1) The document discusses the monetary model of exchange rates and its predictions. The model predicts that exchange rates will follow the relative money supplies and inflation rates of the two currencies. 2) The model assumes that real money demand is constant, but evidence shows that money demand decreases with higher interest rates. This means the original model is too simplistic. 3) When updated to reflect interest rate effects on money demand, the model implies exchange rates, inflation rates, and interest rates will equalize in the long run between countries according to purchasing power parity and uncovered interest rate parity.

1. Eco 328
Monetary model of exchange rates

2. The simple monetary model
Last time we developed a simple monetary model for exchange rates

3. Expected depreciation
   
   .
ratesgrowth
outputreal
inalDifferenti
,,
ratesgrowth
supplymoneynominal
inalDifferenti
,,
,,,,
aldifferentiInflation
,,
rateexchangenominaltheof
ondepreciatiofRate
,€/$
€/$
    


tEURtUStEURtUS
tEURtEURtUStUStEURtUS
t
t
gg
gg
E
E



According to the model an exchange rate is expected to evolve in the
following fashion

4. 4
When we use the monetary model for forecasting, we are
answering a hypothetical question: What path would exchange
rates follow from now on if prices were flexible and relative PPP
held?
Forecasting Exchange Rates: An Example
Assume that U.S. and European real income growth rates are
identical and equal to zero (0%). Also, the European price level
is constant, and European inflation is zero.
Based on these assumptions, we examine two cases.
Case 1: A one-time increase in the money supply.
Case 2: An increase in the rate of money growth.
Exchange Rate Forecasts Using the Simple Model

5. 5
Case 1: A one-time increase in the money supply.
a) There is a 10% increase in the money supply M.
b) Real money balances M/P remain constant because real
income is constant.
c) These last two statements imply that price level P and money
supply M must move in the same proportion, so there is a
10% increase in the price level P.
d) PPP implies that the exchange rate E and price level P must
move in the same proportion, so there is a 10% increase in
the exchange rate E.
Exchange Rate Forecasts Using the Simple Model

6. 6
Case 2: An increase in the rate of money growth.
At time T the United States will raise the rate of money supply
growth to rate of μ + Δμ from a steady fixed rate μ.
a) Money supply M is growing at a constant rate.
b) Real money balances M/P remain constant, as before.
c) These last two statements imply that price level P and money
supply M must move in the same proportion, so P is always a
constant multiple of M.
d) PPP implies that the exchange rate E and price level P must
move in the same proportion, so E is always a constant multiple
of P (and hence of M).
Exchange Rate Forecasts Using the Simple Model

7. 7
Forecasting Exchange Rates Before time
T, money,
prices, and
the
exchange
rate all grow
at rate μ.
Foreign
prices are
constant. In
panel (a),
we suppose
at time T
there is an
increase Δμ
in the rate of
growth of
home
money
supply M.
An Increase in the Growth Rate of the Money Supply in the Simple Model

8. 8
Forecasting Exchange Rates In panel
(b), the
quantity
theory
assumes
that the
level of real
money
balances
remains
unchanged.
An Increase in the Growth Rate of the Money Supply in the Simple Model

9. 9
Forecasting Exchange Rates After time
T, if real
money
balances
(M/P) are
constant,
then
money M
and prices
P still
grow at the
same rate,
which is
now μ +
Δμ, so the
rate of
inflation
rises by
Δμ, as
shown in
panel (c).
An Increase in the Growth Rate of the Money Supply in the Simple Model

10. 10
Forecasting Exchange Rates PPP and an
assumed
stable
foreign
price level
imply that
the
exchange
rate will
follow a
path similar
to that of
the
domestic
price level,
so E also
grows at the
new rate μ +
Δμ, and the
rate of
depreciation
rises by Δμ,
as shown in
panel (d).
An Increase in the Growth Rate of the Money Supply in the Simple Model

11. 11
Evidence for the Monetary Approach
Inflation Rates and Money
Growth Rates, 1975–2005
Inflation and Money Growth: The monetary approach to prices and exchange rates suggests that,
increases in the rate of money supply growth should be the same size as increases in the rate of
inflation.

