Lecture 2: Frictional unemployment

I. The matching function

Frictional unemployment

• 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

Questions we want to ask

• 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?

The matching function

• 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

Hirings per unit of time

),( ttt VUmH • It is assumed to have the properties of a

production function:– Constant returns to scale– Increasing in its arguments– Concave

The dynamics of unemployment

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The Beveridge curve

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Properties of the Beveridge Curbve

• 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

The Beveridge curve

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θ

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Closing the model: labor demand

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The equilibrium trajectory:

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Labor demand shocks

• 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

A fall in labor demand:

u

θ

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In (u,v):

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Reallocation shocks

• 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?)

An increase in s:

u

θ

E

E’

In (u,v):

u

v

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E’

A deterioration in the matching process

• The Beveridge curve shifts out again

• No effect of labor demand

• Contrary to a (pure) reallocation shock, labor flows fall

Business cycles

• 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

The Loop:

u

v

Long-term unemployment

• 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

How do we do it?

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