1 The data for these figures are found in an Excel file, exchange rate data file.xls, onBlackboard..

Chapter 4: Exchange Rates

Exchange Rates in the Short Run

Figure 4.1 provides graphs of month to month changes in the value of the Canadian dollar

(C$), and Canadian stock prices between 1990 and 2003. Notice that for much of this period there

has been considerable volatility in both of these series; the exchange rate fluctuates randomly as does

the stock market. It was not uncommon for the C$ to gain or lose as much as 4% of its value during

any given month. This type of volatility was not limited to the C$. The currencies of virtually all major

countries fluctuated with similar random gyrations over this period. See Figures 4.2 and 4.3 for

graphs of similar data series over the same time period. As the graphs show, volatility is common for

stock prices as well. It is also true of many other financial assets such as corporate or government

bonds. Because of this similarity, most economists rely on asset market models to explain short run

exchange rate behavior.1

The chief characteristic of an asset market model is its emphasis on forward looking behavior.

Again, remember that an asset is a form of wealth--something that retains or (hopefully) increases in

value over time. Examples of assets abound in the real world: money, shares of stock, bonds,

paintings, houses, etc. What determines the price of these things? Consider a house. The amount you

are willing to pay for a house depends upon a number of things including its size, state of repair, and

location. In turn, the value of all of these things depends upon your predictions about the future. For

instance, if you think that the neighborhood may become very popular in the future, even if it isn't

today, you might be willing to pay more today because you think that the house will be worth more

in the future.

2

Figure 4.1Canadian Financial Market Behavior

3

Figure 4.2Japanese Financial Market Behavior

4

Figure 4.3Brazil Financial Market Behavior

5

The same logic holds for foreign exchange. If you think investments in Canada may increase in value,

you might be willing to buy them today in anticipation of earning a profit. In the process, you would

need to buy C$'s, thus driving up their value. Alternatively, suppose that you think that the value of

the C$ itself will rise in the future (perhaps because of an anticipated rise in Canadian interest rates),

then you should be willing to buy it today in anticipation of its rise in value. This also puts upward

pressure on the value of the C$.

How can we formalize these ideas? Simple. We begin with the notion of speculation.

Speculators are market participants who deliberately take on risk in the anticipation of making a

profit. For instance, if speculators expect that the C$ will rise in value over the next several weeks,

they might purchase C$'s today. Is this risky? Yes. There is no guarantee that the value of the

Canadian dollar will rise. If instead it were to fall, then speculators might be forced to sell at a loss.

There are other ways for speculators to make money in this market. Let exp(Et+1) equal the

expected value of the exchange rate at time t+1 (e.g., one month from now), based on information

known at time t (e.g., today). That is, this is the value that speculators expect will prevail in the

future. Given this expectation, how can speculators make money in foreign exchange? Recall the

forward market. There, the forward rate, F, is set today for transactions that will occur in the future.

The speculator takes a position in forward exchange based on the value of F (which she knows

today) and her guess of the future spot rate, exp(Et+1).

For instance, if F < exp(Et+1), then the speculator should enter into a contract today to BUY

forward foreign exchange (at price F per unit) expecting to sell it in the spot market at exp(Et+1),

when the contract comes due. On the other hand, if F > exp(Et+1), then the speculator should

contract today to SELL forward foreign exchange in the future (at rate F), expecting to be able to

6

buy (what she must then sell) at exp(Et+1). These strategies are reproduced below:

Rules for Profitable Speculation

If F < exp(Et+1), BUY forward (i.e. go long in foreign exchange).

If F > exp(Et+1), SELL forward (i.e. go short in foreign exchange).

Now, note that if expectations are widely shared in the market, then speculators as a group will tend

to act the same way (i.e. if one buys (sells), all are buying (selling)). In the first case, as most

speculators seek to buy forward, the increased demand will tend to drive F (the price of forward

exchange) up and exp(Et+1) down as market observers begin to anticipate a large number of future

foreign sales when speculators act to close out their forward contracts. Similarly, in the second case,

if speculators act as a group, then large amounts of sales will tend to drive F down and exp(Et+1) up.

(Can you explain why?). In either event, if speculators act as group there is a tendency for F and

exp(Et+1) to equalize. When and if that happens, the foreign exchange market is said to exhibit

uncovered interest rate parity (UIRP). UIRP is a common feature of asset market exchange rate

models. Summarizing so far, with strong common beliefs among speculators, there is a tendency for:

F = exp(Et+1) (UIRP). (4.1)

Recall that:

F = Et×(i - i* + 1) (4.2)

where Et is today's spot exchange rate, i is the home interest rate, and i* is the foreign interest rate.

Combining equations (4.1) and (4.2) and rearranging terms yields the following:

Et = exp(Et+1)/(i - i* + 1) (4.3)

This equation provides the basic model for explaining short run exchange rate behavior. It states that

the value of today's exchange rate depends upon several things: domestic and foreign financial

7

conditions (signified by the interest rate terms), and expectations about future values of the exchange

rate. Consider first the role of interest rates. If domestic interest rates rise, then according to the

model, there will be a tendency for the value of Et to fall. What does that mean? Since Et is the price

of foreign exchange (denominated in dollars), as Et falls, foreign money is getting weaker; the dollar

is getting stronger. Since i is the rate of return in domestic financial markets, a rise in i encourages

foreigner's to shift funds here, in the process demanding more dollars thereby increasing the value

of the dollar (i.e. lowering Et). A rise in i* sets in process the opposite pattern of behavior, thereby

raising the level of Et and lowering the value of the dollar.