12. 12
Evidence for the Monetary Approach
Money Growth and the Exchange Rate: The monetary approach to prices and exchange rates also
suggests that, increases in the rate of money supply growth should be the same size as increases in the rate
of exchange rate depreciation.
Money Growth Rates and the Exchange Rate, 1975–2005

13. 13
Hyperinflations
The monetary approach assumes long-run PPP, which generally
works poorly in the short run. There is one notable exception to
this general failure of PPP in the short run: hyperinflation.
• Economists traditionally define a hyperinflation as a sustained
inflation of more than 50% per month (which means that
prices are doubling every 51 days).
• In common usage, some lower-inflation episodes are also
called hyperinflations. An inflation rate of 1,000% per year is
a common rule of thumb (22% per month).
• Hyperinflations usually occur when governments face a
budget crisis, are unable to borrow to finance a deficit, and
instead choose to print money.

14. The First Hyperinflation of the Twenty-First Century
By 2007 Zimbabwe was almost at an
economic standstill, except for the
printing presses churning out the
banknotes.
• A creeping inflation—58% in 1999,
132% in 2001, 385% in 2003, and
586% in 2005—was about to
become hyperinflation, and the long-
suffering people faced an
accelerating descent into even deeper
chaos.
• By 2007 inflation had risen to
12,000%! Among the five worst
hyperinflations episodes of all time,
according to Jeffrey D. Sachs.
• In 2008, the local currency
disappeared from use, replaced by
U.S. dollars and South African rand.
14

15. 15
A government may redenominate a new
unit of currency equal to 10N (10 raised to
the power N) old units. Sometimes N can
get quite large.
On June 1, 1983, the peso argentino
replaced the (old) peso at a rate of 10,000
to 1. Then on June 14, 1985, the austral
replaced the peso argentino at 1,000 to 1.
Finally, on January 1, 1992, the convertible
peso replaced the austral at a rate of 10,000
to 1 (i.e., 10,000,000,000 old pesos).
In 1946 the Hungarian pengö became
worthless. By July 15, 1946, there were
76,041,000,000,000,000,000,000,000
pengö in circulation.
Currency Reform

16. Sweeping up the trash,… I mean pengos :/
16

17. 17
PPP in Hyperinflations
Purchasing Power Parity during Hyperinflations The scatterplot shows the relationship between
the cumulative start-to-finish exchange rate depreciation against the U.S. dollar and the
cumulative start-to-finish rise in the local price level for hyperinflations in the twentieth century.
Note the use of logarithmic scales.

18. 18
Money Demand in Hyperinflations
The Collapse of Real Money Balances during Hyperinflations This figure shows that real
money balances tend to collapse in hyperinflations as people economize by reducing their
holdings of rapidly depreciating notes. The horizontal axis shows the peak monthly inflation
rate (%), and the vertical axis shows the ratio of real money balances in that peak month
relative to real money balances at the start of the hyperinflationary period. The data are shown
using log scales for clarity.

19. Back to our monetary model
19
From PPP we know the in the long run the exchange should approximate the ratio
of the price levels
From the Quantity Theory of Money we know the price level comes from the
money supply relative to the demand for real money balances – which comes from
real output/income

20. Also, our model for the rate of exchange rate depreciation
from relative PPP
20
   
   .
ratesgrowth
outputreal
inalDifferenti
,,
ratesgrowth
supplymoneynominal
inalDifferenti
,,
,,,,
aldifferentiInflation
,,
rateexchangenominaltheof
ondepreciatiofRate
,€/$
€/$
    


tEURtUStEURtUS
tEURtEURtUStUStEURtUS
t
t
gg
gg
E
E



In the long run, the rate of depreciation is determined by
the differential in the growth rates of the nominal money supplies
– set by the respective central banks
minus the differential in real output growth rates
– determined by long run economic fundamentals (i.e.
savings/investment and depreciation rates, rate of
technological advancement, labor laws and labor force
participation, tax policy, etc.)

