = (1−f )i+f (i∗ +µe )−µp − R f 2 σ ee + σ pp − 2f σ ep . (11.46)
2
We optimse with regard to f , and obtain
δU
1
= −i + (i∗ + µe ) − R [2f σ ee − 2σ ep ] = 0.
δf
2
(11.47)
Solving (11.84) for f leaves us with
f=
σ ep
1
+
(i∗ + µe − i).
σ ee Rσ ee
(11.48)
If we substitute in for r we have
f=
σ ep
r
−
.
σ ee Rσ ee
356
(11.49)
Foreign investors will maximise a function on the form
1
U = (1 − b∗ )i∗ + b∗ (i − µe ) − µp∗ − R [b∗ 2σ ee + σ p∗ p∗ + 2b∗ σ ep∗ ] .
2
(11.50)
We optimse with regard to b∗ , and obtain
δU
1
= −i∗ + (i − µe ) − R [2f σ ee + 2σ ep∗ ] = 0.
∗
δb
2
(11.51)
Solving (11.51) for b∗ leaves us with
b∗ = −
σ ep∗
1
−
(i∗ + µe − i).
σ ee
Rσ ee
(11.52)
If we substitute in for r we have
b∗ = −
σ ep∗
r
+
.
σ ee
Rσ ee
(11.53)
2. Explain the risks of holding a currency in this model.
As you have found, f and b∗ can both be written as two terms:
one that depends on r and one that does not depend on r. Give an
interpretation of these two terms. Explain how a fall in r affects
f and b∗ . What is the effect for currency flows?
Solution The risk of holding currency is the risk of inflation. If
inflation rise, the currency will lose value. The investor wants to
invest in foreign currency to hedge against inflation risk, and to
earn money on differences in return, reflected by the risk premium.
The term that does not depend on r is the minimum variance
portfolio. This gives the share of holdings of foreign (in the case
of domestic investors) or domestic (in the case of foreign investors)
currency that minimises the risk of inflation to the currency holdings.
357
The term that does depend on r is the speculative portfolio. A fall
in r will lead to an increase in the domestic investors speculative
portfolio holdings of foreign currency. We see that a fall in r will
lead to a fall in the foreign investors holdings of domestic currency.
The implication is a flow from the domestic currency to the foreign
currency.
3. In addition to domestic investors and foreigners there is a domestic
central bank. The holdings of the central bank is denoted as B g
and F g for domestic currency and foreign currency respectively.
Explain why we must have that
B g + B + B ∗ = 0,
(11.54)
F g + F + F ∗ = 0.
(11.55)
and
Solution A financial asset must by definition be the liability of
someone else. If I hold a bond, someone has issued that bond.
Money is the liability of the government that has issued it.
4. Start with the condition F g + F + F ∗ = 0. Insert your findings
for F and F ∗ . Show that
δF g
>0
δ
(11.56)
if all investors have positive holdings of both currencies.
Solution We have that
σ ep
r
F =−
−
σ ee Rσ ee
g
B
+F
358
∗
σ ep∗
r
B
∗
− 1+
−
+F .
σ ee
Rσ ee
(11.57)
We want to identify the condition when
δF g
δ
> 0. This will hold if
∗
σ ep
r
B
σ ep∗
r
B
δF g
=
−
+
1
+
−
.
δ
σ ee Rσ ee
2
σ ee
Rσ ee
2
(11.58)
This can be rewritten as
δF g
=f
δ
∗
B
B
∗
+ (1 − b )
> 0.
2
2
(11.59)
If B > 0 and f > 0 domestic investors hold both currencies, and
the first term is greater than zero. If (1 − b∗ ) > 0 foreign investors
holdings of foreign currency is greater than zero. If B ∗ > 0 their
holdings of domestic currency is greater than zero. The last term
must then be greater than zero, and the total must therefore be
greater than zero. The condition will always be satisfied if both
domestic and foreign investors hold a positive amount of both
currencies.
5. Draw a diagram with on the y-axis, and F g on the x-axis. Insert the equilibrium condition of F g using the assumption above.
Explain how F g will change with a change in f , assuming
(a) a fixed exchange rate, and
(b) a floating exchange rate.
Solution For diagrams, see below. In a fixed exchange rate regime
the central bank must adjust its foreign reserves as supply of foreign currency to the central bank changes. In a floating exchange
rate regime the central bank will not intervene in the foreign exchange market. In this case the exchange rate must change to
equilibrate the market.