What about expectations? As noted above, the value of any asset depends in part on what

you think its value will be in the future. In the model, if you expect foreign exchange to rise in the

future (i.e., if exp(Et+1) rises), then Et will also rise. Moreover, any change in exp(Et+1) will lead to

an immediate change in Et. What could cause expectations to change? Almost anything, but

especially changes in actual or anticipated government policies. Market participants are constantly

searching the news for information that may have an effect on exchange rates. Thus, the upshot of

equation (4.3) is that exchange rates should be very volatile, since new information is constantly

reaching the market. As this "news" is processed it translates into buy or sell orders which in turn

cause exchange rates to move up and down.

Case Study on Brazil

Figure 4.3 contains information on the behavior of the Brazilian currency, the real. Consider

first the general movements in the line in the upper graph. From 1990 until well into 1994, the

monthly change in the exchange rate is positive. This means that each and every month over that

2 Recall again the situations in Canada and Japan over this same period. There, some monthsthe price of the dollar rose, while in other months it fell.

3 Note as well that stock prices tended to also tended to rise most of the months during thisera.

4 This policy was very similar to that undertaken by the Argentine government at about thesame point in time and for the same reason. Recall our discussion of Argentina in the section onthe elasticities model. We will discuss in greater detail below why and how a fixed exchangepolicy might be used to deal with inflation.

8

four span the price of the dollar rose from where it had been in the previous month.2 In fact, from

mid 1992 into 1994 the monthly increase in the exchange rate rises from about 20 percent to over

40 percent. What does this mean? Recall that we are measuring the price of the US dollar in terms

of the Brazilian currency. The graph indicates that in at least one month the price of the dollar paid

by Brazilians increased by 40 percent.

What causes this big difference in exchange rate behavior? The answer is that during this

time period, the Brazilian economy was experiencing massive problems with inflation. In 1993, for

instance, consumer prices rose 1877 percent (that is, they were almost 19 times higher on the last

day of the year than on the first). As we will see in the next section, countries with high inflation

rates will tend to see the price of foreign money rise in terms of their own. The exchange rate is

simply another price. When all other prices are on the rise, so too will be the exchange rate.3

Now, consider the middle part of the diagram. The rapid and continuous rise in the exchange

rate disappears, and the line hovers on the X axis. What does this mean? Clearly, the price of the

dollar has suddenly stopped changing. In fact, in 1994, the Brazilian government, as part of a

program to try to deal with inflation, adopted a fixed exchange rate vis a vis the dollar.4 This fixed

rate policy lasted until late 1998, when the government devalued the real (by announcing a large

9

increase in the price of the dollar) and then allowed the real to be set by market forces. Once this

happened, the Brazilian exchange rate began to behave much more like the Canadian and Japanese

rates shown in the figures.

Additional comment on short run exchange rate behavior

1. Equation (4.3) is derived from the uncovered interest rate parity condition, UIRP. UIRP

assumes that the two assets in the model have identical risk characteristics. Hence, since

these two assets are identical except in terms of currency of denomination, the expected

return on each should be identical in the minds of potential investors. Note, however, that

it is seldom the case in the real world that assets issued in different countries will have

identical risk characteristics. Rather, it is more likely that the market will perceive one or

the other to be inherently more risky to hold. In that case, market participants will require

an additional return, known as a risk premium, rp, to be willing to hold that asset. If so, then

both UIRP and equation (4.3) will no longer hold. Instead, the exchange rate equation will

become

Et = exp(Et+1)/(i - i* + 1 - rp) (4.4)

Unfortunately, risk premia are virtually impossible to measure in the real world. Moreover,

they are likely to be highly volatile. Hence, when real world concerns about risk are included

in the model, the theory predicts that exchange rates will be even more volatile than (4.3)

suggests, and it also becomes much more difficult to test the theory.

Exercises #4.1

1. According to equation (4.3), if the foreign interest rate falls, all other things constant, whatshould happen to the price of foreign money in the short run?

2. According to equation (4.3), if expectations about the future exchange rate suddenly fall, all

5 The lira no longer exists as a currency. In 1999, with the launch of the euro, the lira ceasedto circulate as a currency. Nonetheless, since the euro’s onset, the lira has maintained a fixedvalue against the euro, so it is straightforward to link movements in the euro with identical

10

other things constant, what should happen to E?3. If rp is positive in equation (4.4), then foreign assets are perceived as being more risky than

domestic counterparts. In that case, according to (4.4), what will happen to the exchangerate if the risk premium suddenly rises (even though risk itself does not change)? Does thismake sense? Explain.

4. Two conditions in the foreign exchange market are often assumed to hold true. These arecovered and uncovered interest rate parity (CIRP and UIRP). What is the CIRP condition?Under what conditions is it most likely to hold? Explain. What is the UIRP condition. Whatrole does UIRP play in exchange rate economics? How well does it work in this role?

Exchange Rates in the Long Run

Given the short run volatility we see in exchange rates, is there anything we can say about

their long run movements, such as the average annual change over a decade? Perhaps surprisingly,

the answer is yes. In particular, while economists expect exchange rates to fluctuate considerably,

due to asset market conditions, in the long run we expect that their movement will be anchored

down by goods market considerations. The long run pattern we would expect is known as

purchasing power parity (PPP). PPP is an idea with a long intellectual history. Scholars discussed

the concept in 16th century. Its modern development began with the work of a Swedish economist,

Gustav Cassel following shortly after the end of World War I. Since that time, PPP has become one

of the most studied concepts in international finance. Nonetheless, it remains a somewhat

controversial topic, in part, because it is so difficult to determine whether or not it holds in the data.

We will discuss all of these issues in the next few pages.

