Introduction to Macroeconomics: [1ex] The Phillips Curve [1ex] (based ...

Introduction to Macroeconomics: The Phillips Curve (based on Chapter 8 of the textbook by Olivier Blanchard)

Ulrich Gunter Department of Economics, University of Vienna

Summer Term 2011

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The Phillips Curve An Introduction

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

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He found a negative relation between ination and unemployment, suggesting that there may be a trade-o

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In the 1970s, the original relation broke down with many countries witnessing high ination AND high unemployment

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The purpose of this chapter is to derive the so-called Phillips curve and to study its modication in the last decades

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The Phillips Curve for the U.S.

Figure: Ination vs. Unemployment in the U.S. (OECD, 1959-1970) 3 / 24

Derivation of the Phillips Curve

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Recall that for the derivation of the AS relation we used the following equation, where A = 1

Pt = Pte (1 + µ)F (ut , z ) I

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(1)

We use the subscript t for time here, i.e. Pt stands for the price level at time t Assuming that F (ut , z ) = 1 − αut + z we get

Pt = Pte (1 + µ)(1 − αut + z )

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Derivation of the Phillips Curve I

By denition we have 1 + πt =

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Pe Pt and 1 + πte = t Pt −1 Pt −1

Dividing (1) by Pt −1 and using the above expressions we get 1 + πt = (1 + πte )(1 + µ)(1 − αut + z )

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

The left hand side, for small values of πt , πte and µ, suggests using the following propositions

(1 + πte )(1 + µ) ≈ [1 + (πte + µ)]

(1 + πt )/[1 + (πte + µ)] ≈ [1 + πt − (πte + µ)] 5 / 24

Ination, Expected Ination, and Unemployment

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Therefore we nally get

πt = πte + (µ + z ) − αut I

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(2)

Equation (2) states that higher expected ination leads to higher ination It also implies that given πte an increase in µ or z leads to higher ination On the other hand, given πte an increase in the unemployment rate ut leads to lower ination

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The Original Phillips Curve I

Imagine an economy with an average rate of ination equal to zero  not a plausible assumption nowadays, but it nearly held for the time period Phillips was analysing

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If average ination is equal to zero then it is reasonable to expect that ination will be zero in the future, i.e. πte = 0

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As a result, equation (2) becomes

πt = (µ + z ) − αut I

This is the negative relation between unemployment and ination that Phillips found for the UK, i.e. the original relation

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The Wage-Price Spiral I

The original Phillips curve states that lower unemployment leads to higher ination

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The mechanism behind this relation is captured by the so-called wage-price spiral: I low unemployment leads to higher nominal wages I I

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these higher costs of production prompt rms to increase prices because of the higher price level workers ask for higher nominal wages the next time wages are set the price level therefore increases again and workers will further ask for an increase in nominal wages the race between prices and wages results in a steady wage and price ination

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The Trade-O between Ination and Unemployment I

The original Phillips curve implies that if policy makers are willing to tolerate higher ination they can maintain any (low) unemployment rate

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Some economists, however, argued that an unemployment rate below the natural rate could not be sustained forever

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Their main argument was that a permanent trade-o between ination and unemployment could only exist if wage setters systematically underpredicted ination (but we know from the AS-AD model that systematically wrong price expectations of workers are unlikely in the medium run)

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The Modied Phillips Curve

Reasons for the Breakdown of the Original Relation I

The original relation between ination and unemployment broke down in most OECD countries around 1970 for two reasons

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First, the oil shocks in the 1970s lead to a large increase in the price of oil; consequently rms had to increase prices given unemployment (similar to an increasing µ in the AS relation)

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Second, and more importantly, the behaviour of ination changed: rather than being sometimes positive and sometimes negative, ination started to be consistently positive; furthermore ination became more persistent (high ination in one period likely to be followed by high ination in the next period) 10 / 24

The Breakdown of the Original Relation in the U.S.

Figure: Ination vs. Unemployment in the U.S. (OECD, 1970-2007) 11 / 24

Ination in the U.S.

