2003-7-20 1
Chapter 10,The Phillips
Curve
10-1,Inflation,Expected Inflation,and
Unemployment
10-2,The Phillips Curve
10-3,A Summary and many Warnings
2003-7-20 2
10-1,Inflation,Expected
Inflation,and Unemployment
We have already known the function in chapter 9:
Pt = Pte (1+μ) F (ut,z)
It will be convenient here to assume a specific form
for the function F:
F (ut,z)= 1 - αut + z
Replacing in the earlier equation gives:
Pt = Pte (1+μ)(1 - αut + z)
To continue
2003-7-20 3
With a few manipulation,this relation can be rewritten
as a relation between the inflation rate,the expected
inflation rate,and the unemployment rate
π t =π te + (μ+z) - αut (10.1)
Where π t denotes the inflation rate,and π te denotes
the corresponding expected inflation rate.
In short,equation (10.1) tells us:
? Higher expected inflation leads to higher inflation
? Given expected inflation,the higher the markup chosen by
firms,μ,or the higher the factors that affect wage
determination,z,the higher inflation.
? Given expected inflation,the higher unemployment,the
lower inflation.
2003-7-20 4
10-2,The Phillips Curve
The Early Incarnation
Mutations
Back to the Natural Rate of Unemployment
2003-7-20 5
The Early Incarnation
Think of an economy where inflation on average
equals to zero,it is reasonable for people to expect
that inflation rate will be equal to zero over the next
year as well,
Assuming that π te =0 in equation (10.1),then
π t = (μ+z) - αut (10.2)
This is precisely the negative relation between
unemployment and inflation,The story behind it is
simple:Given expected prices,lower unemployment
leads to higher nominal wages,Higher nominal wages
lead to higher prices.
2003-7-20 6
Wage-price spiral
This mechanism has sometimes been called the
wage-price spiral,and this phrase captures well the
basic mechanism at work:
? Low unemployment leads to higher nominal wages.
? In response to higher wages,firms increase their prices.
? In response to higher prices,workers ask for higher nominal
wages.
? Firms further increase prices,so workers ask for further
increases in wages.
? And so on,with the result being steady wage and price
inflation.
2003-7-20 7
Mutations
From 1970 on,the original Phillips curve
relation broke down,There are two main
reasons:
? The change in the price of oil,The effect of this
increase in nonlabor costs was to force firms to
increase their prices given wages,to increase μ,An
increase in μ leads to an increase in inflation,even
at a given rate of unemployment.
? Wage setters changes the way they formed
expectations,This change came from a change in
the process of inflation itself,This is the main
reason for the breakdown of Philips curve relation.
2003-7-20 8
The importance of expectation
Suppose expectations are formed according to
π te =θπt-1 (10.3)
To see the implications of different values ofθ for the
relation between inflation and unemployment,replace
equation (10.3) in equation (10.1),Doing so gives
π te
π t = θπt-1 + (μ+z) – αut
? When θ equals zero,we get the original Phillips curve.
? When θ is positive,the inflation rate depends not only on
the employment rate but also on last year’s inflation rate.
To continue
2003-7-20 9
The importance of expectation
? When θ equals 1,the relation becomes
π t -π t-1 = (μ+z) – αut (10.4)
So,when θ =1,the unemployment rate affects not the
inflation rate,but rather the change in the inflation rate,High
unemployment leads to decreasing inflation; low
unemployment leads to increase inflation.
To distinguish equation (10.4) from the original Phillips
curve (equation [10.2]),it is often called the modified
Phillips curve.