However, before we discuss PPP, let's be sure we understand the notion of long run

exchange rate behavior. Consider Figure 4.4. There, find plotted the average annual value of the

U.S. dollar in Italian lira over the period 1948-2003.5 In addition, two trend lines have been inserted

movements in the lira.

11

that attempt to describe the general path of the exchange rate over the period. In particular, from

1948 through 1971, much of the world, including Italy was on a system of fixed exchange rates. The

lira was fixed against the US dollar at a rate of 625. In 1971 the system of fixed exchange rates

collapsed, and like many other currencies, the lira began to float against the dollar. Since then, there

have been periods of rises and falls, but there has also been a clear upward trend in the lira price of

a dollar. That trend is identified as the straight upward sloping line in the figure. A theory of the

long run

Figure 4.4Long run exchange rate behavior

6 Note carefully that P represents the cost of a bundle of goods, and not just the price of asingle product. What goods are in the bundle? It depends upon what prices we are trying tomeasure. To measure consumer prices, one looks at a bundle of goods, including food, clothing,housing, etc., typically purchased by consumers. Producer prices reflect the cost of a set of goodsused by producers in the production process. In either case, P represents the cost of the wholepackage at any one point in time. In this context, P is known as a price level.

12

behavior of exchange rates seeks to explain such patterns as the upward trend that has persisted

since the early 1970s.

The notion of PPP is one of the oldest concepts in economics. It refers to the idea that the

same basket of goods should cost the same when prices are measured in the same currency

regardless of where it is located. So, for instance, suppose that P is the price of a bundle of goods

in the United States, and let P* equal the price of an identical bundle in Italy (measured, of course,

in lira).6 If the two bundles are to have the same price, the following equation must hold:

P = EPPP×P*, or, equivalently

EPPP = P/P*. (4.5)

Equation (4.5) defines what is known as the PPP exchange rate. The theory of PPP says that the

long run equilibrium value of the actual exchange rate will be EPPP. According to the theory, at any

point in time, E will probably not equal EPPP. This is because, as we have already seen, the foreign

exchange market is very volatile, subject to sudden shifts in demand and supply in response to

changes in expectations and other financial market considerations. However, given enough time,

the theory of PPP says that the exchange rate should converge toward PPP.

Why should we expect PPP as the natural equilibrium for an exchange rate? The answer has

to do with natural market forces. Suppose, for instance, that PPP did not hold, and, in particular,

P < E×P*

7 An alternative but equivalent description of the adjustment process to achieve PPP is that thevalue of a unit of a particular currency is its purchasing power, which is simply 1/P. PPP obtainswhen two currencies have identical purchasing power. If one currency purchased more goods, itsvalue would rise, and vice versa.

8 On the other hand, one can look at prices of individual items across countries to get a senseof how well PPP holds. This is the approach taken by the Economist in its Big Mac Index.

13

If that were the case, the price of goods overseas, valued in local currency would be higher than

local goods. This would lead domestic residents to cut back their purchases of foreign goods, and,

in the process cut back their purchases of foreign money. At the same time, demand for local goods

would rise as foreigners would try to take advantage of bargains available here. As part of this,

foreigners would need more of our currency, selling more of theirs in the process. As a result of

this activity, we would expect P to rise and E and P* to fall (can you explain why?). As that happens

we move closer to PPP. All of this may take some time, especially movements in P and P*, so PPP

is unlikely to obtain quickly. However, given enough time, market forces should lead to PPP.7

If PPP holds, then

E = EPPP = P/P* (4.6)

Equation (4.6) is known as absolute PPP . According to (4.6), if absolute PPP holds on a regular

basis, all one should have to do is to compare observed values of E with observed values of P/P*.

As it turns out, absolute PPP is a difficult concept to observe in the real world, because national

governments do not report data on price levels. Rather, they report data on price indices, such as

the consumer price index.8 We will see shortly, this adds an additional complication to testing for

PPP.

An alternative form of PPP--relative PPP--exists. To see how this concept works we must

digress for a moment to discuss "hat" algebra.

9 Note that relative PPP is weaker condition that absolute PPP. If absolute PPP holds, so toowill relative, but not vice versa.

14

______________________________________________________________________________

"Hat" Algebra

Let the symbol "^" denote percentage change, so that ^x equals the percentage change in x, then:

If x = m×n, ^x = ^m + ^n.

or

If y = p/q, ^y = ^p - ^q.

______________________________________________________________________________

Relative PPP begins with absolute PPP and utilizes "hat" algebra to obtain:

^E = ^P - ^P*. (4.7)

Now, note that ^P ( ^P*) is the rate of inflation at home (abroad). Equation (4.7) merely states that

there will be a long run tendency for the home currency (e.g. the dollar) to fall in value (i.e. for E

to rise) if inflation is higher in the United States than abroad, and vice versa.9

Figure 4.5 provides some evidence in support of the notion that PPP holds in the real world.

Two series are plotted on the diagram: the actual annual change in the exchange rate, ^E, and the

change predicted by PPP--equation (4.7), the inflation differential, ^P -

^P*. Note several things about

the figure. First, in most cases PPP does tend to predict the direction of change in the exchange

rate. The actual values tend to be much more volatile than the predicted, but the two series cross

each other repeatedly throughout the sample period. Early in the diagram, the predicted line moves

upward, and in most years there are also increases in the actual exchange rate. In the late 1970s,

both lines move down. In the mid 1980s, there is another downward movement in the predicted

15

change in the exchange rate, and the actual rate also exhibits significant declines. Finally, the

predicted movement in the exchange becomes almost zero in the mid 1990s, but the actual exchange

rate still varies considerably. This example illustrates the both the positive and negative aspects of

PPP as a theory of exchange rate behavior. Despite the fact that the two lines seem to move in

relation to each other, the degree of correlation is weak. Even in annual terms, exchange rates are

much more volatile than theory would predict. Thus, at best, PPP is a "weak" predictor of exchange

rate movements.

