week_8_the philips curve, the nairu and the role of expectations
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The Phillips curve, theNAIRU and the role of
expectations
The Phillips curve
The NAIRU
Expectations
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The Phillips curve
Is a central empirical result that identifiesa trade-off between the rate ofunemployment and the rate of inflation
It is first of all an empirical relation...That has induced lots of theoretical work...
And lots of Nobel prizes (Friedman, Phelps, etc)
But there is not a single theoretical version of
the Phillips curve equation Also it is the missing link between WS-PS
(last week) and AS-AD (next week)
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The Phillips curve
From WS-PS to the Phillips curve
The natural rate of unemploymentrevisited
The role of expectations
The Phillips curve: an empiricalrelation
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The Phillips curve: an empirical relation
The Phillips curve is an empirical relationbetween unemployment and the rate ofinflation discovered by William Phillips in 1958 It shows a negative relation between
unemployment and inflation
It can be derived by analysing deviations fromequilibrium in the WS-PS model
Its general form is:
( )shocksupplyntunemploymecyclicalinflationexpectedinflation
vuune +=
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The Phillips curve: an empirical relation
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2 4 6 8 10 12unemployement_rate
Phillips curve for France
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The Phillips curve: an empirical relation
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Phillips curve for Italy
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The Phillips curve: an empirical relation
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inflatio
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Phillips curve for Japan
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The Phillips curve: an empirical relation
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1972
1973
1974
1975
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1979
1980
1981
1982
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inflatio
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Phillips curve for the USA
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The Phillips curve
From WS-PS to the Phillips curve
The natural rate of unemploymentrevisited
The role of expectations
The Phillips curve: an empiricalrelation
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From WS-PS to the Phillips curve
Quick reminder on WS-PS WS : wages are a function of the expected level of
prices, the level of unemployment and the marketconditions
PS : prices are a function of wages rate and the mark-uprate
The structural rate of unemployment can befound by setting P=P e. It is the rate ofunemployment when expectations are fulfilled.
( ) WP += 1
( )zuFPW e ,=
( )zuFn,
1
1
+
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From WS-PS to the Phillips curve
Structural rate of unemployment un
(long run)
( )zuF n ,11 +
A
un
WS
PS
Real WageP
W
Unemployment
rate u
+11
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But in the short run we do not necessarily have P=P e
For example, imagine that some unexpected inflationoccurs, so that PP e
What will unemployment ube compared to un?
Replacing WS in PS (eliminating W) gives thefollowing One can see that ifP=P eone recovers the equation for
un
( )( )
+==
WP
zuFPWe
1:PS
,:WS
( )e
P 1F u,z
P 1=
+
From WS-PS to the Phillips curve
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From WS-PS to the Phillips curve
We now have two WS-PS equations:
( )zuFP
P
e,
1
1=
+
A short run equation
By subtracting one from the other, we get a relationbetween deviations from equilibrium
The long run equilibrium equation
( )zuFn,
1
1
+
( ) ( )zuFzuFP
P
ne,,
1
1
1
1=
+
+
( ) ( )zuFzuFP
P
ne ,,111 =+
( ) ( ) ( )[ ]zuFzuFP
PP
ne
e
,,1 +=
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From WS-PS to the Phillips curve
This gives a theoretical underpinning to thePhillips curve (remember that Fis a negativefunction ofu)
Actual inflation is a function of: Expected inflation e
Cyclical unemployment (u-u n)
Shocks on supply v
( ) ( ) ( )[ ]zuFzuFP
PP
ne
e
,,1 +=
( ) vuu ne +=
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inflation
rate
Unemployment rate u
un
e + v
The inverse of the slope of the Phillipscurve is called the sacrifice ratio (1/),
This is how much extra unemployment
you have to accept in order to reduce
inflation by 1 percentage point1
( )vuu
ne
+=
From WS-PS to the Phillips curve
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inflation
rate
Unemployment rate uun
e + v
e+ v
1. An increase in
inflation
expectations by
agents
2. Shifts the
Phillips curve
upwards
( ) vuu ne +=
3. This explains the
fuzzy curves in the
1st section:
Inflation expectations
were changing at the
same time!
