The Phillips Curve

Christina Zauner

Introduction

Derivation of thePhillips Curve fromthe AS Curve

The OriginalPhillips Curve

The Expectations-AugmentedPhillips Curve

The NAIRU

Wage Indexation

Conclusion

The Phillips Curve

Christina Zauner

Department of Economics, University of Vienna

May 25th, 2011

The Phillips Curve

Christina Zauner

Introduction

Derivation of thePhillips Curve fromthe AS Curve

The OriginalPhillips Curve

The Expectations-AugmentedPhillips Curve

The NAIRU

Wage Indexation

Conclusion

The Phillips CurveAn Introduction

I In 1958 A. W. Phillips plotted the rate of inflationagainst the rate of unemployment (using UK data)

I He found a negative relation between inflation andunemployment, suggesting that there is a trade-off

I In the 1970s the original relation broke down with manycountries witnessing high inflation AND highunemployment (”stagflation”)

I The purpose of this chapter is to derive the so-calledPhillips curve and to study its modification in the lastdecades

The Phillips Curve

Christina Zauner

Introduction

Derivation of thePhillips Curve fromthe AS Curve

The OriginalPhillips Curve

The Expectations-AugmentedPhillips Curve

The NAIRU

Wage Indexation

Conclusion

The Original Phillips Curve for the U.S.

Figure: Inflation vs. Unemployment in the U.S. (OECD,1959-1970)

The Phillips Curve

Christina Zauner

Introduction

Derivation of thePhillips Curve fromthe AS Curve

The OriginalPhillips Curve

The Expectations-AugmentedPhillips Curve

The NAIRU

Wage Indexation

Conclusion

The AS Curve revisited

I Recall that we derived the AS Curve as:

Pt = Pet (1 + µ)F (ut , z) (1)

I where we assumed that labor productivity A = 1 andwhere we now use the subscript t for time, i.e. Pt

stands for the price level at time t

I Assuming that F (ut , z) = 1− αut + z we get

Pt = Pet (1 + µ)(1− αut + z)

The Phillips Curve

Christina Zauner

Introduction

Derivation of thePhillips Curve fromthe AS Curve

The OriginalPhillips Curve

The Expectations-AugmentedPhillips Curve

The NAIRU

Wage Indexation

Conclusion

Definitions and Approximations

I By definition we have

1 + πt =Pt

Pt−1and 1 + πe

t =Pe

t

Pt−1

I Dividing (1) by Pt−1 and using the above expressionswe get

1 + πt = (1 + πet )(1 + µ)(1− αut + z)

(1 + πt)/[(1 + πet )(1 + µ)] = (1− αut + z)

I For small values of πt , πet and µ, the left hand side can

be approximated as follows:

(1 + πet )(1 + µ) ≈ [1 + (πe

t + µ)]

(1 + πt)/[1 + (πet + µ)] ≈ [1 + πt − (πe

t + µ)]

The Phillips Curve

Christina Zauner

Introduction

Derivation of thePhillips Curve fromthe AS Curve

The OriginalPhillips Curve

The Expectations-AugmentedPhillips Curve

The NAIRU

Wage Indexation

Conclusion

Inflation, Expected Inflation, and Unemployment

I Using these approximations we finally get

πt = πet + (µ+ z)− αut (2)

I Equation (2) states that higher expected inflation leadsto higher inflation given πe

t , µ, and z

I It also implies that given πet and ut an increase in µ or

z leads to higher inflation

I On the other hand, given πet , µ, and z an increase in

the unemployment rate ut leads to lower inflation

The Phillips Curve

Christina Zauner

Introduction

Derivation of thePhillips Curve fromthe AS Curve

The OriginalPhillips Curve

The Expectations-AugmentedPhillips Curve

The NAIRU

Wage Indexation

Conclusion

The Original Phillips Curve

I Imagine an economy with an average rate of inflationequal to zero – not a plausible assumption nowadays,but it nearly held for the time period Phillips wasanalyzing

I If average inflation is equal to zero then it is reasonableto expect that inflation will be zero in the future, i.e.πe

t = 0

I As a result, equation (2) becomes

πt = (µ+ z)− αut

I This is the negative relation between unemploymentand inflation that Phillips found for the UK, i.e. theoriginal relation

The Phillips Curve

Christina Zauner

Introduction

Derivation of thePhillips Curve fromthe AS Curve

The OriginalPhillips Curve

The Expectations-AugmentedPhillips Curve

The NAIRU

Wage Indexation

Conclusion

The Wage-Price Spiral

I The original Phillips curve states that lowerunemployment leads to higher inflation

I The mechanism behind this relation is captured by theso-called wage-price spiral:

I low unemployment leads to higher nominal wagesI these higher costs of production prompt firms to

increase pricesI because of the higher price level workers ask for higher

nominal wages the next time wages are setI the price level therefore increases again and workers will

further ask for an increase in nominal wagesI the race between prices and wages results in a steady

wage and price increase

The Phillips Curve

Christina Zauner

Introduction

Derivation of thePhillips Curve fromthe AS Curve

The OriginalPhillips Curve

The Expectations-AugmentedPhillips Curve

The NAIRU

Wage Indexation

Conclusion

The Trade-Off between Inflation andUnemployment

I The original Phillips curve implies that if policy makersare willing to tolerate higher inflation they can maintainany (low) unemployment rate

I Some economists, however, argued that anunemployment rate below the natural rate could not besustained forever.