Figure 4.5Example of Relative PPP

PPP has a number of uses. The first was as a guide for the re-establishment of fixed

exchange rates at the end of World War I. Prior to the war, exchange rates of many countries had

10 This will be discussed at length in another part of the course.

11 The Economist magazine uses a version of this approach based on the price of Big Macsandwiches at various McDonald’s outlets around the world. Their analysis is known as the BigMac index, and it has appeared in the magazine several times per year over the past decade. Goto http://www.Economist.com for the latest data. For more information on the usefulness of theindex to measure under or over valuation of a country’s currency, see M. Pakko & P. Pollard,“For Here or To Go? Purchasing Power Parity and the Big Mac,” Review, Federal Reserve Bankof St. Louis, Jan/Feb 1996. You can view a copy of this article in Adobe format at:http://research.stlouisfed.org/publications/review/. Go to the website, click on past issues, thenclick on 1996.

16

been fixed by setting fixed values of their currencies in terms of gold.10 During the war, countries

abandoned these fixed prices and allowed their currencies to float. As a consequence, different

countries experienced different rates of change in their rates. At the end of the war, countries

wanted to return to the old exchange rate system, but it was unclear as to what level to set the rates.

Viewing PPP as an equilibrium value for the exchange rate, some countries used it as a guide.

Perhaps the most common use of PPP is to provide a measure of the “disequilibrium” in a

given market exchange rate. To see how this is done, let’s return to equation (4.6). If PPP holds,

E = EPPP = P/P*

Now, rearrange divide the two terms on the left by E (the actual exchange rate):

1 = EPPP/E BUT ONLY if PPP holds

In other words, calculate the PPP exchange rate and divide it by the actual rate on that day. If the

resulting number equals 1, the PPP holds. Suppose, as is likely, that it doesn’t. Suppose instead that

it equals .75. Then the PPP (or equilibrium rate) is 25% lower than the actual rate. That is foreign

currency is 25% more expensive today that its true equilibrium value. Now, if foreign currency is

too expensive, home currency is too cheap. The term that is used in this case is that foreign currency

is overvalued by the market while home currency is undervalued.11

17

The third use for PPP is to allow researchers and bureaucrats to compare data on economic

performance from different countries at the same time. The way that this is done is to use PPP

exchange rates. Using market exchange rates can be very problematic when looking at data from

different countries. Developing countries tend to have very low prices for many goods and services

(e.g. haircuts), especially when measured in terms of currencies from developed countries such as

the United States. In these countries, measures of overall economic activity, when measured at

market exchange rates will understate how much is being produced. PPP exchange rates correct for

this bias in the data, by deriving exchange rates that equalize the prices of these products.

International organizations such as the World Bank and the International Monetary Fund now use

these exchange rates for the data reported in many of their publications.

So far, we have avoided any discussion of how available data can be used to construct PPP

measures. Recall that data on price levels do not exist. Instead what are available on a wide basis

are data on price indices such as a country’s Consumer Price Index (CPI). A CPI is an index number

whose value equals 100 during the data’s base year. It is calculated using the following formula:

(4.8)

where o = the base year, pti is the price of good i in period t, and Ti is the weight that good i receives

in the price index. The numerator and denominator of the CPI equation are nothing more than the

12 Note that this is not as extreme an assumption as you might think. It is simple to convert thedata from one base year to another. The only requirement is that the data equal 100 in the baseyear. So, suppose, for example, that you think the appropriate base year should be 1996, and theseries has a base year of 1990. Simply divide every number in the series by the value of the seriesin 1996, and then multiply each result by 100. The new series will be base 1996.

18

cost of a basket of goods evaluated at two points in time. In other words, the numerator is the price

level, faced by a consumer at time t, Pt, while the denominator is the price level faced by the

consumer in the base year, Po. In other words,

CPIt = Pt/Po

Suppose that there is a foreign CPI that is constructed in the same fashion. Then

CPIFt = P*

t /P*o

Now, suppose that we divide home CPIt by CPIFt . This equals

(4.9)

Now, if we are willing to assume that absolute PPP (given by equation (4.6)) held in the base year,

then Eo = Eo PPP. That is, the actual exchange rate in the base year was also the PPP rate that year.12

Now, cross multiply terms in (4.9), and the resulting equation provides an empirical measure of the

PPP exchange rate for every year of available data:

(4.10)

Equation (4.10) provides a mechanism to construct data to allow tests of whether or not PPP holds

as standard phenomenon. One such test simply involves correlating the movements in the actual

19

exchange rate, E, with its PPP counterpart, EPPP. Another way to test PPP is to look at the behavior

over time of a country’s real exchange rate, ER. Recall

ER = EP*/P

Using hat algebra,

E^

R = E^

+ P^

* - P^

(4.11)

Now, if PPP holds, then the right hand side of (4.11) will equal zero (recall equation (4.7)). If so,

then the percentage change in the real rate over time equals zero. In other words, if PPP holds for

a country, then its real exchange rate should not change.

As it turns out, and as Figure 4.5 demonstrates, PPP rarely holds perfectly. It is much less

likely to hold at any point in time for the exchange rate between any two developed economies.

Such economies are characterized by flexible exchange rates and heavy trading volume in the foreign

exchange market. PPP tends to hold much better if one of the two countries is experiencing high

inflation. It also holds better the less volatile is a country’s nominal exchange rate, E.

Additional comments on PPP

1. Relative PPP does not imply that relative price movements cause exchange rate movements

or vice versa, merely that one would expect these movements to be correlated, at least in the

long run.