From WS-PS to the Phillips curve
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The Phillips curve
From WS-PS to the Phillips curve
The natural rate of unemploymentrevisited
The role of expectations
The Phillips curve: an empiricalrelation
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The NAIRU
Disregarding random shocks, what happens if
when we are at the natural rate ofunemployment, u =un?The actual rate of inflation equals the expected rate
of inflation =e...
This is consistent with the WS-PS prediction. But what is the expected rate of inflation
equal to ? How do we solve for a number?
( )shocksupplyntunemploymecyclicalinflationexpectedinflationvuu
ne+=
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We have to specifythe inflation expectations ! i.e. Make an assumption on how expectations are
formed.
First, we introduce time indices:
One of the simplest forms is adaptiveexpectations:
The Phillips curve becomes:
1= te
t
( ) tn
t
e
tt vuu +=
( )t
n
tttvuu +=
1
( )t
n
ttvuu +=
The NAIRU
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In other words, un
is the unemployment rate that
leaves the rate of inflation unchanged. This is the
NAIRU (Non Accelerating-Inflation Rate of
Unemployment).
If ut < un, inflation will accelerate (disregarding shocks v)
If ut > un, inflation will decelerate (disregarding shocks v)
If ut = un, there is no acceleration, or deceleration of inflation
( )t
n
ttvuu +=
The NAIRU
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ut < un u
t
> un
Acceleration of
the inflation rate
Unemployment rate u
0
un
( )t
n
ttvuu +=
The NAIRU
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The NAIRU
So the natural rate of unemploymentidentified previously also has aninterpretation in terms of inflationAs for the previous case, calling it natural
suggests it is fixed. In fact, the natural rate isendogenous as well
More on this in week 10...
But there is a bigger problem:One can see that to obtain NAIRU, one has to
make an assumption on expectations
This is a tricky issue!
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The Phillips curve
From WS-PS to the Phillips curve
The natural rate of unemploymentrevisited
The role of expectations
The Phillips curve: an empiricalrelation
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The role of expectations
The Phillips curve is given by:
This is accepted from an empirical point of view
The Phillips curve originated as an empirical relation ! The area of debate is on the theoretical
underpinnings of this relation (particularly duringthe 60s and 70s):
In particular, how do agents determine expectedinflation?
The debate centres on the following question : Shouldone focus on trying to explain correctly the mechanismthat generates these expectations, or should one just try
to find a method that produces the correct answer?
( )t
n
t
e
ttvuu +=
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The historical starting point is the assumption of adaptiveexpectations: Agents estimate future inflation based on current inflation:
This makes sense from a behavioural point of view...
The Phillips curve becomes :
This is the Phillips curve that produces the equation for theNAIRU
However, this can generate very strange predictions, withvery dumb behaviour from agents (exercise on this for
next week)
The role of expectations
1
e
t t =
( )t
n
tttvuu +=
1
( )t
n
ttvuu +=
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In order to avoid these problems, neoclassical economists(Lucas, Sargent, Wallace, etc.)introduced rationalexpectations: Agents estimate future inflation levels using all the available information,
including their knowledge of the economic models and mechanisms. This
gives the following equation, where is a random error
The Phillips curve becomes :
In this version, the Phillips curve is vertical: there is notrade-off between inflation and unemployment!
The role of expectations
( )t
n
ttttvuu ++=
( ) ttn
tvuu +=
( ) ttttet E +== 1
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The rational expectations assumption attempts to address the mainproblem that comes with adaptive expectations: the systematicerrors of agents
with , tbeing a random variable
The role of expectations
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0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Inflation
Expectedinflation
Agents make mistakes intheir predictions in theshort run
They are not omniscient
In the long run, they donot make any systematicerrors, and predictcorrectly the averagelevel of inflation
Agents are rational andcorrect their mistakes
tt
e
t +=
-
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It is important to point out that these two approaches have differentobjectives, hence the debate on how to model expectations
The adaptive expectations mechanism : Central argument: one must provide a plausible explanation to how
agents anticipate the future variations of a variable This approach supplies an explanation, but its predictions are not
consistent with the rationality hypothesis (central for economics)
The rational expectations mechanism : Central argument: a rational agent does not make systematic errors
This approach, however, gives no indication about the way expectationsare reached : in reality, how do badly-informed agents manage to guessthe right solution?
Black box : The mechanism exists, but is not revealed
The role of expectations
( )tttt
e
tE +==
1
1= te
t