CHAPTER
8
The Natural Rate of
Unemployment and
the Phillips Curve
Prepared by:
Fernando Quijano and Yvonn Quijano
And Modified by Gabriel Martinez
The Natural Rate of Unemployment
and the Phillips Curve
 In this chapter, we take AD-AS analysis to
the next level (we all know how to just shift
the curves).
 Can AD-AS be used to explain the short-run,
medium-run relation between inflation and
unemployment?
 Yes, but first AS needs to be modified into
the Phillips Curve.
© 2003 Prentice Hall Business Publishing
Macroeconomics, 3/e
Olivier Blanchard
The Natural Rate of Unemployment
and the Phillips Curve
Inflation Versus
Unemployment in the United
States, 1900-1960
During the period 1900-1960
in the United States, a low
unemployment rate was
typically associated with a
high inflation rate, and a
high unemployment rate was
typically associated with a
 The Phillips curve, based on
low or negative inflation rate.
the data above, shows a
negative relation between
inflation and unemployment.
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Macroeconomics, 3/e
Olivier Blanchard
Inflation, Expected
Inflation, and Unemployment
8-1
P  P e (1  m) F (u, z )
 The above equation is the aggregate supply
relation derived in chapter 7.
 This relation can be rewritten to establish a
relation between inflation, expected inflation,
and the unemployment rate.
 In other words, the Phillips Curve is a
dynamic version of the AS curve.
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Olivier Blanchard
Inflation, Expected
Inflation, and Unemployment
P  P e (1  m) F (u, z )
 For simplicity and concreteness, assume the
function F takes the form:
F (u, z )  1   u  z
 Then, replace this function into the one above:
P  P (1  m)(1   u  z )
e
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Olivier Blanchard
Inflation, Expected
Inflation, and Unemployment
P  P e (1  m)(1  u  z )
 This equation can be modified to show a
relation between inflation, expected inflation,
and the unemployment rate:
p  p  m  z    u
e
 Notice p rises if pe rises, falls if u (or ) rise,
and rises if m or z rise.
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Olivier Blanchard
Inflation, Expected
Inflation, and Unemployment
p  p e  m  z    u
 According to this equation:
– An increase in the expected inflation, pe, leads to an
increase in inflation, p.
– Given expected inflation pe, an increase in the markup,
m, or an increase in the factors that affect wage
determination, z, lead to an increase in inflation.
– Given expected inflation, pe, an increase in the
unemployment rate, u, leads to a decrease in inflation,
p.
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Olivier Blanchard
Inflation, Expected
Inflation, and Unemployment
p  p e  m  z    u
 When referring to inflation, expected inflation, or
unemployment in a specific year, the equation
above needs to include time indexes, as follows:
p t  p te  m  z    ut
 The variables p, pet, and ut refer to inflation, expected
inflation and unemployment in year t. m and z are
assumed constant and don’t have time indexes.
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Olivier Blanchard
Levels versus Growth Rates
Real GDP
12000.0
10000.0
8000.0
6000.0
4000.0
2000.0
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Jan-04
Jan-01
Jan-98
Jan-95
Jan-92
Jan-89
Jan-86
Jan-83
Jan-80
Jan-77
Jan-74
Jan-71
Jan-68
Jan-65
Jan-62
Jan-59
Jan-56
Jan-53
Jan-50
Jan-47
0.0
Olivier Blanchard
Levels versus Growth Rates
Real GDP growth rate