2003-7-20 10
Back to the Natural Rate of
Unemployment
By definition,the natural rate of unemployment is that
unemployment rate such that the actual price level
turns out equal to the expected price level,More
conveniently here,the natural rate of unemployment
is the unemployment rate such that the actual
inflation rate is equal to the expected inflation rate,
Denote the natural unemployment rate by un,Then,
imposing the condition that actual inflation and
expected inflation be the same (π t =π te ) in
equation (10.1) gives
To continue
2003-7-20 11
Back to the Natural Rate of
Unemployment
0 = (μ+z) – αut
Solving for the natural rate un:
un = (μ+z) / α (10.6)
From equation (10.6),αun =(μ+z),Replacing (μ+z) by
αun in equation (10.1) and rearranging gives
π t-π te = -α(ut - un ) (10.7)
If the expected rate of inflation (π te ) is well
approximated by last year’s inflation rate (π t-1),the
relation finally becomes
π t-π t-1 = -α(ut - un ) (10.8)
To continue
2003-7-20 12
Back to the Natural Rate of
Unemployment
Equation (10.8) gives us another way of thinking about
the Phillips curve,as a relation between the actual
unemployment rate,the natural unemployment rate,
and the change in the inflation rate,The change in
inflation depends on the difference between the
actual and the natural unemployment rates,When
the actual unemployment rate is higher than the
natural unemployment rate,inflation decreases;
when the actual unemployment rate is lower than
the natural unemployment rate,inflation increases.
To continue
2003-7-20 13
Back to the Natural Rate of
Unemployment
Equation (10.8) also gives us another way of thinking
about the natural rate of unemployment,It is the rate
of unemployment required to keep inflation constant,
This is why the natural rate is also called the
nonaccelerating inflation rate of unemployment,
or NAIRU.
2003-7-20 14
10-3,A Summary and many
Warnings
A Summary
The Inflation Process and the Phillips Curve
Differences in the natural Rate Across
Countries
Variations in the Natural Rate Over Time
The Limits of Our Understanding
2003-7-20 15
A Summary
The aggregate supply relation is well captured in the
United states today by the Phillips curve,which is a
relation between the change in the inflation rate and
the deviation of unemployment from its natural rate
(equation [10.8]),When unemployment exceeds the
natural rate,inflation decreases,When unemployment
is below the natural rate,inflation increases.
The relation has held quite well since 1970,But its
earlier history points to the need for several warnings,
All of them point to one main fact,The relation can
change,and it often has.
2003-7-20 16
The Inflation Process and the
Phillips Curve
Think of an economy that has two types of labor
contracts,A proportion λ of labor contracts is indexed,
Nominal wages in those contracts move one for one
with variations in the actual price level,A proportion 1-
λ of labor contracts is not indexed,Nominal wages are
set on the basis of expected inflation,Finally,assume
expected inflation is equal to last year’s inflation.
Under this assumption,equation (10.7) becomes
π t=[λπt+(1-λ )π t-1-α (ut - un )
To continue
2003-7-20 17
The Inflation Process and the
Phillips Curve
When λ=0,all wages are set on the basis of expected
inflation—which is equal to last year’s inflation,π t-1 –
and the equation reduces to equation (10.8),When λ
is positive,however,a proportion λ of wages is set on
the basis of actual rather than expected inflation.
Reorganizing the equation gives
π t-π t-1 = -α (ut - un )/(1-λ )
Indexation increases the effect of unemployment on
inflation,The higher the proportion of indexed
contracts—the higher λ—the larger the effect of the
unemployment rate on the change in inflation—the
higher the coefficient α /(1-λ ).
2003-7-20 18
Differences in the natural Rate
Across Countries
Recall from equation (10.6) that the natural rate of
unemployment depends on all that factors that affect
wage setting,represented by the catchall variable z;
on the markup set by firms μ; and on the response of
inflation to unemployment,represented by α, To the
extent that these factors differ across countries,there
is no reason to expect different countries to have the
same natural rate of unemployment,And indeed,
natural rates differ across countries.
2003-7-20 19
Variations in the Natural Rate
Over Time
In estimating equation (10.6),we treated μ+z as a
constant,But there is no reason to believe that μ
and z are constant over time,The composition of
the labor force,the structure of wage bargaining,
the system of employment benefits,and so on,
are likely to change over time,leading to changes
in the natural rate of unemployment.
2003-7-20 20
The Limits of Our Understanding
The theory of the natural rate gives macroeconomists
directions where to look for differences in natural rates
across countries or for variations in the natural rate
over time in a given country,But the truth is that
macroeconomists’ understanding of exactly which
factors determine the natural rate of unemployment is
still very limited,In particular,there is considerable
uncertainty about the exact list of factors behind z,and
about the dynamic effects of each factor on the natural
unemployment rate.