21. But what we have learned from inflationary episodes poses a
problem for the model
Before we assumed
money demand was a
constant multiple of
income
This means if real income
is constant real money
demand, M/P, would be
constant regardless of
how much the money
supply grew
21

 
incomeRealconstant?A
money
realfor
Demand
YL
P
M d


22. The interest rate = opportunity cost
Consider first, the interest rate
-this is your opportunity cost of holding money
-as the interest rate goes up, what happens to
your money demand?
-so we know in reality, our model is too simple,
money demand must be a decreasing function of
the nominal interest rate
22

23. Recall UIP
23
   €
€/$
€/$
$ 11 i
E
E
i
e


24. Uncovered interest rate parity
This means that the foreign interest rate
should equal the home interest rate
plus expected depreciation of the home currency
24
 
  

depositseuroon
returnofratedollarExpected
dollartheof
ondepreciatiofrateExpected
€/$
€/$
depositseuroon
rateInterest
€
depositsdollaron
returnofrateDollar
=
depositsdollaron
rateInterest
$
E
E
ii
e



25. Now consider PPP
From relative PPP we know the expected rate of depreciation
should equal the expected inflation differential
25

 aldifferentiInflation
,,
rateexchangenominaltheof
ondepreciatiofRate
,€/$
,€/$
tEURtUS
t
t
E
E



26. 26
PPP and UIP together imply a striking relationship
Inflation and Interest Rates in the Long Run

 aldifferentiinflationExpected
ondepreciati
dollarofrateExpected
€/$
€/$ e
EUR
e
US
e
E
E


and  
rateinterest
euroNet
€
rateinterest
dollarNet
$
ondepreciati
dollarofrateExpected
€/$
€/$
ii
E
Ee



In the long run the inflation differential equals the interest rate differential!
This result is known as the Fisher effect
(why?)

27. Recall from Intermediate Macro the Fisher equation
Rearrange
27
e
EUR
e
USii   €$
To get
e
EUR
e
US ii  €$
When we subtract expected inflation from the nominal
interest rate we get the real interest rate
If PPP and UIP hold, then expected real interest rates
are equalized across countries.

rUS
e
 rEUR
e
This is called Real Interest Parity

28. Recall also from Intermediate Macro that long run per capita
output growth depends primarily on the rate of technological
progress
With open boarders knowledge diffusion and capital mobility this
rate should be expected to equalize across countries
In the long run, all countries will share a common expected real
interest rate, the long-run expected world real interest rate, r*
Therefore
Which makes the Fisher effect even clearer
28

rUS
e
 rEUR
e
 r*
., *
€
*
$
e
EUR
e
EUR
e
EUR
e
US
e
US
e
US rrirri 

29. For example
If the world real interest rate is r* = 2%,
and the country’s long-run expected inflation rate goes up by
two percentage points from 3% to 5%,
then its long-run nominal interest rate also goes up by two
percentage points
from the old level of 2 + 3 = 5% to a new level of 2 + 5 = 7%.
29

30. An interesting note
In Intermediate Macro we recognized that open boarders
knowledge diffusion and capital mobility should equalize real
interest rates in the long run
From UIP and PPP we now know that arbitrage in goods and
financial markets is enough to ensure it
30

31. 31
Evidence on the Fisher Effect
Inflation Rates and Nominal Interest Rates, 1995–2005 This scatterplot shows the
relationship between the average annual nominal interest rate differential and the annual
inflation differential relative to the United States over a ten-year period for a sample of 62
countries.