3.50%
3.00%
2.50%
2.00%
1.50%
1.00%
0.50%
Jan-03
Jan-01
Jan-99
Jan-97
Jan-95
Jan-93
Jan-91
Jan-89
Jan-87
Jan-85
Jan-83
Jan-81
Jan-79
Jan-77
Jan-75
Jan-73
Jan-71
Jan-69
Jan-67
Jan-65
Jan-63
Jan-61
Jan-59
Jan-57
Jan-55
Jan-53
Jan-51
Jan-49
Jan-47
0.00%
-0.50%
-1.00%
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Olivier Blanchard
Levels versus Growth Rates
M1/GPD vs Prime Rate
25.00
Interest Rate (percent)
20.00
15.00
10.00
5.00
0.00
0.00
0.05
0.10
0.15
0.20
0.25
0.30
M1/GPD
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Olivier Blanchard
Levels versus Growth Rates
Changes in i versus changes in M/Y
0.05
0.04
Change in interest rate
0.03
0.02
0.01
-0.30
-0.20
-0.10
0.00
0.00
-0.01
0.10
0.20
0.30
D i= - 0.0016 - 0.0403 D M/Y
-0.02
-0.03
-0.04
Change in M1/GDP
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Olivier Blanchard
© 2003 Prentice Hall Business Publishing
Macroeconomics, 3/e
Jan-05
Jan-04
Jan-03
Jan-02
Jan-01
Jan-00
Jan-99
Jan-98
Jan-97
Jan-96
Jan-95
Jan-94
Jan-93
Jan-92
Jan-91
Jan-90
Jan-89
Jan-88
Jan-87
Jan-86
Jan-85
Jan-84
Jan-83
Jan-82
Jan-81
Levels versus Growth Rates
Consumer Price Index
250.0
200.0
150.0
100.0
50.0
0.0
Olivier Blanchard
Ja
n8
Ja 1
n8
Ja 2
n8
Ja 3
n8
Ja 4
n8
Ja 5
n8
Ja 6
n8
Ja 7
n8
Ja 8
n8
Ja 9
n9
Ja 0
n9
Ja 1
n9
Ja 2
n9
Ja 3
n9
Ja 4
n9
Ja 5
n9
Ja 6
n9
Ja 7
n9
Ja 8
n9
Ja 9
n0
Ja 0
n0
Ja 1
n0
Ja 2
n0
Ja 3
n0
Ja 4
n05
Levels versus Growth Rates
Inflation Rate
14.00%
12.00%
10.00%
8.00%
6.00%
4.00%
2.00%
0.00%
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Olivier Blanchard
Levels versus Growth Rates
Real GDP
Unem ploym ent Rate
Jan-04
Jan-04
Jan-01
Jan-01
Jan-98
Jan-98
Jan-95
Jan-95
Jan-92
Jan-92
Jan-89
Jan-89
Jan-86
Jan-86
0
Jan-83
Jan-83
0.0
Jan-80
Jan-80
2
Jan-77
Jan-77
2000.0
Jan-74
Jan-74
4
Jan-71
Jan-71
4000.0
Jan-68
Jan-68
6
Jan-65
Jan-65
6000.0
Jan-62
Jan-62
8
Jan-59
Jan-59
8000.0
Jan-56
Jan-56
10
Jan-53
Jan-53
10000.0
Jan-50
Jan-50
12
Jan-47
Jan-47
12000.0
At what rate of growth of GDP is unemployment constant?
(see Figure 2-2)
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-0.50%
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-1.00%
Jan-53
Jan-53
Jan-51
Jan-50
Jan-49
Jan-47
Jan-47
Jan-55
At what rate of growth of GDP is unemployment constant?
(see Figure 2-2)
Macroeconomics, 3/e
Jan-03
Jan-04
Jan-01
Jan-99
Jan-01
Jan-97
Jan-98
Jan-95
Jan-93
Jan-95
Jan-92
Jan-91
Jan-89
Jan-87
Jan-89
Jan-86
Jan-85
Jan-83
Jan-83
Jan-81
Jan-80
Jan-79
Jan-77
Jan-75
Jan-77
Jan-73
Jan-74
Jan-71
Jan-71
3.00%
Jan-69
Jan-67
Jan-68
Jan-65
Jan-65
Jan-63
Jan-61
Jan-62
Jan-59
Jan-59
Jan-57
Jan-56
Levels versus Growth Rates
Real GDP growth rate
3.50%
Unem ploym ent Rate
2.50%
12
10
2.00%
8
1.50%
6
1.00%
4
0.50%
2
0.00%
Olivier Blanchard
0
8-2
The Phillips Curve
Phillips Curve
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Olivier Blanchard
The Phillips Curve and AD-AS
p
AS_Inflation
AD_Inflation
Phillips
Curve
AD_Inflation
AD_Inflation
AD_Inflation
AD_Inflation
AD_Inflation
Y
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Olivier Blanchard
The Phillips Curve and Policy
 It was thought that governments could use
the Phillips Curve to attain society’s
objectives.
 Society simply needed to choose its
preferred point along the curve.
 A liberal government would choose a highinflation, low-unemployment point.
– Kennedy/Johnson’s Great Society programs.
 A conservative government would choose a
low-inflation, high-unemployment point.
– Volker, Greenspan, the ’94 Republican Revolution.
