The Phillips curve
• In last week’s lecture, we brought the labour
market equations into the IS-LM framework and
derived the aggregate supply-aggregate
demand framework. The advantage of AS-AD
over IS-LM is that you can use the AS-AD to talk
about prices and unemployment.
• A.W. Phillips (a NZ raised in Australia) found a
negative relation between inflation and
unemployment in the United Kingdom on data
from the previous century.
Phillips curve in Australia 1960s
6
Inflation rate (percent)
5
1967
4
1969
1964
1968
3
1960
1966
1961
1965
2
1963
1
1962
0
1.0
1.5
2.0
2.5
Unemployment rate (percent)
3.0
3.5
Moving from prices to inflation
• Our labour market equations were in price
levels, where here we would like to talk in
terms of inflation. Can we put our labour
market equations in terms of inflation?
• Our labour market equilibrium equation:
P = Pe (1 + μ ) F(u, z)
• The we “linearize” F(.) by setting:
F (u, z) = 1 – α u + z
Moving from prices to inflation
• So we get:
P = Pe (1 + μ ) (1 – α u + z)
• This can be rewritten in inflation (π)and
expected inflation (πe) as:
π = πe + (μ + z) - α u
• The derivation is in the appendix for
Chapter 8 and is NOT required to know.
Simply know that this is only true for “low”
levels of inflation.
The new labour market equation
• Our new labour-market equilibrium
condition is:
π = πe + (μ + z) - α u
– A rise in expected inflation increases current
inflation one-for-one.
– A rise in unemployment lowers inflation by the
amount α.
– A rise in the mark-up increases inflation, as do
factors, z, that increase the wage-setting term,
F(u, z).
Policy implications
• If this new relation between inflation and
unemployment is true, it means that
governments had a tool to control inflation.
• If governments were willing to raise inflation,
they would achieve a lower level of
unemployment.
• Governments could permanently drive
unemployment below the “natural rate of
unemployment” by permanently raising inflation.
Policy implications
• There is an “inflation-unemployment tradeoff”. Governments could “choose” an
optimal inflation-unemployment mix along
the Phillips curve that best suited them.
• Labor governments might choose a tradeoff with lower unemployment. Liberal
governments might choose a trade-off with
lower inflation.
Inflation
Phillips curve break-down
18
16
14
12
10
8
6
4
2
0
-2 0
1977
1983
1993
1970
2
4
6
Unemployment
8
2003
10
12
What caused the breakdown?
• The governments assumed that the expected
inflation rate, πe, didn’t change.
• But the Phillips curve relationship:
π = πe + (μ + z) - α u
• The y-intercept is πe + (μ + z) and the slope is –
α. So any change in πe shifts the Phillips curve
relation out.
• Governments in the 1970s assumed that the
Phillips curve didn’t move. They were obviously
wrong.
Inflation expectations
• So the Phillips curve depends crucially on
how people form expectations of inflation.
• Let’s say that inflationary expectations are
slow to adjust, so:
πte = θπt-1
• The we can make this substitution into the
Phillips curve equation:
πt = θπt-1 + (μ + z) - α ut
Expectations
πt = θπt-1 + (μ + z) - α ut
• For θ = 0, we have a Phillips curve that
does not move. For θ = 1, we have the
relation:
πt - πt-1 = (μ + z) - α ut
• So the change in inflation depends on the
unemployment rate.
• We can also represent this equation in
terms of the natural rate of unemployment.
Natural rate of unemployment
• If inflation is equal to expected inflation, we are
at our “natural rate”, so we have:
π = πe + (μ + z) - α un
• But π = πe, so we can simplify to:
0 = (μ + z) - α un
α un = (μ + z) or un = (μ + z) / α
• Our natural rate of unemployment is:
– Higher the higher is the firm mark-up; and
– Lower the greater is the reaction of wage increases to
unemployment, α.
Natural rate of unemployment
• Substituting into our Phillips curve relation for θ
= 1, we get:
πt - πt-1 = α un - α ut = - α (ut – un)
• So if unemployment is lower than the natural
rate, inflation will increase by α.
• The way to lower inflation is to have
unemployment higher than the natural rate.
• The only way to keep inflation steady is to have
unemployment equal to the natural rate- the
non-accelerating rate of unemployment
(NAIRU).
Policy implications
• There is no permanent trade-off between
inflation and unemployment, as governments
assumed in the 1960s and 1970s.
• If the government tries to push unemployment
permanently below the natural rate, it will have
permanently rising inflation rates.
• This is what happened to governments in the
1970s. The Phillips curve kept shifting as
inflationary expectations rose.