I Their main argument was that a permanent trade-offbetween inflation and unemployment could only exist ifwage setters systematically underpredicted inflation

The Phillips Curve

Christina Zauner

Introduction

Derivation of thePhillips Curve fromthe AS Curve

The OriginalPhillips Curve

The Expectations-AugmentedPhillips Curve

The NAIRU

Wage Indexation

Conclusion

The Modified Phillips CurveReasons for the Breakdown of the Original Relation

I The original relation between inflation andunemployment broke down in most OECD countriesaround 1970 for two reasons

I First, the oil shocks in the 1970s lead to a large increasein the price of oil; consequently firms had to increaseprices given unemployment (similar to an increase in µin the AS relation)

I Second, and more importantly, the behaviour ofinflation changed: rather than being sometimes positiveand sometimes negative, inflation started to beconsistently positive; furthermore inflation became morepersistent (high inflation in one period likely to befollowed by high inflation in the next period)

The Phillips Curve

Christina Zauner

Introduction

Derivation of thePhillips Curve fromthe AS Curve

The OriginalPhillips Curve

The Expectations-AugmentedPhillips Curve

The NAIRU

Wage Indexation

Conclusion

The Breakdown of the Original Relation in theU.S.

Figure: Inflation vs. Unemployment in the U.S. (OECD,1970-2007)

The Phillips Curve

Christina Zauner

Introduction

Derivation of thePhillips Curve fromthe AS Curve

The OriginalPhillips Curve

The Expectations-AugmentedPhillips Curve

The NAIRU

Wage Indexation

Conclusion

Inflation in the U.S.

Figure: Inflation Rate in the U.S. (Blanchard, 1900-2004)

The Phillips Curve

Christina Zauner

Introduction

Derivation of thePhillips Curve fromthe AS Curve

The OriginalPhillips Curve

The Expectations-AugmentedPhillips Curve

The NAIRU

Wage Indexation

Conclusion

The Modified Phillips CurveChange in Formation of Expectations

I Expecting inflation to be zero when in fact it hasbecome consistently positive is not rational ⇒ workerswill change the way they formed expectations

I Suppose workers expectations are formed as follows:

πet = θπt−1

I The higher θ, the more last year’s inflation leadsworkers (and firms) to revise their expectations aboutpresent inflation

I Relation (2) therefore becomes

πt = θπt−1 + (µ+ z)− αut

The Phillips Curve

Christina Zauner

Introduction

Derivation of thePhillips Curve fromthe AS Curve

The OriginalPhillips Curve

The Expectations-AugmentedPhillips Curve

The NAIRU

Wage Indexation

Conclusion

The Modified Phillips CurveDerivation

I Before the 1970s, apparently θ = 0, i.e. since averageinflation was equal to zero it was rational to assumethat the price level will not change

πt = (µ+ z)− αut

I Afterwards, when inflation was consistently positive,workers changed their expectations so that θ > 0

πt = θπt−1 + (µ+ z)− αut

I In particular, evidence suggests that after the 1970sθ = 1, i.e. people expect that inflation this period isequal to inflation last period (persistence, ”naive/staticexpectations”)

πt = πt−1 + (µ+ z)− αut

The Phillips Curve

Christina Zauner

Introduction

Derivation of thePhillips Curve fromthe AS Curve

The OriginalPhillips Curve

The Expectations-AugmentedPhillips Curve

The NAIRU

Wage Indexation

Conclusion

The Modified Phillips CurveImplications

I Rewriting the last equation yields

πt − πt−1 = (µ+ z)− αut (3)

I Thus, when θ = 1 then the unemployment rate doesnot affect the rate of inflation but the change in theinflation rate (or by how much the actual inflation ratediffers from the expected inflation rate, i.e. theunexpected inflation)

I Higher unemployment decreases the change in theinflation rate while lower unemployment increases thechange in the inflation rate

I Equation (3) is called the modified Phillips curve or theexpectations-augmented Phillips curve

The Phillips Curve

Christina Zauner

Introduction

Derivation of thePhillips Curve fromthe AS Curve

The OriginalPhillips Curve

The Expectations-AugmentedPhillips Curve

The NAIRU

Wage Indexation

Conclusion

The Modified Phillips Curve for the U.S.