2. PPP is not a complete model of exchange rate behavior, since we do not yet have a theory

of what causes prices to move.

3. Evidence of short run deviations from PPP (of which there is an abundance) does not violate

the theory, since such deviations are expected. Evidence of long run PPP (of which there

is some) does not rule out short run deviations.

20

Exercises #4.2

1. Suppose that you have the following data on exchange rates and prices:E P P*

1995 .49 100 1001996 .52 106 1021997 .55 112 1041998 .56 115 1051999 .60 120 106

a. Where was inflation higher (home or overseas) over the sample period?b. What is the base year?c. Calculate the PPP exchange rate for each year of the sample period.d. Compare the actual rate with the PPP rate. How well does PPP hold?e. Change the base year to 1997 and repeat parts c. and d. Does your answer change at all?

2. Suppose that a Big Mac costs $2.50 in New York and SF 15 in Geneva. Suppose furtherthat the spot exchange rate on that day is SF 5 = $1. Calculate the purchasing power parityexchange rate between the Swiss franc and the dollar. Based on your calculation is the SFovervalued or undervalued? Explain. Suppose now that a Big Mac costs £1.25 in Londonwhile the spot exchange rate is £ .40 = $1. Is the pound overvalued or undervalued? Explain.Is the Big Mac a good basis for PPP calculations? Why or why not?

The Monetary Approach to Exchange Rate Determination

Purchasing power parity provides a theory of the long run equilibrium value of the exchange

rate. However, as we have already noted, it is not a complete theory of long run exchange rate

behavior. That is, PPP maintains that the exchange rate movements should be correlated with

movements in price levels. However, PPP makes no statement about why prices move. To close

the circle we need to add elements to the model. This is done with a theory of exchange rate

behavior known as the monetary approach to exchange rate determination (MAER). The MAER

is the workhorse theory of long run exchange rate behavior. It was developed in the 1970s by

economists at the University of Chicago and has been widely studied over the past 30 years.

The MAER has two fundamental building blocks. The first, is purchasing power parity. The

21

second is that agents in the two countries in question have well-defined stable demands for money

and that the price level in each country moves to clear the money market. These elements are spelled

out in the equations that follow.

Et = Et PPP = Pt/P*t (4.6)

MSt /Pt = Lt (4.12)

MSt*/P*

t = L*t (4.13)

where MS represents the money supply and L represents the demand for real money balances. Note

that (4.12) and (4.13) can be solved for domestic and foreign price levels respectively.

Pt = MSt /Lt (4.14)

P*t = MS

t*/L*

t (4.15)

Combining (4.6), (4.14), and (4.15) yields

Et = (MSt \M

St*)(L*

t \Lt) (4.16)

Or, using hat algebra on (4.16)

E^

= M^

S - M^

S* + L^

* - L^

(4.17)

Finally, we assume that the demand for real money balances depends positively on income and

negatively on the interest rate so that money demand changes with changes in either of these

variables.

L^

= l1 Y^

- l2 i^

(4.18)

L^

* = l*1 Y^

* - l*2 i^* (4.19)

where the l1's are sensitivities of money demand to changes in income and the l2's are sensitivities of

money demand to changes in interest rates. Substituting (4.18) and (4.19) into (4.17) yields the

22

fundamental equation of the MAER:

E^

= M^

S - M^

S* + l*1 Y^

* - l*2 i^* - l1 Y

^ + l2 i

^(4.20)

Equation (4.20) spells out the basic predictions of the MAER. In particular, holding all other

variables constant

a. a rise in the growth rate of home (foreign) money creation will cause an increase

(decrease) in the rate of growth of the exchange rate (i.e. an depreciation

(appreciation) of the local currency).

b. a rise in the growth rate of home (foreign) output will cause a decrease (increase) in

the growth rate of the exchange rate (an appreciation (depreciation) of local

currency).

c. a rise in the home (foreign) interest rate will cause an increase (decrease) in the rate

of growth of the exchange rate (a depreciation (appreciation) of local currency).

Predictions in part a. should seem straightforward. In essence, they say that if a country prints more

of its own money (everything else held constant) it will decrease in value in foreign exchange

markets. This is because a rise in home (foreign) money will introduce inflationary pressures in the

home (foreign) economy.

Predictions b. and c. show how changes in variables that influence money demand

(everything else held constant) also can influence the exchange rate. In particular, growth in home

(foreign) income raises money demand and (according to equation (4)) puts downward pressure on

home (foreign) prices. Working through PPP, this lowers (raises) the exchange rate. Growth in the

home (foreign) interest rate lowers money demand and raises home (foreign) prices. Again, working

through PPP, this raises (lowers) the exchange rate.

23

Note prediction c. The direction of change of the exchange rate to a change in interest rates

is exactly the opposite of the change predicted by the short run model of exchange rate behavior.

Why do the two theories make opposite predictions? The answer has to do with the difference

between the short run and the long run. In the earlier model, a rise in the home (foreign) interest

rate is assumed to indicate a short run tightening of monetary policy. As such, it reflects a reduction

in the availability of home (foreign) money. And, when home (foreign) money becomes more scarce

its value rises. In the MAER, a rise in the home (foreign) interest rate is assumed to reflect a rise

in the expected rate of future inflation. In this scenario, money in the future is assumed to be worth

less than it is today (because of a rise in anticipated inflation) and hence home (foreign) money loses

value today.

Exercises #4.3

1. Suppose that economic growth in Mexico suddenly slows. According to the MAER model,what should happen to the dollar price of the Mexican peso? Why does the model make thisprediction?

2. Suppose that interest rates in the United States fall, while those in Britain remain unchanged.According to the MAER model, what should happen to the dollar price of the British pound?Why does the model make this prediction?