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The Phillips Curve and Policy
 Before the Phillips Curve was
discovered, governments had no
interest in taking advantage of it
(obviously).
 This meant that prices rose in some
periods, the fell in other periods, and
on average (in the long run) one could
expect inflation of zero.
p et = 0
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Olivier Blanchard
The Phillips Curve
 If we set pet = 0, then:
p t  p  m  z    ut
e
t
p t  m  z    ut
 This is the negative relation between unemployment
and inflation that Phillips found for the United
Kingdom, and Solow and Samuelson found for the
United States.
 The original Phillips curve.
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Olivier Blanchard
The Phillips Curve
p t  m  z    ut
 This negative inflation-unemployment
relation can be used.
– Societies with great aversion to unemployment could
choose to raise inflation.
 So, if u = 6% for p = 0%.
 We could make u = 2% for p = 5%.
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The Phillips Curve
– But what happens if a government always
chooses to raise inflation (in order to reduce u)?
 The wage-price spiral:
– Suppose Pet =Pt-1:
– If prices rose last period, expected prices will rise
today.
– Higher Pet  high nominal wage
 firms raise prices
 Next period, workers ask for higher nominal
wages
 firms raise prices …
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The Phillips Curve
 If prices are constantly rising, will pet = 0?
0
p t  p  m  z    ut
e
t
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?
Olivier Blanchard
Mutations
Inflation versus
Unemployment
in the United States,
1948-1969
The steady decline in
the U.S.
unemployment rate
throughout the 1960s
was associated with a
steady increase in the
inflation rate.
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mz
Mutations
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-
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Mutations
 The negative relation between
unemployment and inflation held
throughout the 1960s, but it vanished
after that, for two reasons:
– An increase in the price of oil
changed the markup of prices over wages,
shifting the Phillips curve up.
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Olivier Blanchard
Mutations
– More importantly,
wage setters changed the way they formed
expectations, because there had been a
change in the behavior of the rate of inflation.
 The inflation rate became consistently positive,
and
 Inflation became more persistent.
p t  m  z    ut
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p t  p te  m  z    ut
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Mutations
U.S. Inflation, 1900-2000
Before the 1960s, the
U.S. inflation rate was
sometimes positive,
sometimes negative.
Since then, it has been
positive.
Inflation has also become more persistent: A high
inflation rate this year is likely to be followed by a high
inflation rate next year.
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mz
pet + m’  z
Mutations
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Mutations
Inflation versus
Unemployment
in the United States,
1970-2000
Beginning in 1970,
the relation between
the unemployment
rate and the inflation
rate disappeared in
the United States.
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The Phillips Curve and AD-AS
Phillips
Curve
p
AS /
AS / Inflation
Inflation
AS /
Inflation
AS /
Inflation
AD /
Inflation
AD /
Inflation
AD /
Inflation
AD /
Inflation
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Yn
Y
Olivier Blanchard
The Formation of Expectations
 If inflation is persistently positive, agents will
include this variable in their calculations.
 There are many ways to model this idea:
– “Agents know how the economy works and all the
incentives that the Fed has. They make a good guess
of the Fed’s next move and determine pet.”
– “Agents set pet equal to a long average of past rates of
inflation.”
– “Agents set pet equal to last period’s inflation.”
– “Agents make wild guesses.”
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The Formation of Expectations
 Let’s model this as “agents set pet= pt-1,
approximately.”
 Suppose expectations of inflation are formed
according to
πet = θπt- 1
 The parameter  captures people’s belief of
the effect of last year’s inflation rate, pt-1, on
this year’s expected inflation rate, pet.
 The value of  steadily increased in the 1970s,
from zero to one.
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The Formation of Expectations
p t  p te  m  z    ut
 In the equation above, when  = 0, the relation
between the inflation rate and the
unemployment rate is:
p t  m  z    ut
 When  is positive, the inflation rate depends
on both the unemployment rate and last year’s
inflation rate:
p t  p te  m  z    ut
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The Formation of Expectations
p t  p t 1  m  z    ut
 When  =1, the unemployment rate affects
not the inflation rate, but the change in the
inflation rate.
p t  p t 1  m  z    ut
 Since 1970, a clear negative relation
emerged between the unemployment rate
and the change in the inflation rate.
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The Formation of Expectations
Change in Inflation
versus Unemployment
in the United States,
1970-2000
Since 1970, there has
been a negative
relation between the
unemployment rate
and the change in the
inflation rate in the
United States.