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

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The Modied Phillips Curve Change in Formation of Expectations I

Expecting ination to be zero when in fact it has become consistently positive is not rational ⇒ workers changed the way they formed expectations

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Suppose workers expectations are formed as follows:

πte = θπt −1 I

The higher θ, the more last year's ination leads workers (and rms) to revise their expectations about present ination

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Relation (2) therefore becomes

πt = θπt −1 + (µ + z ) − αut

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The Modied Phillips Curve Derivation I

Before the 1970s, apparently θ = 0, i.e. since average ination was equal to zero it was rational to assume that the price level will not change πt = (µ + z ) − αut

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Afterwards, when ination 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 1970s θ = 1, i.e. people expect that ination this period is equal to ination last period (persistence)

πt = πt −1 + (µ + z ) − αut 14 / 24

The Modied Phillips Curve Implications I

Rewriting the last equation yields

πt − πt −1 = (µ + z ) − αut

(3)

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Thus, when θ = 1 then the unemployment rate does not aect the rate of ination but the change in the rate of ination

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Higher unemployment decreases the change in the rate of ination while lower unemployment increases the change in the rate of ination

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Equation (3) is called the modied Phillips curve or the

expectations-augmented Phillips curve

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The Modied Phillips Curve for the U.S.

Figure: Change in Ination/Unemployment (OECD, 1970-2007) 16 / 24

The Phillips Curve and the Natural Unemployment Rate Establishing the Relation

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Recall that the natural rate of unemployment is the unemployment rate at which the actual price level equals the expected price level Further note that Pt = Pte ⇔ πt = πte

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Thus, at the natural rate of unemployment ination equals expected ination

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This result, together with equation (2), implies that 0 = (µ + z ) − αun

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The Phillips Curve and the Natural Unemployment Rate Establishing the Relation I

Solving for the natural rate of unemployment yields

un = I

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µ+z α

Since equation (2) can also be written as   µ+z e πt − πt = −α ut − α we can substitute the expression for un from above to get

πt − πte = −α(ut − un )

(4)

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The Phillips Curve and the Natural Unemployment Rate I

If the expected rate of ination is well approximated by last periods ination then we nally get

πt − πt −1 = −α(ut − un ) I

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(5)

Equation (5) states that the change in ination depends on the dierence between the actual and the natural rate of unemployment When ut is higher (lower) than un , ination decreases (increases) From (5) we can also conclude that un is the unemployment rate required to keep ination constant ⇒ nonaccelerating ination rate of unemployment (NAIRU)

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Excursion: Wage Indexation Motivation I

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If ination is increasing fast, wage setters have an interest to negotiate nominal wages more frequently An alternative would be wage indexation, i.e. a provision that automatically increases wages in line with ination

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In what follows, we analyse the hypothesis that wage indexation leads to a stronger response of ination to unemployment

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

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Excursion: Wage Indexation Implications I

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

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The nominal wages of the contracts which are not indexed are set on the basis that ination will be equal to last periods ination

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Under these assumptions expected ination is a weighted average: πte = λπt + (1 − λ)πt −1

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Therefore condition (4) can be written as

πt = [λπt + (1 − λ)πt −1 ] − α(ut − un )

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Excursion: Wage Indexation Implications

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Rewriting yields

 πt − πt −1 = −α

1 1−λ



(ut − un )

(6)

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Note that 1/(1 − λ) > 1 and that this factor is increasing in λ, implying that the higher the proportion of indexed contracts the higher the eect of unemployment (represented by α) on ination

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Equation (6) therefore conrms our initial hypothesis about the implications of wage indexation

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Excursion: Wage Indexation Intuitive Explanation

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The intuition behind our result is straightforward

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Without wage indexation, lower unemployment increases wages which in turn leads to higher prices; since wages do not respond to prices right away, there is no further increase in prices

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

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Conclusion I

Equation (1) can be reformulated to yield a relation between the change in the rate of ination and the deviation of the unemployment rate from its natural level

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The natural rate of unemployment depends on the structural parameters µ and z as well as on the response of ination to unemployment (represented by α)

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These parameters dier among countries and therefore they have dierent natural rates of unemployment

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Furthermore, and contrary to our initial assumption, these parameters change over time, implying that the natural rate of unemployment changes over time

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