Chapter 10,The Phillips
Curve
10-1,Inflation,Expected Inflation,and
Unemployment
10-2,The Phillips Curve
10-3,A Summary and many Warnings
2003-7-20 2
10-1,Inflation,Expected
Inflation,and Unemployment
We have already known the function in chapter 9:
Pt = Pte (1+μ) F (ut,z)
It will be convenient here to assume a specific form
for the function F:
F (ut,z)= 1 - αut + z
Replacing in the earlier equation gives:
Pt = Pte (1+μ)(1 - αut + z)
To continue
2003-7-20 3
With a few manipulation,this relation can be rewritten
as a relation between the inflation rate,the expected
inflation rate,and the unemployment rate
π t =π te + (μ+z) - αut (10.1)
Where π t denotes the inflation rate,and π te denotes
the corresponding expected inflation rate.
In short,equation (10.1) tells us:
? Higher expected inflation leads to higher inflation
? Given expected inflation,the higher the markup chosen by
firms,μ,or the higher the factors that affect wage
determination,z,the higher inflation.
? Given expected inflation,the higher unemployment,the
lower inflation.
2003-7-20 4
10-2,The Phillips Curve
The Early Incarnation
Mutations
Back to the Natural Rate of Unemployment
2003-7-20 5
The Early Incarnation
Think of an economy where inflation on average
equals to zero,it is reasonable for people to expect
that inflation rate will be equal to zero over the next
year as well,
Assuming that π te =0 in equation (10.1),then
π t = (μ+z) - αut (10.2)
This is precisely the negative relation between
unemployment and inflation,The story behind it is
simple:Given expected prices,lower unemployment
leads to higher nominal wages,Higher nominal wages
lead to higher prices.
2003-7-20 6
Wage-price spiral
This mechanism has sometimes been called the
wage-price spiral,and this phrase captures well the
basic mechanism at work:
? Low unemployment leads to higher nominal wages.
? In response to higher wages,firms increase their prices.
? In response to higher prices,workers ask for higher nominal
wages.
? Firms further increase prices,so workers ask for further
increases in wages.
? And so on,with the result being steady wage and price
inflation.
2003-7-20 7
Mutations
From 1970 on,the original Phillips curve
relation broke down,There are two main
reasons:
? The change in the price of oil,The effect of this
increase in nonlabor costs was to force firms to
increase their prices given wages,to increase μ,An
increase in μ leads to an increase in inflation,even
at a given rate of unemployment.
? Wage setters changes the way they formed
expectations,This change came from a change in
the process of inflation itself,This is the main
reason for the breakdown of Philips curve relation.
2003-7-20 8
The importance of expectation
Suppose expectations are formed according to
π te =θπt-1 (10.3)
To see the implications of different values ofθ for the
relation between inflation and unemployment,replace
equation (10.3) in equation (10.1),Doing so gives
π te
π t = θπt-1 + (μ+z) – αut
? When θ equals zero,we get the original Phillips curve.
? When θ is positive,the inflation rate depends not only on
the employment rate but also on last year’s inflation rate.
To continue
2003-7-20 9
The importance of expectation
? When θ equals 1,the relation becomes
π t -π t-1 = (μ+z) – αut (10.4)
So,when θ =1,the unemployment rate affects not the
inflation rate,but rather the change in the inflation rate,High
unemployment leads to decreasing inflation; low
unemployment leads to increase inflation.
To distinguish equation (10.4) from the original Phillips
curve (equation [10.2]),it is often called the modified
Phillips curve.