32. 32
Evidence on the Fisher Effect
This figure shows actual real interest rate differentials over three decades for the United Kingdom,
Germany, and France relative to the United States. These differentials were not zero, so real interest
parity did not hold continuously. But the differentials were on average close to zero, meaning that real
interest parity (like PPP) is a general long-run tendency in the data.
Real Interest Rate Differentials, 1970–1999

33. Money demand is a decreasing function of the nominal
interest rate
Now we need to adjust our long run model of the exchange
rate to reflect the fact that people choose to hold less money as
the nominal interest rate increases
This comes from the opportunity cost of not having the funds
in an account which earns a higher return as the rate goes up
And also due to inflation – with inflation your cash is actually
earning a negative return – loss of purchasing power!
33

34. 34
• A rise in national dollar income (nominal income) will cause a
proportional increase in transactions and, hence, in aggregate
money demand (as is true in the simple quantity theory).
• A rise in the nominal interest rate will cause the aggregate
demand for money to fall.
• Dividing by P, we derive the demand for real money balances:
The Demand for Money:
  
($)income
Nominal
function
decreasing
A
($)moneyfor
Demand
)( YPiLM d


 
income
Real
function
decreasing
A
moneyrealfor
Demand
)( YiL
P
M d

Return now to the money market

35. Money demand is decreasing in the nominal rate, but
increasing in GDP
As inflation rises, the Fisher effect tells us that the nominal
interest rate i must rise by the same amount
The general model of money demand then tells us that L(i)
must fall because it is a decreasing function of i
Thus, for a given level of real income, real money balances
must fall as inflation rises
If income increases, reflected in a real economic expansion,
then more money will be demanded at any interest rate i.
Therefore an increase in real income will shift the demand
curve for money outward
35

36. 36
Panel (a) shows the real money demand function for the United States. The downward slope implies
that the quantity of real money demand rises as the nominal interest rate i$ falls. Panel (b) shows that
an increase in real income from Y1
US to Y2
US causes real money demand to rise at all levels of the
nominal interest rate i$.
The Standard Model of Real Money Demand

37. 37
When nominal interest rates change the general model has different
implications from the simple model.


 
   
demandsmoneyrealRelative
bydivided
suppliesmoneynominalRelative
$
$
levelspriceofRatio
rateExchange
€/$
)(/)(
/
)(
)(
EUREURUSUS
EURUS
EUREUR
EUR
USUS
US
EUR
US
YiLYiL
MM
YiL
M
YiL
M
P
P
E 















Money, Interest Rates, and Prices in the Long Run:
A General Model

38. 38
Exchange Rate Forecasts Using the General Model Before time
T, money,
prices, and
the exchange
rate all grow
at rate μ.
Foreign
prices are
constant. In
panel (a), we
suppose at
time T there
is an
increase Δμ
in the rate of
growth of
home money
supply M.
An Increase in the Growth Rate of the Money Supply in the Standard Model

39. 39
Exchange Rate Forecasts Using the General Model This causes an
increase Δμ in
the rate of
inflation; the
Fisher effect
means that
there will be a
Δμ increase in
the nominal
interest rate;
as a result, as
shown in
panel (b), real
money
demand falls
with a discrete
jump at T.
An Increase in the Growth Rate of the Money Supply in the Standard Model

40. 40
Exchange Rate Forecasts Using the General Model If real
money
balances are
to fall when
the nominal
money
supply
expands
continuously,
then the
domestic
price level
must make a
discrete
jump up at
time T, as
shown in
panel (c).
An Increase in the Growth Rate of the Money Supply in the Standard Model

41. 41
Exchange Rate Forecasts Using the General Model Subsequently,
prices grow at
the new
higher rate of
inflation; and
given the
stable foreign
price level,
PPP implies
that the
exchange rate
follows a
similar path to
the domestic
price level, as
shown in
panel (d).
An Increase in the Growth Rate of the Money Supply in the Standard Model

42. 42
Monetary Regimes and Exchange Rate Regimes
An overarching aspect of a nation’s economic policy is the desire
to keep inflation within certain bounds.
• To achieve such an objective requires that policy makers be
subject to some kind of constraint in the long run. Such
constraints are called nominal anchors.
• Long-run nominal anchoring and short-run flexibility are the
characteristics of the policy framework that economists call
the monetary regime.
The Long Run: The Nominal Anchor

43. 3 choices for nominal anchor
The three main nominal anchor choices emerge
exchange rate target
money supply target
inflation target plus interest rate policy
43

44. 44
Exchange rate target:
o Relative PPP says that home inflation equals the rate of
depreciation plus foreign inflation.
o A simple rule would be to set the rate of depreciation equal
to a constant.