6. Illustrate the effect of fall in r. Use three graphs:
359
(a) first assume a fixed exchange rate,
(b) second assume a floating exchange rate,
(c) then assume that the rate is fixed until the foreign reserves
reach a certain level F g . At this point the rate is allowed to
float.
Lecture 9
1. The following was stated in the Lecture on May 28:
“We have two maximisation problems. For the home
country we have
1−m
(QCF )m s.t. A = Y + B = CH + QCF ,
M ax U = CH
(11.60)
and for the foreign country
∗
M ax U =
∗
CH
Q
1−m∗
∗
(CF∗ )m s.t. A∗ = Y ∗ −
B
C∗
= H +CF∗ .00
Q
Q
(11.61)
From these two maximisation problems we derived consumption
functions. For the home country we found
CH = (1 − m)(Y + B),
CF = m
Y +B
,
Q
(11.62)
and for the foreign country
∗
CH
= Qm∗ (Y ∗ −
B
),
Q
CF = (1 − m∗ )(Y ∗ −
B
).
Q
(11.63)
The four consumption functions are correct. However, the maximisation problem for the foreign consumers is not. Given the
360
Figure 11.9: Fixed exchange rate. Fall in r
e
Monetary policy,
fixed rate
Supply of foreign
currency to the
central bank
Fg
Figure 11.10: Floating exchange rate. Fall in r
e
Supply of foreign
currency to the
central bank
Monetary policy,
floating rate
Fg
361
four consumption functions, make the necessary adjustment of
the maximisation problem.
Solution As a general rule we have that if the maximisation problem is formulated as
U = X n Y 1−n s.t. A = X + pY,
(11.64)
the solution will be on the form
X = nA,
Y
Y = (1 − n) .
p
(11.65)
If you take a closer look, all four consumption functions stated
above are on this form. However, if the maximisation problem for
the foreign country was correct as stated we should expect that
∗
= (1 − m∗ )Q(Y ∗ −
CH
B
),
Q
CF = m∗ (Y ∗ −
B
).
Q
(11.66)
But I have stated that the consumption function given was correct, and the maximisation problem wrong. For the consumption
function to be correct, the maximisation problem must be formulated
∗
M ax U =
∗
CH
Q
m∗
∗
(CF∗ )1−m
∗
B
CH
s.t. A = Y − =
+ CF∗ .
Q
Q
(11.67)
∗
∗
2. Given what you find above, is it reasonable to assume that
1 − m > m∗ ?
(11.68)
Solution m reflects the share of foreign goods in home consumption, and m∗ is the share of home goods in foreign consumption.
362
The statement above claims that the share of home goods in home
country consumption exceeds the share of home goods in the foreign consumption. That sound reasonable.
3. Explain why
m∗ Y ∗ =
mY
Q
(11.69)
will imply a trade balance of zero.
Solution m∗ Y ∗ Q is the foreign consumption of home goods in
home currency, or home exports denominated in home currency.
mY is the home consumption of foreign goods in home currency,
or home imports in home currency. If these to sums are equal, the
trade balance is by definition zero.
4. Using the consumption functions above, and the market clearing
clearing condition of
∗
CH + CH
= Y,
(11.70)
and inserting the consumption functions, we derive the market
clearing real exchange rate as
Q=
mY
(1 − m − m∗ )B
−
.
m∗ Y ∗
m∗ Y ∗
(11.71)
Find the effect on Q of a change in Y ∗ . What does this imply
for the welfare of the home country? Is a positive supply shock
abroad good or bad for the home country?
Solution We find that
δQ
mY − (1 − m − m∗ )B 1
Q
=
−
= − ∗ < 0.
∗
∗
∗
∗
δY
mY
Y
Y
(11.72)
A positive supply shock abroad will imply a real appreciation. A
real appreciation means that the value of the home currency has
363
increased, consumers in the home country can consume more of
the foreign good than before. Should not a real appreciation also
mean less competitiveness? That is not a problem here: remember home output has not changed, and markets still clear, so all
home output is consumed. The foreign country is richer, and will
consume more of both home and foreign goods. A positive supply
shock in one country will in this case be to the advantage of both
countries.
5. We want to illustrate the effect of a temporary shock in Y , and
how different capital flows affect Q differently.
Use the equation for Q stated above. Assume Y ∗ = 20, m = 1/3
and m∗ = 1/3 in all periods. Ignore the existence of interest on
debt.
We look at 4 periods. In period 0 Y is 20, debt is zero, and the
current account is zero. In period 1 output fall from 20 to 10.
In period 2 output bounces back to 20, and remains constant in
period 3 and 4.
