Week_8_The Philips Curve, The NAIRU and the Role of Expectations

7/29/2019 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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1971

1972

1973

1974

1975

1976 19771978

1979

1980 1981

1982

1983

1984

1985

1986

19871

988

198919901991

19921993

1994

1995

1996

199719981999

200020012

002 20032004

20052006

0

5

10

15

inflatio

n

2 4 6 8 10 12unemployement_rate

Phillips curve for France


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1971

1972

1973

1974

1975 19761977

1978

1979

1980

1981

1982

1983

1984

1985

1986

19871988

19891990199

1

19921993

1994

1995

1996

199719981

9992000

2001

20022003

200420052006

0

5

10

15

20

inflatio

n

4 6 8 10 12unemployement_rate

Phillips curve for Italy


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1971

1972

1973

1974

1975

1976

1977

19781979

1980

1981

1982

19831984

1985

198619871988

198919901991

1992 19931994

19951996

19971998

19992000 2001 2002200320042005

20060

5

10

15

20

25

inflatio

n

1 2 3 4 5unemployement_rate

Phillips curve for Japan


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1971

1972

1973

1974

1975

1976

1977

1978

1979

1980

1981

1982

1983

1984

1985

1986

19871988

1989

1990

1991

1992199319941995

19961997

1998

1999

20002001

2002

20032004

20052006

0

5

10

15

inflatio

n

4 6 8 10unemployement_rate

Phillips curve for the USA


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The Phillips curve






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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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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=

+



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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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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

+=



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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!



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The Phillips curve






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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






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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)


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!


( )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


1,5

2

2,5

3

3,5

4

4,5

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


( )tttt

e

tE +==

1

1= te

t

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Week_8_The Philips Curve, The NAIRU and the Role of Expectations