Lecture 2 frictional unemployment
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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

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Lecture 2: Frictional unemployment

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Lecture 2 frictional unemployment

Lecture 2: Frictional unemployment

I. The matching function


Frictional unemployment

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

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

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

Hirings per unit of time

  • It is assumed to have the properties of a production function:

    • Constant returns to scale

    • Increasing in its arguments

    • Concave


The dynamics of unemployment

The dynamics of unemployment


The beveridge curve

The Beveridge curve

v

du/dt = 0

u


Properties of the beveridge curbve

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 curve1

The Beveridge curve

θ

du/dt = 0

u


Closing the model labor demand

Closing the model: labor demand


Closing the model posting vacancies

Closing the model: posting vacancies


The equilibrium value of

The equilibrium value of θ


The equilibrium trajectory

The equilibrium trajectory:

θ

du/dt = 0

u


Labor demand shocks

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

A fall in labor demand:

θ

E

E’

u


In u v

In (u,v):

v

E

E’

u


Reallocation shocks

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

An increase in s:

θ

E

E’

u


In u v1

In (u,v):

v

E

E’

u


A deterioration in the matching process

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

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

The Loop:

v

u


Long term unemployment

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

How do we do it?


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