Lecture 2: Frictional unemployment II. Efficiency.

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Lecture 2: Frictional unemployment II. Efficiency

Can unemployment be efficient In efficiency wage models and I/O models, unemployment is inefficient –We want to reduce the insider bargaining power –We want to make contracts complete to eliminate rents In matching models, unemployment is a productive input into the creation of new jobs

Too much or too little unemployment? To have a low unemployment rate, vacancies must be high But vacancies consume resources  we can have too many vacancies On the other hand, the unemployed are also costly because they do not produce  we can have too much unemployment

Congestion externalities An increase in search exerts positive externalities on the other side of the market –Unemployment reduces the length of vacancies; vacancies reduce the length of unemployment Because m() is concave, negative externality on the same side of the market –More unemployment reduces job finding rate

Appropriability As in the I/O model, a surplus arises from turnover costs Part of the surplus is appropriated by the worker  the firm only appropriates a fraction of the surplus created by a vacancy Symmetrical problem on the worker’s side on evaluating the value of being unemployed: only a fraction of the value of future jobs will be appropriated

What to do next? Have a more complex wage formation model, borrowed from the dynamic I/O model Derive equilibrium conditions Set up a dynamic welfare maximization problem Compare its optimality conditions to the equilibrium conditions

The wage bargaining problem

How is θ determined?

The evolution of θ:

The welfare problem

The F.O.C:

Comparing equilibrium and optimum (b=0)

The congestion externality The benefit of a vacancy: –The SP looks at its marginal effect on job creation –The firm looks at the average probability of filling the vacancy Future jobs: –The match looks at the opportunity cost of foregone future other jobs, driven by average job finding probability –The SP looks at the marginal effect of an extra unemployed on job creation

The appropriability problem The benefit of a vacancy: –The SP looks at the whole value of the jobs λ –The firm only expects a fraction 1-φ of W Future foregone jobs: –The SP values their whole social value λ –The match considers that it loses only the worker’s share φ W

When is the equilibrium efficient? Congestion externalities  private transition rates > marginal effects on hirings  too much unemployment and vacancies Appropriability problem  firms and workers only appropriate a fraction of their job search effort  not enough unemployment and vacancies If these two effects cancelled each other, equilibrium would be efficient

Assume eqm θ is efficient:

The Hosios Condition:

Inefficient unemployment Because of congestion externalities and appropriability problems, the equilibrium is generally inefficient Unemployment is inefficiently low iff

What is going on? Little incentive to look for another job as I appropriate little of the surplus But unemployment is useful in creating new jobs: –Vacancy costs would be reduced This effect is sizable as η u is large

What is the market failure? Congestion externalities could be avoided if there was a price for entering the job search pool Appropriability could be avoided if wages could be contracted ex-ante Moen (1995) develops a « Club Theory » approach of matching and shows the outcome is efficient

Example 1: The Pond

Introduce N clubs

Example 2: The hold-up problem

Competitive search equilibrium: Firms and workers must join club to match Each club characterized by –Its local tightness θ –Its local wage w(θ) In CSE: –Workers choose their club optimally –Each nonempty club yields zero value to firms

The firms’ participation decision

The worker’s choice of a club