 The line that best fits the scatter of points for the
period 1970-2000 is:
πt - πt- 1 = 6% - 1.0ut
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The Formation of Expectations
 The original Phillips curve is:
p t  m  z    ut
 The modified Phillips curve, also called the
expectations-augmented Phillips curve, or the
accelerationist Phillips curve, is:
p t  p  m  z    ut
e
t
 This is now called, simply, the “Phillips Curve.”
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Back to the Natural
Rate of Unemployment
 For the pet= 0 Phillips Curve to hold, price-setters
would have had to be consistently mistaken about
their predictions of inflation.
 Friedman and Phelps doubted a long-run trade-off
between unemployment and inflation.
 They argued that the unemployment rate could not
be sustained below a certain level, a level they
called the “natural rate of unemployment.”
– The pet= 0 Phillips Curve implied that there was no such
thing as a natural rate of unemployment.
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Back to the Natural
Rate of Unemployment
 The natural rate of unemployment is the
unemployment rate such that the actual
inflation rate p is equal to the expected
inflation rate pet.
 This means 0  m  z    ut
Then, un
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
m  z


Macroeconomics, 3/e
Olivier Blanchard
Back to the Natural
Rate of Unemployment
un

m  z


Given
then,
 un  m  z 
p t  p  m  z    ut
then,
e
t
p t  p te   un   ut
Finally, assuming that pet is well
approximated by pt-1,
πt - πt- 1 = - α( ut - un )
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Back to the Natural
Rate of Unemployment
πt - πt- 1 = - α( ut - un )
 This is an important relation because it gives
another way of thinking about the Phillips curve.
 It tells us a relation between (cyclical
unemployment: the difference between the actual
and the natural unemployment rates) and (the
change in the inflation rate).
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Olivier Blanchard
Back to the Natural
Rate of Unemployment
πt - πt- 1 = - α( ut - un )
 Moreover, the equation above gives us
another way of thinking about the natural
rate of unemployment.
 Suppose we want to keep inflation
constant, pt = pt-1.
 Then
0   un   ut
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Back to the Natural
Rate of Unemployment
ut  u n
 The non-accelerating-inflation rate of
unemployment, (or NAIRU), is the rate
of unemployment required to keep the
inflation rate constant.
– If u = NAIRU, price expectations and prices
grow at the same rate.
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Olivier Blanchard
8-3
A Summary and
Many Warnings
Variations in the Natural Rate of Unemployment
Across Countries
un

m  z


 The factors that affect the natural rate of
unemployment above differ across countries.
Therefore, there is no reason to expect all
countries to have the same natural rate of
unemployment.
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Variations in the Natural Rate
of Unemployment over Time
p t  p t 1  m  z    ut
 In the equation above, the terms m and z vary over time,
leading to changes in the natural rate of unemployment.
 The U.S. natural rate of unemployment has decreased
from 6% to between 4% and 5% today.
– Maybe globalization reduces m, by exposing domestic firms to
foreign competition.
 A high unemployment rate does not necessarily reflect a
high natural rate of unemployment.
– If inflation were decreasing fast, the actual rate of unemployment
should be far above the natural rate.
– But, on the other hand, if inflation were stable, the natural rate of
unemployment would be close to the actual rate of unemployment.
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Olivier Blanchard
Variations in the Natural Rate of
Unemployment Across Countries
Change in Inflation Versus Unemployment—European Union, 1961-2000
The Phillips curve relation between the change in the inflation rate and the
unemployment rate has shifted to the right over time, suggesting a steady
increase in the natural unemployment rate in the European Union since 1960.
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High Inflation and the
Phillips Curve Relation
General Lesson:
 The relation between unemployment and
inflation is likely to change with the level and
the persistence of inflation.
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Olivier Blanchard
High Inflation and the
Phillips Curve Relation
 If expectations adjust very quickly, very
small deviations of u from un will lead to
higher inflation.
 In other words, when inflation is high, it is
also more variable.
– Expectations of inflation become an important
variable in wage determination.
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Olivier Blanchard
High Inflation and the
Phillips Curve Relation
 People that are very inflation-conscious
typically work their price-expectationadjustment mechanism into their job
contracts.
 Persistent and high inflation usually leads to
the establishment of wage indexation, a
rule that automatically increases wages in
line with inflation, … but it also causes
inflation to be more persistent and volatile.
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Olivier Blanchard