45. 45
Exchange rate target:
o The drawback is the final term in the equation: PPP implies
that over the long run the home country “imports” inflation
from the foreign country over and above the chosen rate of
depreciation.
o Under a peg, if foreign inflation rises by 1% per year, then so,
too, does home inflation.
o Thus, countries almost invariably peg to a country with a
reputation for price stability (e.g., the United States).

46. 46
Money supply target:
o A simple rule of this sort is: set the growth rate of the money
supply equal to a constant, say, 2% a year.
o Again the drawback is the final term: real income growth can be
unstable. In periods of high growth, inflation will be below the
desired level. In periods of low growth, inflation will be above
the desired level.

47. 47
Inflation target plus interest rate policy:
o The Fisher effect says that home inflation is the home nominal
interest rate minus the world real interest rate.
o If the latter can be assumed to be constant, then as long as the
average home nominal interest rate is kept stable, inflation can
also be kept stable.
  
rateinterestrealWorld
*
rateinterestNominalinflationExpected
riH
e
H 

48. 48
Inflation target plus interest rate policy:
o For example, if the world real interest rate is r* = 2.5%,
o and the country’s long-run inflation target is 2%,
o then its long-run nominal interest rate ought to be on average
equal to 4.5%
  
rateinterestrealWorld
*
rateinterestNominalinflationExpected
riH
e
H 

49. 49
Exchange Rate Regimes and Nominal Anchors
This table illustrates the possible exchange rate regimes that are consistent with
various types of nominal anchors. Countries that are dollarized or in a currency union
have a “superfixed” exchange rate target. Pegs, bands, and crawls also target the
exchange rate. Managed floats have no preset path for the exchange rate, which allows
other targets to be employed. Countries that float freely are judged to pay no serious
attention to exchange rate targets; if they have anchors, they will involve monetary
targets or inflation targets with an interest rate policy. The countries with “freely
falling” exchange rates have no serious target and have high rates of inflation and
depreciation. Many countries engage in implicit targeting (e.g., inflation targeting)
without announcing an explicit target. Some countries may use a mix of more than
one target.

50. 50
Nominal Anchors in Theory and Practice
• An appreciation of the importance of nominal anchors has
transformed monetary policy making and inflation performance
throughout the global economy in recent decades.
• In the 1970s and 1980s, most of the world was struggling with
high inflation.
• In the 1990s, policies designed to create effective nominal
anchors were put in place in many countries.
• Most of those policies have turned out to be credible, too, thanks
to political developments in many countries that have fostered
central-bank independence.

51. 51
Nominal Anchors in Theory and Practice
Global Disinflation
Cross-country data from 1980 to 2012 show the gradual reduction in the annual rate of
inflation around the world. This disinflation process began in the advanced economies
in the early 1980s. The emerging markets and developing countries suffered from even
higher rates of inflation, although these finally began to fall in the 1990s.

52. Quiz
1. When the price level increases at rates of 50% per month it is called
a) Hyperinflation
b) Deflation
c) Stagflation
d) Good economic policy
2. The problem with our simple model was it assumed the proportion of
income held as real money balances was
a) Decreasing in the rate of interest
b) Constant
c) Decreasing in output
d) Increasing in the rate of interest
3. In truth the quantity of real money balances demanded by the public is
a) Decreasing in the rate of interest
b) Constant
c) Decreasing in output
d) Increasing in the rate of interest
4. The long run equalization of the interest rate differential with the inflation
differential is known as the
a) Fisher effect
b) PPP
c) UIP
d) QTM
52