Figure: Change in Inflation/Unemployment (OECD, 1970-2007)

The Phillips Curve

Christina Zauner

Introduction

Derivation of thePhillips Curve fromthe AS Curve

The OriginalPhillips Curve

The Expectations-AugmentedPhillips Curve

The NAIRU

Wage Indexation

Conclusion

The Phillips Curve and the NaturalUnemployment RateEstablishing the Relation

I Recall that the natural rate of unemployment is theunemployment rate at which the actual price levelequals the expected price level

I Further note that Pt = Pet ⇔ πt = πe

t

I Thus, at the natural rate of unemployment inflationequals expected inflation

I This result, together with equation (2), implies that

0 = (µ+ z)− αun

The Phillips Curve

Christina Zauner

Introduction

Derivation of thePhillips Curve fromthe AS Curve

The OriginalPhillips Curve

The Expectations-AugmentedPhillips Curve

The NAIRU

Wage Indexation

Conclusion

The Phillips Curve and the NaturalUnemployment RateEstablishing the Relation

I Solving for the natural rate of unemployment yields

un =µ+ z

α

I Since equation (2) can also be written as

πt − πet = −α

(ut −

µ+ z

α

)I we can substitute the expression for un from above to

getπt − πe

t = −α(ut − un) (4)

The Phillips Curve

Christina Zauner

Introduction

Derivation of thePhillips Curve fromthe AS Curve

The OriginalPhillips Curve

The Expectations-AugmentedPhillips Curve

The NAIRU

Wage Indexation

Conclusion

The Phillips Curve and the NaturalUnemployment Rate

I If the expected rate of inflation is well approximated bylast periods inflation then we finally get

πt − πt−1 = −α(ut − un) (5)

I Equation (5) states that the change in inflation dependson the difference between the actual and the naturalrate of unemployment

I When ut is higher (lower) than un, inflation decreases(increases)

I From (5) we can also conclude that un is theunemployment rate required to keep inflation constant⇒ nonaccelerating inflation rate of unemployment(NAIRU)

The Phillips Curve

Christina Zauner

Introduction

Derivation of thePhillips Curve fromthe AS Curve

The OriginalPhillips Curve

The Expectations-AugmentedPhillips Curve

The NAIRU

Wage Indexation

Conclusion

Excursion: Wage IndexationMotivation

I If inflation is increasing fast, wage setters have aninterest to negotiate nominal wages more frequently

I An alternative would be wage indexation, i.e. aprovision that automatically increases wages in line withinflation

I In what follows, we analyse the hypothesis that wageindexation leads to a stronger response of inflation tounemployment

I Consider an economy that has two types of labourcontracts: a proportion λ, with λ ∈ (0, 1), of contractsis indexed while a proportion (1− λ) is not

The Phillips Curve

Christina Zauner

Introduction

Derivation of thePhillips Curve fromthe AS Curve

The OriginalPhillips Curve

The Expectations-AugmentedPhillips Curve

The NAIRU

Wage Indexation

Conclusion

Excursion: Wage IndexationImplications

I Nominal wages of the indexed contracts move one forone with variations in the actual price level

I The nominal wages of the contracts which are notindexed are set on the basis that inflation will be equalto last periods inflation

I Under these assumptions expected inflation is aweighted average: πe

t = λπt + (1− λ)πt−1

I Therefore condition (4) can be written as

πt = [λπt + (1− λ)πt−1]− α(ut − un)

The Phillips Curve

Christina Zauner

Introduction

Derivation of thePhillips Curve fromthe AS Curve

The OriginalPhillips Curve

The Expectations-AugmentedPhillips Curve

The NAIRU

Wage Indexation

Conclusion

Excursion: Wage IndexationImplications

I Rewriting yields

πt − πt−1 = −α(

1

1− λ

)(ut − un) (6)

I Note that 1/(1− λ) > 1 and that this factor isincreasing in λ, implying that the higher the proportionof indexed contracts the higher the effect ofunemployment (represented by α) on inflation

The Phillips Curve

Christina Zauner

Introduction

Derivation of thePhillips Curve fromthe AS Curve

The OriginalPhillips Curve

The Expectations-AugmentedPhillips Curve

The NAIRU

Wage Indexation

Conclusion

Excursion: Wage IndexationIntuitive Explanation

The intuition behind (6) is straight forward:

I Without wage indexation, lower unemploymentincreases wages which in turn leads to higher prices;since wages do not respond to prices right away, there isno further increase in prices

I With wage indexation, an increase in prices (due tolower unemployment and a subsequent rise in wages)leads to an automatic increase in wages and thus tofurther price increases etc.

I The larger the fraction of indexed contracts (λ), thestronger is the second effect

The Phillips Curve

Christina Zauner

Introduction

Derivation of thePhillips Curve fromthe AS Curve

The OriginalPhillips Curve

The Expectations-AugmentedPhillips Curve

The NAIRU

Wage Indexation

Conclusion

Conclusion

I The AS Curve can be reformulated to yield a relationbetween the change in the rate of inflation and thedeviation of the unemployment rate from its naturallevel

I The natural rate of unemployment depends on thestructural parameters µ and z as well as on the responseof inflation to unemployment (represented by α)

I These parameters differ among countries and thereforedifferent countries will have different natural rates ofunemployment