2003-7-20 10
Back to the Natural Rate of
Unemployment
By definition,the natural rate of unemployment is that
unemployment rate such that the actual price level
turns out equal to the expected price level,More
conveniently here,the natural rate of unemployment
is the unemployment rate such that the actual
inflation rate is equal to the expected inflation rate,
Denote the natural unemployment rate by un,Then,
imposing the condition that actual inflation and
expected inflation be the same (π t =π te ) in
equation (10.1) gives
To continue
2003-7-20 11
Back to the Natural Rate of
Unemployment
0 = (μ+z) – αut
Solving for the natural rate un:
un = (μ+z) / α (10.6)
From equation (10.6),αun =(μ+z),Replacing (μ+z) by
αun in equation (10.1) and rearranging gives
π t-π te = -α(ut - un ) (10.7)
If the expected rate of inflation (π te ) is well
approximated by last year’s inflation rate (π t-1),the
relation finally becomes
π t-π t-1 = -α(ut - un ) (10.8)
To continue
2003-7-20 12
Back to the Natural Rate of
Unemployment
Equation (10.8) gives us another way of thinking about
the Phillips curve,as a relation between the actual
unemployment rate,the natural unemployment rate,
and the change in the inflation rate,The change in
inflation depends on the difference between the
actual and the natural unemployment rates,When
the actual unemployment rate is higher than the
natural unemployment rate,inflation decreases;
when the actual unemployment rate is lower than
the natural unemployment rate,inflation increases.
To continue
2003-7-20 13
Back to the Natural Rate of
Unemployment
Equation (10.8) also gives us another way of thinking
about the natural rate of unemployment,It is the rate
of unemployment required to keep inflation constant,
This is why the natural rate is also called the
nonaccelerating inflation rate of unemployment,
or NAIRU.
2003-7-20 14
10-3,A Summary and many
Warnings
A Summary
The Inflation Process and the Phillips Curve
Differences in the natural Rate Across
Countries
Variations in the Natural Rate Over Time
The Limits of Our Understanding
2003-7-20 15
A Summary
The aggregate supply relation is well captured in the
United states today by the Phillips curve,which is a
relation between the change in the inflation rate and
the deviation of unemployment from its natural rate
(equation [10.8]),When unemployment exceeds the
natural rate,inflation decreases,When unemployment
is below the natural rate,inflation increases.
The relation has held quite well since 1970,But its
earlier history points to the need for several warnings,
All of them point to one main fact,The relation can
change,and it often has.
2003-7-20 16
The Inflation Process and the
Phillips Curve
Think of an economy that has two types of labor
contracts,A proportion λ of labor contracts is indexed,
Nominal wages in those contracts move one for one
with variations in the actual price level,A proportion 1-
λ of labor contracts is not indexed,Nominal wages are
set on the basis of expected inflation,Finally,assume
expected inflation is equal to last year’s inflation.
Under this assumption,equation (10.7) becomes
π t=[λπt+(1-λ )π t-1-α (ut - un )
To continue
2003-7-20 17
The Inflation Process and the
Phillips Curve
When λ=0,all wages are set on the basis of expected
inflation—which is equal to last year’s inflation,π t-1 –
and the equation reduces to equation (10.8),When λ
is positive,however,a proportion λ of wages is set on
the basis of actual rather than expected inflation.
Reorganizing the equation gives
π t-π t-1 = -α (ut - un )/(1-λ )
Indexation increases the effect of unemployment on
inflation,The higher the proportion of indexed
contracts—the higher λ—the larger the effect of the
unemployment rate on the change in inflation—the
higher the coefficient α /(1-λ ).
2003-7-20 18
Differences in the natural Rate
Across Countries
Recall from equation (10.6) that the natural rate of
unemployment depends on all that factors that affect
wage setting,represented by the catchall variable z;
on the markup set by firms μ; and on the response of
inflation to unemployment,represented by α, To the
extent that these factors differ across countries,there
is no reason to expect different countries to have the
same natural rate of unemployment,And indeed,
natural rates differ across countries.
2003-7-20 19
Variations in the Natural Rate
Over Time
In estimating equation (10.6),we treated μ+z as a
constant,But there is no reason to believe that μ
and z are constant over time,The composition of
the labor force,the structure of wage bargaining,
the system of employment benefits,and so on,
are likely to change over time,leading to changes
in the natural rate of unemployment.
2003-7-20 20
The Limits of Our Understanding
The theory of the natural rate gives macroeconomists
directions where to look for differences in natural rates
across countries or for variations in the natural rate
over time in a given country,But the truth is that
macroeconomists’ understanding of exactly which
factors determine the natural rate of unemployment is
still very limited,In particular,there is considerable
uncertainty about the exact list of factors behind z,and
about the dynamic effects of each factor on the natural
unemployment rate.
