The Phillips curve, the NAIRU and the role of

expectations

The Phillips curveThe NAIRU

Expectations

The Phillips curve

Is a central empirical result that identifies a trade-off between the rate of unemployment 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)

The Phillips curve

From WS-PS to the Phillips curve

The natural rate of unemployment revisited

The role of expectations

The Phillips curve: an empirical relation

The Phillips curve: an empirical relation

The Phillips curve is an empirical relation between unemployment and the rate of inflation discovered by William Phillips in 1958 It shows a negative relation between

unemployment and inflation It can be derived by analysing deviations from

equilibrium in the WS-PS model

Its general form is:

shocksupply ntunemployme cyclicalinflation expectedinflation

vuu ne

The Phillips curve: an empirical relation

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Phillips curve for France

The Phillips curve: an empirical relation

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Phillips curve for Italy

The Phillips curve: an empirical relation

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Phillips curve for Japan

The Phillips curve: an empirical relation

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Phillips curve for the USA

The Phillips curve

From WS-PS to the Phillips curve

The natural rate of unemployment revisited

The role of expectations

The Phillips curve: an empirical relation

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 market conditions

PS : prices are a function of wages rate and the mark-up rate

The structural rate of unemployment can be found by setting P=P e. It is the rate of unemployment when expectations are fulfilled.

WP 1

zuFPW e ,

zuF n ,1

1

From WS-PS to the Phillips curve

Structural rate of unemployment un (long run)

zuF n ,1

1

A

un

WS

PS

Real Wage P

W

Unemployment rate u

1

1

But in the short run we do not necessarily have P=P e

For example, imagine that some unexpected inflation occurs, so that P≠P e

What will unemployment u be compared to un?

Replacing WS in PS (eliminating W) gives the following One can see that if P=P e one recovers the equation for

un

WP

zuFPW e

1 : PS

, :WS

e

P 1F u,z

P 1

From WS-PS to the Phillips curve

From WS-PS to the Phillips curve

We now have two WS-PS equations:

zuFP

Pe

,1

1

A short run equation

By subtracting one from the other, we get a relation between deviations from equilibrium

The long run equilibrium equation

zuF n ,1

1

zuFzuFP

Pne,,

1

1

1

1

zuFzuFP

Pne,,

1

11

zuFzuFP

PPne

e

,,1

From WS-PS to the Phillips curve

This gives a theoretical underpinning to the Phillips curve (remember that F is a negative function of u)

Actual inflation Π is a function of: Expected inflation π e Cyclical unemployment (u-u n) Shocks on supply v

zuFzuFP

PPne

e

,,1

vuu ne

inflation rate π

Unemployment rate u

β

un

Πe + v

The inverse of the slope of the Phillips curve is called the sacrifice ratio (1/β),

This is how much extra unemployment you have to accept in order to reduce inflation by 1 percentage point

1

vuu ne

From WS-PS to the Phillips curve

inflation rate π

Unemployment rate uun

Πe + v

Πe’ + 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

The Phillips curve

From WS-PS to the Phillips curve

The natural rate of unemployment revisited

The role of expectations

The Phillips curve: an empirical relation

The NAIRU

Disregarding random shocks, what happens if when we are at the natural rate of unemployment, u =un ? The actual rate of inflation equals the expected rate

of inflation π =π 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?

shocksupply ntunemployme cyclicalinflation expectedinflation

vuu ne

We have to specify the inflation expectations ! i.e. Make an assumption on how expectations are

formed. First, we introduce time indices:

One of the simplest forms is adaptive expectations:

The Phillips curve becomes:

1 tet

tn

tett vuu

tn

ttt vuu 1

tn

tt vuu

The NAIRU

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

tn

tt vuu

The NAIRU

ut < un ut > un

Acceleration of the inflation rate

Δπ

Unemployment rate u

0

un

tn

tt vuu

The NAIRU

The NAIRU

So the “natural” rate of unemployment identified previously also has an interpretation in terms of inflation As for the previous case, calling it “natural”

suggests it is fixed. In fact, the “natural” rate is endogenous 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!

The Phillips curve

From WS-PS to the Phillips curve

The natural rate of unemployment revisited

The role of expectations

The Phillips curve: an empirical relation

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 during the 60’s and 70’s): In particular, how do agents determine expected inflation? The debate centres on the following question : Should one

focus on trying to explain correctly the mechanism that generates these expectations, or should one just try to find a “method” that produces the correct answer?

tn

tett vuu

The historical starting point is the assumption of adaptive expectations: 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 the NAIRU

However, this can generate very strange predictions, with very “dumb” behaviour from agents (exercise on this for next week)

The role of expectations

1et t

tn

ttt vuu 1

tn

tt vuu

In order to avoid these problems, neoclassical economists (Lucas, Sargent, Wallace, etc.) introduced rational expectations:

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 ε is a random error

The Phillips curve becomes :

In this version, the Phillips curve is vertical : there is no trade-off between inflation and unemployment!

The role of expectations

tn

tttt vuu

ttnt

vuu

ttttet E 1

The rational expectations assumption attempts to address the main problem that comes with adaptive expectations: the systematic errors of agents

with , εt being a random variable

The role of expectations

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Inflation

Expectedinflation

Agents make mistakes in their predictions in the short run

They are not “omniscient”

In the long run, they do not make any systematic errors, and predict correctly the average level of inflation

Agents are rational and correct their mistakes

ttet

It is important to point out that these two approaches have different objectives, 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 expectations

are reached : in reality, how do badly-informed agents manage to guess the right solution?

“Black box” : The mechanism exists, but is not revealed…

The role of expectations

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