CHAPTER 14
CHAPTER14
Expectations: The
Basic Tools
Prepared by:
Fernando Quijano and Yvonn Quijano
© 2006 Prentice Hall Business Publishing
Macroeconomics, 4/e
Olivier Blanchard
Chapter 14:Expectations: The Basic
Tools
14-1
Nominal Versus Real
Interest Rates
 Interest Rates expressed in terms of dollars
(or, more generally, in units of the national
currency) are called nominal interest rates
 Interest rates expressed in terms of a basket
of goods are called real interest rates.
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Chapter 14:Expectations: The Basic
Tools
Nominal Versus Real
Interest Rates
Figure 14 - 1
Definition and
Derivation of the Real
Interest Rate
it = nominal interest rate for
year t.
rt = real interest rate for year
t.
(1+ it): Lending one dollar
this year yields (1+ it) dollars
next year. Alternatively,
borrowing one dollar this
year implies paying back (1+
it) dollars next year.
Pt = price this year.
Pet+1= expected price next
year.
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Chapter 14:Expectations: The Basic
Tools
Nominal Versus Real
Interest Rates
Pt
Pt
1
Given 1  rt  (1  it ) e , and knowing that e 
P t 1
P t 1 (1   e t )
P e t 1  Pt
then, the expected rate of inflation equals e
 t 1 
Pt
1  it
Consequently, (1  rt ) 
1   et  1
If the nominal interest rate and the expected rate
of inflation are not too large, a simpler expression
is:
rt  it   e t 1
The real interest rate is (approximately) equal to
the nominal interest rate minus the expected rate
of inflation.
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Olivier Blanchard
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Chapter 14:Expectations: The Basic
Tools
Nominal Versus Real
Interest Rates
rt  it   e t
Here are some of the implications of the relation
above:
 If
 e t  0  it  rt
 If  e t  0  it  rt
e
i



t   rt
 if t
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Olivier Blanchard
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Chapter 14:Expectations: The Basic
Tools
Nominal and Real Interest Rates in
the United States Since 1978
Figure 14 - 2
Nominal and Real
One-Year T-bill
Rates in the United
States since 1978
Although the
nominal interest
rate has declined
considerably since
the early 1980s, the
real interest rate
was actually higher
in 2001 than in
1981.
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Olivier Blanchard
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Chapter 14:Expectations: The Basic
Tools
14-2
Expected Present
Discounted Values
Figure 14 - 2
Computing Present
Discounted Values
The expected present discounted value of a
sequence of future payments is the value today
of this expected sequence of payments.
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Olivier Blanchard
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Chapter 14:Expectations: The Basic
Tools
Computing Expected Present
Discounted Values
(a) One dollar this year is worth
1+it dollars next year.
(c) One dollar is worth
(1  it )(1  it 1 ) dollars two years
from now.
(b) If you lend/borrow 1/(1+it)
dollars this year, you will
receive/repay
1
(d) The present discounted value of a
dollar two years from today is
1
equal to
(1  it
(1  it )  1
dollar next year.
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(1  it )(1  it 1 )
Olivier Blanchard
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Chapter 14:Expectations: The Basic
Tools
Computing Expected Present
Discounted Values
The word “discounted” comes from the fact that
the value next year is discounted, with (1+it)
being the discount factor. (The 1-year nominal
interest rate, it, is sometimes called the discount
rate.
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Olivier Blanchard
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Chapter 14:Expectations: The Basic
Tools
A General Formula
The present discounted value of a sequence of
payments, or value in today’s dollars equals:
1
1
$Vt  $zt 
$ zt 1 
$ zt  2    
(1  it )
(1  it )(1  it 1 )
When future payments or interest rates are
uncertain, then:
1
1
e
e
$Vt  $zt 
$ z t 1 
$
z
t 2    
e
(1  it )
(1  it )(1  i t 1 )
Present discounted value, or present value
are another way of saying “”expected present
discounted value.”
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Olivier Blanchard
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Chapter 14:Expectations: The Basic
Tools
Using Present Values: Examples
1
1
e
e
$Vt  $zt 
$ z t 1 
$
z
t 2    
e
(1  it )
(1  it )(1  i t 1 )
This formula has these implications:
 Present value depends positively on today’s
actual payment and expected future
payments.
 Present value depends negatively on current
and expected future interest rates.
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Olivier Blanchard
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Chapter 14:Expectations: The Basic
Tools
Constant Interest Rates
To focus on the effects of the sequence of
payments on the present value, assume that
interest rates are expected to be constant over
time, then:
1
1
e
e
$Vt  $zt 
$ z t 1 
$
z
t 2    
2
(1  i )
(1  i )
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Olivier Blanchard
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Chapter 14:Expectations: The Basic
Tools
Constant Interest Rates
and Payments
When the sequence of payments is equal—called
them $z, the present value formula simplifies to:


1
1
$Vt  $z 1 
  
(1  i ) n1 
 (1  i )
The terms in the expression in brackets
represent a geometric series. Computing the
sum of the series, we get:
1  [1 / (1  i ) n ]
$Vt  $z
1  [1 / (1  i )]
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Olivier Blanchard
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Chapter 14:Expectations: The Basic
Tools
Constant Interest Rates and
Payments, Forever
Assuming that payments start next year and go
on forever, then:
1
1
1 
1

$Vt 
$z 
1
    $z

2 $z     
(1  i )
(1  i )  (1  i )
(1  i )

Using the property of geometric sums, the
present value formula above is:
1
1
$Vt 
$z
1  i (1  (1 / (1  i ))
Which simplifies to:
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$z
$Vt 
i
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Olivier Blanchard
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Chapter 14:Expectations: The Basic
Tools
Zero Interest Rates
If i = 0, then 1/(1+i) equals one, and so
does (1/(1+i)n) for any power n. For
that reason, the present discounted
value of a sequence of expected
payments is just the sum of those
expected payments.
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Olivier Blanchard
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Chapter 14:Expectations: The Basic
Tools
Nominal Versus Real Interest Rates,
and Present Values
1
1
e
e
$Vt  $zt 
$ z t 1 
$
z
t 2    
e
(1  it )
(1  it )(1  i t 1 )
Replacing nominal interest with real interest rates
to obtain the present value of a sequence of real
payments, we get:
1
1
e
e
Vt  zt 
z t 1 
z
t 2    
e
(1  rt )
(1  rt )(1  r t 1 )
Which can be simplified to:
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$Vt
 Vt
Pt
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Chapter 14:Expectations: The Basic
Tools
14-3
Nominal and Real Interest
Rates, and the IS-LM Model
 When deciding how much investment to
undertake, firms care about real interest rates.
Then, the IS relation must read:
Y  C(Y  T )  I (Y , r )  G
 The interest rate directly affected by monetary
policy—the one that enters the LM relation—is
the nominal interest rate, then:
M
 YL(i )
P
The real interest rate is:
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r  i
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e
Olivier Blanchard
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Chapter 14:Expectations: The Basic
Tools
Nominal and Real Interest
Rates, and the IS-LM Model
Note an immediate implication of these three
relations:
 The interest rate directly affected by monetary
policy is the nominal interest rate.
 The interest rate that affects spending and
output is the real interest rate.
 So, the effects of monetary policy on output
depend on how movements in the nominal
interest rate translate into movements in the
real interest rate.
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Olivier Blanchard
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Chapter 14:Expectations: The Basic
Tools
Money Growth, Inflation, Nominal
14-4
and Real Interest Rates
This section focuses on the following assertions:
 Higher money growth leads to lower nominal
interest rates in the short run, but to higher
nominal interest rates in the medium run.
 Higher money growth leads to lower real
interest rates in the short run, but has no
effect on real interest rates in the medium
run.
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Olivier Blanchard
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Chapter 14:Expectations: The Basic
Tools
Revisiting the IS-LM Model
Reducing the IS relation, LM relation and relation
between the real and nominal interest rate gives
us:
IS Y  C(Y  T )  I (Y , i   e )  G
M
 UYL(i )
LM
P
 The IS curve is still downward sloping.
 The LM curve is upward sloping.
 The equilibrium is at the intersection of the IS
curve and the LM curve.
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Olivier Blanchard
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Chapter 14:Expectations: The Basic
Tools
Revisiting the IS-LM Model
Figure 14 - 4
Equilibrium Output
and Interest Rates
The equilibrium level of
output and the
equilibrium nominal
interest rate are given
by the intersection of
the IS curve and the LM
curve. The real interest
rate equals the nominal
interest rate minus
expected inflation.
If r  i     r   i   
e
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e
If  e is constant,   e  0   r   i
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Chapter 14:Expectations: The Basic
Tools
Nominal and Real Interest Rates
in the Short Run
Figure 14 - 5
The Short-run Effects
of an Increase in
Money Growth
An increase in money
growth increases the
real money stock in the
short run. This increase
in real money leads to
an increase in output
and a decrease in both
the nominal and the real
interest rate.
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Olivier Blanchard
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Chapter 14:Expectations: The Basic
Tools
Nominal and Real Interest Rates
in the Medium Run
In the medium run,Y  Yn , then:
Yn  C(Yn  T )  I (Yn , r )  G
The relation between the nominal interest rate