Note that the results are not in line with what was presented
during the lecture...
(a) Assume no capital flows. Illustrate the paths of Y , Q, A, B
and total debt.
Solution See table 11.1.
(b) Assume that the country does not allow A to change in period
1. However debt accumulated in period 1 is to be repaid with
equal amounts in period 2, 3 and 4. Illustrate the paths of Y ,
Q, A, B and total debt at end of period.
Solution See table 11.2.
364
Figure 11.11: Exchange rate fixed if F g > F g . Fall in r
e
Supply of foreign
currency to the
central bank
Monetary policy,
fixed rate
Monetary policy,
floating rate
Fg
g
F min
Table
Periods 0
Y
20
Q
1
A
20
B
0
debt
0
11.1:
1
10
0.5
10
0
0
First
2 3 4
20 20 20
1 1 1
20 20 20
0 0 0
0 0 0
Table 11.2: Second
Periods 0 1
2
3
4
Y
20 10
20
20
20
Q
1 0 1.167 1.167 1.167
A
20 20 50/3 50/3 50/3
B
0 10 -10/3 -10/3 -10/3
debt
0 10 10/6 10/3
0
365
(c) Assume that the country adjusts absorption in period 1, but
with the goal of having the same absorption in period 1, 2,
3 and 4. In the end of period 4 total debt should be zero.
Illustrate the paths of Y , Q, A, B and total debt.
Solution See table 11.3. Q appreciate less in period 1 compared to the result above. It also depreciates less in period 2.
Lecture 10
Solve the following problems:
1. Given
Seignoraget = (1 −
1
)(1 + µ)−η = µ(1 + µ)−η−1 ,
1+µ
(11.73)
find
δSeignoraget
.
δµ
(11.74)
Solution
δSeignoraget
= (1 + µ)−η−1 − µ(η + 1)(1 + µ)−η−2 = 0. (11.75)
δµ
2. Given
L = π 2 + b[(1 − σ)un + a(π e − π)]2 ,
(11.76)
δL
.
δπ
(11.77)
find
Solution
δL
= 2π − 2ab[(1 − σ)un + a(π e − π)] = 0.
δπ
366
(11.78)
3. Given
1−m
L = CH
(QCF )m + λ (Y + B − CH − QCF ) ,
(11.79)
find
δL
.
δCF
(11.80)
Solution
δL
1−m
= mQm (CF )m−1 CH
− Qλ = 0,
δCF
(11.81)
4. Given
1 U = (1−f )i+f (i∗ +µe )−µp − R f 2 σ ee + σ pp − 2f σ ep , (11.82)
2
find
δU
.
δf
(11.83)
Solution
1
δU
= −i + (i∗ + µe ) − R [2f σ ee − 2σ ep ] = 0.
δf
2
(11.84)
Other questions
1. The Barro-Gordon model (45 %)
We can express the Phillips curve as
u = un + a(π e − π).
(11.85)
Here u is the unemployment rate, un is the “non-accelerating inflation rate of unemployment”, or NAIRU. π is the observed rate
of inflation, and π e is the expected rate of inflation. If inflation
367
exceeds expected inflation, the unemployment rate can for a short
period be less than the NAIRU. However, one can not expect inflation to exceed expected inflation over time.
We assume that the government has two policy goals: to keep
inflation stable, and to keep unemployment low. In fact, the government has as a goal to keep unemployment at a level u∗ < un .
We specifically assume that
u∗ = σun ,
(11.86)
where 0 < σ < 1.
The government minimises a loss function, L, that contain these
two elements:
L = π 2 + b[u − u∗ ]2 ,
(11.87)
where b (assumed to be > 0) is the weight on holding unemployment at u∗ . If we substitute in for the equations (11.85) and
(11.86), we obtain
L = π 2 + b[(1 − σ)un + a(π e − π)]2 .
(11.88)
(a) Assume that the government set π = 0, and that this is fully
credible—the public believes the government, so that π e = 0
as well. Show the loss of the government.
Solution The the loss would be
L = b[(1 − σ)un ]2 .
(11.89)
(b) Assume that all agents are rational and have perfect foresight.
Why can the government not achieve the loss in (1a)? What
368
will be the actual rate of inflation in this economy?
Solution The government can set π at will. If it minimises
its loss function, inflation would be set at:
δL
= 2π − 2ab[(1 − σ)un + a(π e − π)] = 0.
δπ
(11.90)
or
(1+a2 b)π = ab[(1−σ)un +a(π e )] ⇒ π =
ab(1 − σ)un a2 bπ e
+
.