3. Suppose that each of the home and foreign money demand parameters are identical acrosscountries (e.g. l1 = l*1). Suppose further that each of the domestic hat variables in equation10 is growing at exactly the same rate as its foreign counterpart. What does the MAERmodel predict will happen to the exchange rate? Why does the model make this prediction?

4. Suppose that domestic money demand is falling at 2% per year while the money supply isrising at 6% per year. What is happening to the domestic price level?

Fixed Exchange Rates

So far, we have discussed the behavior of flexible (or market determined) exchange rates.

Throughout recent history however, there have been extended periods of time when exchange rates

were not market determined; instead governments announced fixed exchange rates for their

13 These practices have become known as the "rules of the game". Whether they were rigidlyadhered to is now thought to be unlikely. However, they were followed closely enough so that thegold standard prevailed for more than 40 years with remarkable stability.

14 For reasons that will become clearer shortly, the examples discussed in this section will makethe assumption that the home country is Switzerland. Thus exchange rates will be expressed asthe number of SF it takes to buy $1. It is straightforward to convert SF exchange rates into $terms.

15 The mint parity prices chosen by central bankers during this era probably conformed withprices for gold that prevailed in the market at that time.

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currencies and then took actions to try to maintain these rates. As it turns out, even though rates

were fixed, some small movements were allowed from one day to the next.

The first modern historical experience with an international system of fixed exchange rates

was known as the "gold standard", which prevailed from about 1870-1914 and then again (but much

less successfully) in the late 1920s. This arrangement was not a formal agreement between countries,

but arose because of common practices followed by central bankers around the world.13 It worked

as follows:

1. Central bankers would declare a fixed price (denominated in local currency) for a

given quantity of gold. This price was known as the mint parity.

2. Central bankers acted to maintain the mint parity price by offering to buy or sell gold

for domestic currency in unlimited amounts to anyone at the mint parity price.

3. In each country, the mint parity never changed and was never expected to change.

If any two countries followed these rules, this would establish fixed exchange rates between them.

To see that consider the following example:14

Suppose the Swiss central bank sets the mint parity at SF 40 = 1 oz. gold and the Federal

Reserve sets the dollar mint parity at $10 = 1 oz.15 So long as these parities are maintained, arbitrage

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in the gold market assures that

SF 40 = $10

or

SF 4 = $1

Now, how does this relationship between mint parities relate to activities in the foreign exchange

market? Recall that the principal participants in the foreign exchange market are commercial banks;

they buy and sell foreign money today much as they did under the gold standard. Now suppose that

you run a Swiss firm that is considering importing some wine from California. To pay for the wine

you need dollars and go to your local bank to buy them (with SF). Suppose the foreign exchange

desk says that the demand for dollars has been really high this week and even though the mint parity

is 4, the bank wants to charge you SF 4.05 per dollar. Would you pay this price? It depends.

Consider your options.

Case 1 (No shipping costs): If it costs nothing to ship gold between the two countries, then you

should turn down the offer from your bank. Instead, take your SF to the Bank of Switzerland (the

central bank) and buy gold at the rate of SF 40 per oz. Ship the gold to the United States. Sell the

gold to the Fed for $ (at the rate of $10 per oz). In so doing, you have guaranteed yourself an

exchange rate of SF 4 = $1, a rate that is significantly better for you than what your bank was willing

to charge. Thus, in this case, you would never pay more (or less) than SF 4 per $.

Case 2 (shipping costs): In the real world however, shipping gold is not costless. Suppose,

therefore, that it costs SF .9 to ship 1 oz of gold between the two countries. The cost to you of

converting SF into gold and shipping the gold to the United States in order to acquire dollars now

becomes:

16 To understand why this is so, consider the case of a Swiss exporter who has earned dollarsbut is having trouble finding any local bank to buy them. It can sell the dollars to the Fed, buygold, ship it back to Switzerland, and sell the gold for SF at the Bank of Switzerland.

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SF 40 (cost of gold) + SF .9 (shipping costs) = $10

or

SF 4.09 = $1

Thus, in this case, the best you can do if you ship gold is to buy dollars at the rate of SF 4.09 per

$. If your commercial bank offers to sell you dollars at the rate of SF 4.05, you should accept the

price.

Thus, the existence of shipping costs establishes a price ceiling on foreign exchange (in the

example above, the ceiling is SF 4.09). By similar logic, shipping costs also establish a price floor

(in the example it is SF 3.91).16 The actual exchange rate that would prevail at the local banks on

any given day could range from 3.91 to 4.09. To see this more clearly consider Figure 4.6. There

I have plotted three alternative situations that could prevail in the Swiss foreign exchange market.

Graph A illustrates a situation when the prevailing exchange rate lies between the price

ceiling and price floor. In this situation, private market demand equals private market supply and

there is no incentive for firms or individuals to buy or sell gold from the central bank in order to

acquire or sell foreign exchange. Note that small changes in demand and supply will cause some

movement in the exchange rate without any changes in central bank holdings of gold. This situation

is analogous to exchange rate determination under perfect flexibility.

Graph B illustrates the case where private market demand and supply intersect above the

price ceiling. In this case, the equilibrium exchange rate, E*, does not equal the actual exchange rate,

E (i.e. 4.09). As we have already seen, when the exchange rate hits 4.09, individuals have an

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incentive to buy gold from the central bank and ship it overseas. Thus, when the exchange rate hits

4.09, Switzerland begins to lose gold. How much gold actually flows out? This is determined by the

size of excess demand. As the diagram illustrates, in this case Switzerland would lose gold equal in

value to the difference between Q1 and Q2. This loss of gold represents a loss of international

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reserves and corresponds to an official settlements balance deficit in Switzerland's BOP (equal in

value to the difference between Q1 and Q2). In summary, when the exchange rate under the gold

standard hits the price ceiling, the country in question begins to lose gold. Thus, the price ceiling is

sometimes called the gold export point. Note as well that the gold export point represents the lowest

(highest) value of the SF (dollar) allowed under this system.

