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Phillips CurvePhillips Curve
MacroeconomicsCunningham

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Original Phillips CurveOriginal Phillips Curve
A. W. Phillips (1958), The Relation Between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 18611957, Economica.Wage inflation vs. UnemploymentNew Zealander at London School of EconomicsMissing Equation of Keynesian economics?

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5 % = zero inflation

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5 %

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Phillips ConclusionsPhillips Conclusions
There exists a stable relationship between the variables. The relationship has not substantially changed for over 100 years.Negative, nonlinear correlation.Wages remain stable/stationary( =0) when unemployment is 5%.w
dw

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Conclusions, ContinuedConclusions, ContinuedFrom the dispersion of the data points, Phillips concluded that there was a countercyclical loop:
Money wages rise faster as du/dt decreases,
Money wages fall slower as du/dt increases
Implies an inflationary bias, and is consistent with sticky wage theory.
slower
faster
wdw
u

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Problems with Phillips StudyProblems with Phillips Study
Empirical method suspect.Is this an empirical result in search of a theory?To tie to theory, need a way to relate this to real wages in order to connect this to labor market conditions.R.G. Lipsey (1960) attempts to address these points in The Relationship Between Unemployment and the Rate of Change of Money Wage Rates in the UK, 18621957: A Further Analysis.

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Lipseys Lipseys Phillips CurvePhillips CurveDerives the Phillips curve from supplydemand analysis of the labor market.
Ns = N + UNd = N + V
Where U refers to the number unemployed,V refers to the number of job vacancies.
Excess demand Nd Ns = X = V U.So
Where v is the vacancy rate and u is the unemployment rate.
uvxNU
NV
NX
sss ===

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LipseyLipsey, Continued, Continued
Step One. Wage Adjustment Function
== s
sd
NNNk
dNdww
This amounts to saying that the change in the money wage rate is proportional to the excess demand for labor.
Step Two. Establish a theoretical negative correlation between the excess demand for labor and the rate of unemployment.

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LipseyLipsey, Continued, ContinuedIndividual Labor Market ConditionsIndividual Labor Market Conditions
u
s
sd
NNN
x
= Asymptotic(u=0 not possible)
uf
wdw
s
sd
NNN
x
=
Individuallabor market
u
wdw
uf
wage inflation
unemployment

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LipseyLipsey, Continued, Continued
The result is a Phillips curve for an individual market. Next, aggregate across markets for the aggregate Phillips curve.

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SamuelsonSamuelsonSolow Solow (1960)(1960)P. Samuelson and R. Solow. The Problem of Achieving and Maintaining a Stable Price Level: Analytical Aspects of AntiInflation Policy, American Economic Review (May 1960), 17794.
Popularized the curve.Made relevant to policymakers.Relation is general price level inflation vs. unemployment.Recommended to policymakers as a tradeoff.

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SamuelsonSamuelsonSolowSolow, Continued, Continued
Key transformation from PhillipsLipsey to SS is through markmarkup pricingup pricing. Firms set prices by adding a fixed markup to
labor costs. The markup = the industrywide profit margin
+ depreciation of fixed K
t
ttt y
NWaP )1( += unit laborcosts
markup

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SamuelsonSamuelsonSolowSolow, Continued, Continued
tttt NWayP )1( +=
nominaloutput (GDP)
nominalwage bill
ty)productivi(laborLett
tt N
y=
Substituting:
t
tt
WaP
== )1(In logs:
ttt WaP ++= loglog)1log(log

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SamuelsonSamuelsonSolowSolow, Continued, Continued
This implies:
t
t
t
t
t
tWW
PP
=
= worinflation rate = wage inflation rate inflation rate = wage inflation rate
growth rate of labor productivitygrowth rate of labor productivityIncreases in wages matched by productivity increases are not inflationary.There is a relationship between wage inflation and goods price level inflation.

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SamuelsonSamuelsonSolowSolow, Continued, Continued
Generalize further in the form of a Phillips curve relation:
10,0,1 >++= bbuw e
offsetting productivity gainsdemandpressure
inflation expectations(assumed stable, i.e., equal to zero)
= wSubstitute:

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SamuelsonSamuelsonSolowSolow, Continued, Continued
+= )1(1bue
This is the modern Phillips curve.Technical relation between inflation and unemployment.Each point is an equilibrium state of the economy.

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FriedmanFriedmanPhelps Phillips CurvePhelps Phillips CurveMilton Friedman. The Role of Monetary Policy, American Economic Review (March 1968), 117.Edmund Phillips. Phillips Curves, Expectations of Inflation and Optimal Employment Over Time, Economica (August 1967), 25481)
They question the stability of the relationship. They conclude: The tradeoff is shortrun. Different Phillips curves exist for different
inflation rates Changes in inflation expectations shift the
shortrun Phillips curve.

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FriedmanFriedmanPhelps Phillips CurvePhelps Phillips Curveeuf += )(
U
e=0
e=1
U*U1
LRPC
Short runPhillips curves
Natural Rate of UnemploymentNatural Rate of Unemploymentor NAIRUor NAIRU

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FriedmansFriedmansAccelerationistAccelerationist HypothesisHypothesis
euf += )(
Accelerationist Hypothesis:*)()(let uubuf t =
Use adaptive expectations:ett
et 11 )1( +=
So that*)()1( 11 uub t
ettt +=
Problem: is not observable.et 1

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FriedmansFriedmansAccelerationistAccelerationist HypothesisHypothesis
Lag one period, multiply by )1(
*))(1()1()1( 111 uub tett =
Subtract from the original equation:*)(*))(1( 111 uubuub tttt +=
Replaces the expected inflation term
When inflation is fully anticipated, .,, 11 === tttt
ett uuand

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FriedmansFriedmansAccelerationistAccelerationist HypothesisHypothesis
Substituting,))(1(*)( 11 = ttttt uubuub
.00
11
11
====
tttt
tttt
uuuuandBut
.*and*)(0So
uuuub
t
t
==
Which implies that unemployment reverts to the natural rate at the long run Phillips curve once inflation is fully anticipated.

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Another view: Another view: Keynesian PerspectiveKeynesian Perspective
AD1
AS1AS2
1
2
3
AD2

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More FriedmanMore FriedmanIn his Nobel lecture, Friedman offered the possibility of a positivelysloped Phillips curve:
Stabilization policy increases the inflation rate and variability.
This requires nominal contracts to be renegotiated to shorter lengths.
Efficiency is lowered. Inventories grow. Unemployment rises.
The broadcast about relative prices is, at it were, being jammed by the noise coming from the inflation broadcast.
Phillips CurveOriginal Phillips CurvePhillips ConclusionsConclusions, ContinuedProblems with Phillips StudyLipseys Phillips CurveLipsey, ContinuedLipsey, ContinuedIndividual Labor Market ConditionsLipsey, ContinuedSamuelsonSolow (1960)SamuelsonSolow, ContinuedSamuelsonSolow, ContinuedSamuelsonSolow, ContinuedSamuelsonSolow, ContinuedSamuelsonSolow, ContinuedFriedmanPhelps Phillips CurveFriedmanPhelps Phillips CurveFriedmansAccelerationist HypothesisFriedmansAccelerationist HypothesisFriedmansAccelerationist HypothesisAnother view: Keynesian PerspectiveMore Friedman