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Lecture 2: Frictional unemployment

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Lecture 2: Frictional unemployment

I. The matching function

- We have seen foundations for « classical unemployment »
- Frictional unemployment arises from continuous reallocation of workers between jobs
- In the models we have seen, unemployment would fall to zero absent the rigidities
- We need to enrich these models

- What fraction of average unemployment is frictional?
- Does frictional unemployment play a useful social role?
- If so, what is the efficient level of unemployment?
- How is frictional unemployment affected by growth, creative destruction, etc…?
- Does the frictional component fluctuate?

- Costly process of allocation unemployed workers to vacant positions
- The matching function is the production function for the flow of new hires
- The inputs are:
- The stock of unemployed workers looking for jobs
- The stock of vacant jobs looking for workers

- It is assumed to have the properties of a production function:
- Constant returns to scale
- Increasing in its arguments
- Concave

v

du/dt = 0

u

- Steady state relationship between u and v
- Downward sloping
- Convex
- The analysis can also be made in the (u,θ) plane where θ = v/u

θ

du/dt = 0

u

θ

du/dt = 0

u

- The θ falls when
- c goes up
- r goes up
- φ goes up
- y goes down

- In steady state, this is associated with moves along the Beveridge curve

θ

E

E’

u

v

E

E’

u

- We model it as an increase in s
- The Beveridge curve shifts out (why?)
- The labor demand curve shifts down
- An increase in s is also a negative labor demand shock (why?)

θ

E

E’

u

v

E

E’

u

- The Beveridge curve shifts out again
- No effect of labor demand
- Contrary to a (pure) reallocation shock, labor flows fall

- We can approximmate them by repeated switches between two values of y
- They lead to loops around the Beveridge curve
- Vacancies « lead » the cycle
- Unemployment lags the cycle

v

u

- The model can be used to have heterogeneous search intensity among the unemployed
- LTU: lower search intensity than STU
- And fraction of LTU larger after recessions
- the Beveridge curve deteriorates
- Persistent effects of transitory shocks