and the real interest rate is: i  r   e
 In the medium run, the real interest rate equals
the natural interest rate, rn, then: i  rn   e
 In the medium run, expected inflation is equal to
actual inflation, so: i  rn  
 Finally, in the medium run, inflation is equal to
money growth: i  rn  gm
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Olivier Blanchard
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Chapter 14:Expectations: The Basic
Tools
Nominal and Real Interest Rates
in the Medium Run
i  rn  gm
In the medium run, the nominal interest rate
increases one for one with inflation. This result is
known as the Fisher effect, or the Fisher
Hypothesis.
For example, an increase in nominal money
growth of 10% is eventually reflected by a 10%
increase in the rate of inflation, a 10% increase
in the nominal interest rate, and no change in
the real interest rate.
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Olivier Blanchard
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Chapter 14:Expectations: The Basic
Tools
From the Short Run to
the Medium Run
In the short run, lower nominal interest rates lead
to higher output and inflation. In the medium run,
this situation changes.
In the short run, r  rn  Y  Yn  u  un   
Over time,    Eventually   g' m  ( g' m   )  0  i 
In the medium run, r  rn
Y  Yn
u  un
  gm
i  rn  gm
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Olivier Blanchard
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Chapter 14:Expectations: The Basic
Tools
From the Short Run to
the Medium Run
In words:
 So long as the real interest rate is below the
natural real interest rate, output is higher than
the natural level of output, and unemployment
is below its natural rate.
 From the Phillips curve relation, we know that
as long as unemployment is below the natural
rate of unemployment, inflation increases.
 As inflation increases, it becomes higher than
nominal money growth, leading to negative
real money growth.
 In the medium run, the real interest rate
increases back to it initial value.
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Olivier Blanchard
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Chapter 14:Expectations: The Basic
Tools
From the Short Run to
the Medium Run
Figure 14 - 6
The Adjustment of the Real
and the Nominal Interest
Rate to an Increase in
Money Growth
An increase in money
growth leads initially to a
decrease in both the real
and the nominal interest
rate. Over time, the real
interest rate returns to its
initial value. The nominal
interest rate converges to a
new higher value, equal to
the initial value plus the
increase in money growth.
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Olivier Blanchard
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Chapter 14:Expectations: The Basic
Tools
Evidence on the Fisher Hypothesis
To see if increases in inflation lead to one-for-one
increases in nominal interest rates, economists
look at:
Nominal interest rates and inflation across
countries. The evidence of the early 1990s finds
substantial support for the Fisher hypothesis.
Swings in inflation, which should eventually be
reflected in similar swings in the nominal interest
rate. Again, the data appears to fit the
hypothesis quite well.
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Olivier Blanchard
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Chapter 14:Expectations: The Basic
Tools
Evidence on the Fisher Hypothesis
Figure 14 - 7
The 3-Month Treasury
Bill Rate and Inflation
since 1927
The increase in inflation
from the early 1960s to
the early 1980s was
associated with an
increase in the nominal
interest rate. The
decrease in inflation
since the mid-1980s
has been associated
with a decrease in the
nominal interest rate.
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Olivier Blanchard
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Chapter 14:Expectations: The Basic
Tools
Evidence on the Fisher Hypothesis
Figure 14-7 has at least three interesting
features:
 The steady increase in inflation from the early
1960s to the early 1980s was associated with
a roughly parallel increase in the nominal
interest rate.
 The nominal interest rate lagged behind the
increase in inflation in the 1970s, while the
disinflation of the early 1980s was associated
with an initial increase in the nominal interest
rate.
 The other episode of inflation underscores the
importance of the “medium-run” qualifier in
the Fisher hypothesis.
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Chapter 14:Expectations: The Basic
Tools
Nominal Interest Rates and
Inflation Across Latin America in
the Early 1990s
Figure 1
Nominal
Interest Rates
and Inflation:
Latin America,
1992-1993
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Olivier Blanchard
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Chapter 14:Expectations: The Basic
Tools
Key Terms




nominal interest rate
real interest rate
expected present value
discount factor
© 2006 Prentice Hall Business Publishing




discount rate
present discounted value
present value
Fisher effect, Fisher hypothesis
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