1. The Phillips curve, the NAIRU and the role of expectations

2. 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)

3. The Phillips curve The Phillips curve: an empirical relation
From WS-PS to the Phillips curve
The natural rate of unemployment revisited
The role of expectations

4. 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:

5. The Phillips curve: an empirical relation
Phillips curve for France

6. The Phillips curve: an empirical relation
Phillips curve for Italy

7. The Phillips curve: an empirical relation
Phillips curve for Japan

8. The Phillips curve: an empirical relation
Phillips curve for the USA

9. The Phillips curve The Phillips curve: an empirical relation
From WS-PS to the Phillips curve
The natural rate of unemployment revisited
The role of expectations

10. 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.

11. From WS-PS to the Phillips curve
Structural rate of unemployment un (long run)
Real Wage A un WS PS
Unemployment rate u

12. From WS-PS to the Phillips curve
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

13. From WS-PS to the Phillips curve
We now have two WS-PS equations:
A short run equation
The long run equilibrium equation
By subtracting one from the other, we get a relation between deviations from equilibrium

14. 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

15. From WS-PS to the Phillips curve
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
inflation rate π
Unemployment rate u β 1 un
Πe + v

16. From WS-PS to the Phillips curve
inflation rate π
Unemployment rate u
2. …Shifts the Phillips curve upwards
3. This explains the “fuzzy” curves in the 1st section:
Inflation expectations were changing at the same time!
Πe’ + v
1. An increase in inflation expectations by agents… un
Πe + v

17. The Phillips curve The Phillips curve: an empirical relation
From WS-PS to the Phillips curve
The natural rate of unemployment revisited
The role of expectations

18. 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?

19. The NAIRU 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:

20. The NAIRU
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
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).

21. Acceleration of the inflation rate Δπ
The NAIRU
Acceleration of the inflation rate Δπ
ut < un
ut > un un
Unemployment rate u

22. 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!

23. The Phillips curve The Phillips curve: an empirical relation
From WS-PS to the Phillips curve
The natural rate of unemployment revisited
The role of expectations

24. 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?

25. The role of expectations
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)

26. The role of expectations
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!

27. The role of expectations
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
Agents make mistakes in their predictions in the short run
They are not “omniscient”
Expectedinflation
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
Inflation

28. The role of expectations
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…