1 + a2 b
1 + a2 b
(11.91)
If π e = 0 the government would set π 6= 0—it would choose
to use the high credibility to “fool” the public. By setting
inflation¿0 it achieves a lower unemployment rate.
The public will understand the incentives of the government.
They will know the government loss function. Expected inflation will therefore equal actual inflation, π = π e . The inflation
rate will be:
π = πe =
ab(1 − σ)un
a2 bπ e
+
1 + a2 b
1 + a2 b
⇒ π = π e = ab(1 − σ)un .
(11.92)
(c) Assume two countries have different values for b in their loss
functions. Why would this create a credibility problem if
the two countries tried to establish a fixed currency between
them?
Solution If two countries shall fix their common exchange
rate, this implies that the two countries must follow the same
monetary policy over time. This implies that their inflation
rates must be approximately equal over time as well. To see
this, assume that PPP must hold over time. However, as we
369
can see above, optimal inflation will depend on the parameter
b. If b is different, optimal inflation will not be the same.
One should expect that the country with high b has higher
inflation. This will strain the credibility of the regime.
2. The Krugman model (45 %)
Country A is a developing country with a long history of high
inflation. The money demand is given on logarithmic form as
mt − pt = −η(Et pt+1 − pt ),
(11.93)
where m is the log of the money supply, m = ln(M ), p is the log
of the price level, and η is a parameter.
Assume that PPP holds, so that the exchange rate on log-form,
e, is given by
et = pt − p∗t .
(11.94)
p∗ is the foreign price level. For simplicity we set p∗ = 0, and assume that foreign inflation is zero. If we assume perfect foresight,
and use continuous time notation, so that
·
et+1 − et = e,
(11.95)
we can write the money demand function as
·
mt − et = −η e.
(11.96)
Money supply, M , reflects the central bank asset sheet. The central bank has two main types of assets, foreign reserves and do-
370
mestic government bonds. We can therefore write M as
M = D + R,
(11.97)
where D is domestic bonds, and R is foreign reserves. The central
bank will support a fixed exchange rate as long as R > 0.
Three results:
·
– If the exchange rate is fixed at a level e = e, then e = 0, so
we must have
e = mt .
(11.98)
This implies that the money supply is fixed at a level mt = m.
– If the money supply, M , grows at a fixed rate µ, the exchange
rate is given as:
et = mt + µη.
(11.99)
– Note that if a variable X grows at a given rate µ, the value
of ln(Xt ) = xt can be stated as a function of the growth rate
and the initial value of x:
xt = x0 + µt.
(11.100)
In the following we assume that the exchange rate is initially fixed.
The exchange rate is fixed at e = e = m. We have that
M = D0 + R0 .
(11.101)
(a) Assume that the central bank’s holdings of domestic government bonds, D, grows at a speed µ. If the exchange rate shall
remain fixed, what must happen to the money supply? Which
371
implication will this have for the level of foreign reserves, R?
Why can this policy be described as “inconsistent”?
Solution If the exchange rate shall remain fixed, the money
supply must remain equal to M . This implies that an absolute
increase in domestic credit must be reflected by an absolute
fall in foreign reserves. But when reserves go to zero, the
central bank can no longer sustain a fixed exchange rate.
(b) The “shadow exchange rate”, ee, is given as
eet = dt + µη.
(11.102)
Explain the term “shadow exchange rate”.
Solution The shadow exchange rate is the exchange rate that
would have been the actual exchange if a speculative attack
had already taken place. This implies that the shadow exchange rate is the exchange rate assuming that R = 0. It will
only depend on the level of D.
(c) According to the Krugman model a speculative attack will
happen in the point T , when the fixed exchange rate equals
the shadow exchange rate, or e = ee. Illustrate the paths of e
and ee. Explain why a speculative attack must happen at T .
Solution Assume that the fixed exchange rate equals the
shadow rate at time T . Let the fixed exchange rate collapses
at a T + 2. In this case the shadow rate will exceed the fixed
rate. The fixed rate is terminated at this point, the exchange
rate must make a jump from e to ee. A discrete jump in the
exchange rate will imply infinite profit opportunities for rational speculators. As everyone have perfect foresight, everyone
372
will try to sell the domestic currency at time T + 1. Hence,
the speculative attack will take place at T + 1. However, at
T + 1 the jump will still be discrete. So everyone will sell at
T . Why not sell at T − 1? Simply because one would lose
money by doing so. If everyone sell at T − 1 the exchange
rate actually will appreciate, as the shadow rate at this time
is lower than the fixed rate.