Graph C depicts a situation essentially the opposite of situation B. Here, the equilibrium

exchange rate, E*, lies below the exchange rate floor, E (i.e. 3.91) which turns out to be the

prevailing exchange rate. That is, in this case there is an excess supply of foreign exchange in the

foreign exchange market. Swiss firms or citizens who are holding these dollars can convert them into

SF by exchanging them for gold from the Fed, shipping the gold to Switzerland, and then selling the

gold to the Bank of Switzerland. Thus, the Bank of Switzerland is gaining international reserves;

Switzerland in this case has an official settlements balance surplus. Following the convention

described above, the price floor is sometimes known as the gold import point. This exchange rate

represents the highest (lowest) allowable value of the SF (dollar).

Clearly the three situations described in Figure 4.6 cannot prevail simultaneously.

Switzerland can experience only one at any given point in time. Is any one of these worse than the

others for Switzerland's central bank? Situation A presents no problem, since no action by the Bank

of Switzerland is required in order to maintain the system. Situation C also presents the potential for

somewhat more trouble. The Bank of Switzerland in this case is acquiring gold (i.e. international

reserves). As it does so, it increases the supply of money in circulation in Switzerland. This could

be inflationary, but the central bank has options that it can take to reduce these pressures.

However, so long as the central bank desires to maintain the status quo, situation B is the

17 Note, this does not imply that situation B is bad for the Swiss economy or standard of living. Whether or not having a fixed exchange rate is a good policy for any country is an issue we willdiscuss later.

18 This system has also been called the gold exchange standard, the IMF system, and the dollarstandard.

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most problematic for the country. This is because here the country is losing gold. The problem is that

it does not have an infinite supply of gold to supply to the market. Ultimately, something must

change or else the system will collapse.17 One thing that is likely to change is that with the gold

outflow, the Swiss money supply should fall. This is because of a presumed fourth rule of the game:

domestic money supplies would be backed by gold. This means that the money supply of a country

participating in this system would be in direct proportion to that country’s holding of gold stocks.

Historians have looked carefully at how closely this rule was actually followed by central bankers

and have found that in many cases, but not all, the rule was often ignored. In any event, if the

money supply were to fall, one would expect that domestic price levels would also fall making

domestic goods more price competitive in world markets via a real depreciation of the country’s

exchange rate.

The second global system of fixed exchange rates was the Bretton Woods System, which

prevailed from 1945 until February 1973 (except from August 1971-December 1971).18 The

mechanics of this system differed somewhat from those of the gold standard. First, the system was

the creation of the International Monetary Fund (IMF), which supervised its operation and, from

time to time, supplied it with additional reserves. The IMF was created at the end of World War II

as an international organization to help safeguard the international financial system.

To participate in the Bretton Woods system countries had to become members of the IMF.

19 From 1945 until 1971 the band was 1 percent on either side of par.

20 Note that the way I have set up this example, the band conforms to the example of the goldstandard.

21 Prior to 1971 this rate was $35 per oz. In 1973 the official price was raised to $42.20, whereit remains today.

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During the Bretton Woods era, when a country joined the IMF it was required to declare a par value

for its currency in terms of dollars. So, for instance, Switzerland might declare a par value for the

SF of, say, SF 4 = $1. It was then up to Switzerland as a condition of membership in the IMF to take

actions to maintain the value of its currency within a band of 2¼ percent on either side of par.19

Thus, in our example, Switzerland's job was to keep its exchange rate in a band from 3.91 to 4.09.20

How did Switzerland maintain its exchange rate within this range? If Switzerland was in

situation A, then it need do nothing. Private demand and supply equalize at an exchange rate that

is permitted by the IMF. If Switzerland found itself in situation B, then it faced an excess demand

for dollars in the private market. To keep the price from rising, it would sell additional dollars to the

market at a price of SF 4.09. The Bank of Switzerland would get these dollars from its international

reserves, some of which might be held in the form of dollar assets such as U.S. Treasury Bills. If

Switzerland did not have sufficient dollars on hand, it could obtain more by selling gold to the United

States in exchange for dollars, at a fixed price of $38 per ounce.21

Situation C represents an excess supply of dollars at existing exchange rates. If Switzerland

was in situation C, it would buy up the excess supply of dollars (at a price of SF 3.91) in order to

keep the exchange rate from falling further. In this case, the Bank of Switzerland finds itself

acquiring U.S. dollars. What were its options? It could continue to hold the dollars in liquid, interest-

bearing form, either by buying U.S. government treasury bills or by depositing the dollars in special

22 Examples of such policies are described in later sections of this handout.

23 Note that U.S. dollar assets are not considered to be international reserves from the point ofview of the United States.

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accounts created by the Federal Reserve. If it didn't want to hold on to these dollars, it could use

them to buy gold from the United States, at the fixed price of $38 per ounce. Why would

Switzerland ever choose to hold dollars instead of gold? The answer has to do with whether or not

government officials had confidence in U.S. policy. So long as Switzerland (or any other country

in the system) believed that U.S. inflation would remain low and hence there would be no pressure

on the dollar price of gold to rise, then holding dollars would be preferable to holding gold. Dollar

assets earn interest, but gold does not. However, if governments were to lose confidence in the U.S.

government ability to keep the price of gold fixed at $38 per ounce, then they would want to try to

convert their dollar assets into gold before any increase in the dollar price of gold.

