LECTURE 7
UNEMPLOYMENT
Last part of the classical theory (long term perspective). We assume labour input is exogenously given; it
depends on demographics. It also depends on the long-term average of the unemployment rate → we call that
the natural unemployment rate.
A model for the natural unemployment rate
The natural unemployment rate (𝑢𝑛 ) is the unemployment rate towards which the economy gravitates in the
long run.
US ≈ 5 − 6%
EMU ≈ 8 − 10% from 1980s onwards; EMU ≈ 2 − 3% until mid 1970s
Japan ≈ 4% since turn of the century; Japan ≈ 2% until beginning 1990s
We assume:
• Labour force is exogenously given: 𝐿𝑡 = 𝐿
𝐿𝑡 = 𝐸𝑡 + 𝑈𝑡
• Every period a fraction 𝑠 (= the job separation rate) of the employed lose their job
• Every period a fraction 𝑓 (= the job finding rate) of the unemployed find a job
• We assume that in the long run 𝑠 and 𝑓 remain constant over time
The change in the number of unemployed is then equal to:
△ 𝑈𝑡+1 = 𝑠 ∙ 𝐸𝑡 − 𝑓 ∙ 𝑈𝑡 = 𝑠 ∙ (𝐿 − 𝑈𝑡 ) − 𝑓 ∙ 𝑈𝑡 = 𝑠 ∙ 𝐿 − (𝑠 + 𝑓) ∙ 𝑈𝑡
The change in the unemployment rate is then equal to:
𝑠
△ 𝑢𝑡+1 = 𝑠 − (𝑠 + 𝑓) ∙ 𝑢𝑡 = (𝑠 + 𝑓) ∙ ( − 𝑢𝑡 )
𝑠+𝑓
𝑠
If the unemployment rate is equal to 𝑠+𝑓 then the change of the unemployment rate will be zero, thus will
remain constant over time. Therefore, that is going to be the natural unemployment rate. In the long run, 𝑢
𝑠
converges to 𝑠+𝑓.
𝑠
𝑢𝑡 < ⇔ △ 𝑢𝑡+1 > 0
𝑠+𝑓
𝑠
𝑢𝑡 = ⇔ △ 𝑢𝑡+1 = 0
𝑠+𝑓
𝑠
𝑢𝑡 > ⇔ △ 𝑢𝑡+1 < 0
𝑠+𝑓
𝑠
The natural unemployment rate (𝑢𝑛 ) is equal to 𝑠+𝑓 and in the long run 𝑢 converges to 𝑢𝑛 .
This is a useful framework to think about the labour market, but it is often insufficient for policy
analysis/predictions:
• Suppose that the government want to have stricter employment protection registration (more difficult for
firms to fire people) → the job separation rate will be less, at the same time: firms will be inclined to hire
𝑠
less people, so 𝑓 declines too → we don’t know what happens to 𝑢𝑛 = 𝑠+𝑓 in this case.
• Suppose that there is a lot of technological progress → lots of new jobs will be created → 𝑓 increases,
however: lots of existing jobs will be destroyed (= creative destruction), so 𝑠 increases too → we don’t
𝑠
know what happens to 𝑢𝑛 = 𝑠+𝑓 in this case.
There is not convincing empirical evidence of what happens with the unemployment rate in neither direction in
both cases. Be extremely careful with the labour market analysis!
Frictional unemployment
Frictional unemployment = the unemployment that we have because of the simple facts that searching for a
job or an employee takes time, because of preferences and skills. It takes a while for a person and a job
vacancy to match.
UNEMPLOYMENT
Last part of the classical theory (long term perspective). We assume labour input is exogenously given; it
depends on demographics. It also depends on the long-term average of the unemployment rate → we call that
the natural unemployment rate.
A model for the natural unemployment rate
The natural unemployment rate (𝑢𝑛 ) is the unemployment rate towards which the economy gravitates in the
long run.
US ≈ 5 − 6%
EMU ≈ 8 − 10% from 1980s onwards; EMU ≈ 2 − 3% until mid 1970s
Japan ≈ 4% since turn of the century; Japan ≈ 2% until beginning 1990s
We assume:
• Labour force is exogenously given: 𝐿𝑡 = 𝐿
𝐿𝑡 = 𝐸𝑡 + 𝑈𝑡
• Every period a fraction 𝑠 (= the job separation rate) of the employed lose their job
• Every period a fraction 𝑓 (= the job finding rate) of the unemployed find a job
• We assume that in the long run 𝑠 and 𝑓 remain constant over time
The change in the number of unemployed is then equal to:
△ 𝑈𝑡+1 = 𝑠 ∙ 𝐸𝑡 − 𝑓 ∙ 𝑈𝑡 = 𝑠 ∙ (𝐿 − 𝑈𝑡 ) − 𝑓 ∙ 𝑈𝑡 = 𝑠 ∙ 𝐿 − (𝑠 + 𝑓) ∙ 𝑈𝑡
The change in the unemployment rate is then equal to:
𝑠
△ 𝑢𝑡+1 = 𝑠 − (𝑠 + 𝑓) ∙ 𝑢𝑡 = (𝑠 + 𝑓) ∙ ( − 𝑢𝑡 )
𝑠+𝑓
𝑠
If the unemployment rate is equal to 𝑠+𝑓 then the change of the unemployment rate will be zero, thus will
remain constant over time. Therefore, that is going to be the natural unemployment rate. In the long run, 𝑢
𝑠
converges to 𝑠+𝑓.
𝑠
𝑢𝑡 < ⇔ △ 𝑢𝑡+1 > 0
𝑠+𝑓
𝑠
𝑢𝑡 = ⇔ △ 𝑢𝑡+1 = 0
𝑠+𝑓
𝑠
𝑢𝑡 > ⇔ △ 𝑢𝑡+1 < 0
𝑠+𝑓
𝑠
The natural unemployment rate (𝑢𝑛 ) is equal to 𝑠+𝑓 and in the long run 𝑢 converges to 𝑢𝑛 .
This is a useful framework to think about the labour market, but it is often insufficient for policy
analysis/predictions:
• Suppose that the government want to have stricter employment protection registration (more difficult for
firms to fire people) → the job separation rate will be less, at the same time: firms will be inclined to hire
𝑠
less people, so 𝑓 declines too → we don’t know what happens to 𝑢𝑛 = 𝑠+𝑓 in this case.
• Suppose that there is a lot of technological progress → lots of new jobs will be created → 𝑓 increases,
however: lots of existing jobs will be destroyed (= creative destruction), so 𝑠 increases too → we don’t
𝑠
know what happens to 𝑢𝑛 = 𝑠+𝑓 in this case.
There is not convincing empirical evidence of what happens with the unemployment rate in neither direction in
both cases. Be extremely careful with the labour market analysis!
Frictional unemployment
Frictional unemployment = the unemployment that we have because of the simple facts that searching for a
job or an employee takes time, because of preferences and skills. It takes a while for a person and a job
vacancy to match.