(d) At p. 74 in “International Money”, in the discussion of the
Krugman model, De Grauwe states:
“The timing of the attack is independent of the
stock of international reserves the authorities start
with.”
Find the expression for T . Comment on this statement. What
is independent of the initial stock of reserves?
Solution We have that by definition e = ln(M ) = ln(D0 +
R0 ). At T we have that
e = m = ln(D0 + R0 ) = ee = d0 + µT + µη.
(11.103)
We can then find T as
T =
ln(D0 + R0 ) − d0 − µη
.
µ
(11.104)
Clearly, the timing of T does depend on R0 . The larger R0 ,
everything else given, the longer it takes before the speculative
attack takes place. However, note that no value of R0 could
stop a speculative attack from taking place—it will only affect
the timing of the attack. A speculative attack is a certain
outcome as long as there is a given growth in domestic credit.
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(e) Illustrate the path of foreign reserves and the money supply.
What happens to money supply at time T ? How much does
it change? Give an intuitive understanding of this result.
Solution In the fixed exchange rate regime, the exchange rate
is given as
e = m.
(11.105)
In the floating regime the exchange rate is given as
eet = mt + ηµ.
(11.106)
However, at time T we have that e = ef
T . So we must simultaneously have that
m = mT + ηµ.
(11.107)
It follows that at time T money supply must fall by
mT − m = −ηµ.
(11.108)
The point here is that the functions for the exchange rate
depends on expectations: if money supply is constant, e = m,
but if money supply is growing, e = m + ηµ. As we are
changing from one regime to the other, the money supply
must fall to assure that the arbitrage condition is fulfilled.
For illustrations, see figure 11.12.
(f) If the central bank increases its holdings of domestic bonds
at a given rate, what might that tell you about fiscal policy
in this country?
Assume that the government is following the policy described
374
Figure 11.12: Anatomy of a speculative attack
log exchange rate
T
Shadow floating rate
Fixed rate
log money supply
time
time
log foreign reserves
Level of foreign reserves at
time of attack
time
375
above. However, the central bank is not increasing its holdings of domestic bonds. Instead the government is borrowing
money abroad. Would this make a difference for the results in
our model? Discuss consequences of the different strategies.
Solution We probably have a case with a government running fiscal deficits—reflected in their issuance of government
bonds. The independence of the monetary authority form the
fiscal authority is however weak, as the monetary authority
evidently is forced to take up the fiscal debt. As there is
fixed exchange rate, the debt can not be monetised directly.
Instead the central bank builds down reserves.
If the central bank’s holdings of foreign reserves do not change,
then the fixed exchange rate regime remains viable for all future. However, it is questionable whether it is possible to
borrow abroad of finance an eternal budget deficit. At some
point the ability to borrow aborad must be expected to dry
up. At this point of time the government must use the foreign reserves to repay old debt, and use the money supply
to finance the deficit. So unless policy changes, the result—a
speculative attack—would probably still follow.
3. High volume—Is it a puzzle? (10 %)
The daily volume in the FX spot market in April 1998 was 600
billion USD. As a comparison, the daily volume in the New York
Stock Exchange in this period was 30 billion USD, and average
daily world trade in goods and services was about 15 billion USD.
Given your knowledge of how the FX-market works, discuss these
fact. What features of the FX market might explain the high
376
volume of the FX-market compared to other markets?
Solution As there are no given solution to this question, every
good discussion should be rewarded.
Two points:
(a) As exchange rate markets are used not only for trade of goods,
but also for the trade of assets between people in different
countries, and because the daily trade in assets are much bigger than the daily trade of goods, the turnover in the asset
markets is probably the most relevant comparison if we want
to understand the volume in the FX-market. However, trade
in assets alone is probably not enough to explain the volume
observed.
(b) In class we have presented the “hot-potato-hypothesis”: the
FX-market is a multiple dealer market with low transparency
and low transaction costs. Dealers do not sit long on large
currency positions (at least they tend to close out at night).
When customers approach a dealer with a large trade, the
dealer will try to reduce position by making transactions with
other dealers. Other dealers will be eager to make such deals
because this is the best way to obtain information about what
is going on. Currency will be traded between dealers like a
“hot-potato”.
377
Table 11.3: Third
Periods 0
1
2
3
4
Y
20
10
20
20
20
Q
1 0.125 1.125 1.125 1.125
A
20 17.5 17.5 17.5 17.5
B
0
7.5
-2.5
-2.5
-2.5
debt
0
7.5
5
2.5
0