Note that, by design, the United States played a very special role in this system. Its primary

job had to do with supplying additional international reserves to the system, while stabilizing their

value. If the Swiss (or any other) government thought that its holdings of international reserves were

too low, it could adopt policies to try to move its economy into a balance of payments surplus

(situation C) vis à vis the United States.22 In the process, it would acquire additional holdings of U.S.

dollar assets and the supply of international reserves would rise.23 However, should the United States

enter into policies that pushed itself into BOP deficit leading other countries to accumulate dollars

beyond desired levels, these countries could exchange their dollars for gold. Since the United States

did not have an unlimited supply of gold, the threat of massive losses of gold in response to

excessive U.S. BOP deficits was viewed as imposing discipline on U.S. economic policy making.

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As Figure 4.6 demonstrates, there were many similarities between the gold standard and the

Bretton Woods system. In both cases, exchange rates enjoyed limited flexibility around a central par

value. One major difference between the two systems was related to whether or not the par value

could be changed. Under the gold standard, the par value was determined by mint parity, and the

principal rule of the game for central bankers was to follow monetary policy aimed at maintaining

a constant price of gold and hence a constant mint parity. Therefore, under the gold standard, market

participants viewed the par value as being immutable, and indeed, over the forty year span of the

classic gold standard era central rates did not change.

Under the Bretton Woods system, things were different. Par values were established as part

of entry into the IMF. Money supplies were no longer explicitly tied to gold in many countries, and

greater flexibility was required of the system. Consequently, IMF rules authorized each country to

be able to change its par value by up to ten percent, without permission from the Fund or by greater

amounts after receiving Fund advice. If a country found itself continually in situation B, one of its

policy options thus became to increase the par value price of the $. In the process, this would shift

the bands upward, hopefully moving the country toward situation A (or even C). An increase in the

par value price of the dollar is known as a devaluation of the local currency. Alternatively, if a

country found itself repeatedly in situation C, it could lower the par value price of the dollar. This

is known as a revaluation; it indicates a general rise in the value of the local currency vis à vis the

dollar.

Between 1946 and 1973, many countries did change their par values. In 1967, after a number

of years of large official settlements balance deficits, Britain devalued the pound. Switzerland

devalued the SF in 1969. Germany revalued the DM in 1961 and again in 1969. And, in 1971, the

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United States devalued the dollar by raising the official price of gold from $35 to $38 per ounce.

The ability to change the par value of a currency meant new opportunities for market

participants to make money by speculating in the foreign exchange market. In particular, suppose

that Switzerland had been in situation B for some time and that speculators had begun to suspect

that Switzerland was about to devalue its currency, say from a par value of 4SF = $1 to 5SF = $1.

This would induce them to enter the market seeking to sell SF for dollars. Why? Under the current

rate they would have paid 4.09 SF per dollar. After the devaluation, they would sell dollars back for

SF at the rate of about 5 SF, earning almost 1 SF for every dollar originally purchased.

Note that speculation puts additional pressure on the central bank to carry out the

devaluation. That is, a rise in speculative activities against the local currency means that the demand

for foreign exchange shifts out. This leads to a wider overall balance of payments deficit and larger

reserve outflows. As reserve levels drop, the central bank is forced to take action. Market

participants knew this, and so, if currency traders began to sense that speculative activity was on the

rise, they would join the process, creating a bandwagon effect. This is known as a run on a currency,

and almost every major country currency was attacked in such a manner during the Bretton Woods

era.

Today, we are no longer on a global system of fixed exchange rates, although some countries

choose to fix the value of their currencies against one or more partner currencies. Such a system is

currently in place in many of the countries of the European Union (EU), where in the late 1990's

fourteen countries moved from a Bretton Woods type system of fixed rates with bands to a system

of immutably fixed rates leading to the adoption of the euro as a common currency.

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Exercises 4.4

1. Over the past two centuries, there have been two extended periods of worldwide fixedexchange rates, the international gold standard and the Bretton Woods system. Compare andcontrast these two systems in terms of the following:

a. the amount and types of exchange rate movement allowable under the two systemsand the factor or factors that determined the limits to exchange rate movements.

b. the role of speculators in stabilizing or destabilizing the systems.c. the role of international organizations in the systems.d. the duties of national central banks in the systems.

2. Suppose that we are in the early days of the Bretton Woods system, and Switzerland hasdeclared a par value for the Swiss franc at SF 4 per dollar. The allowable fluctuation bandis one percent on either side of par. What is the price ceiling for the dollar in terms of Swissfrancs? What is the price floor? Suppose that Switzerland then devalues the franc and setsa new par at SF 5. What are the new price ceiling and floor?

3. Suppose France is on the gold standard and it maintains a strict ratio of gold in its vaults tomoney (French francs) in circulation. Suppose that it runs a balance of payments deficit.What will happen to its overall money supply? What impact if any will this have on theFrench economy? Will this help or hurt the balance of payments situation? Discuss.

4. In a recent article that appeared in the New York Times, Edmund L. Andrews writes “Manyeconomists contend that the Asian central banks have created an informal version of theBretton Woods system of fixed exchange rates”.

a. Which central banks is Andrews referring to, and what action or actions is hedescribing? Hint, there is at least one central bank that this quote clearly describes.

b. For the principal central bank in question, provide a diagram of the action describedin the quote. Label the graph clearly, although you do not need to provide specificvalues.

c. If the central bank in question were to change its policy, what are its options? Usethe graph in part b. to show what would happen to the country’s exchange rate.What would happen to the value of the dollar and to the U.S. balance of payments?