Lecture II: Constructing a theory of equilibrium unemployment Microeconomic foundations of the wage...

Lecture II: Constructing a theory of equilibrium unemployment

Microeconomic foundations of the wage curve

How are wages set?

• Wages can be thought of as the sum of three terms:– A compensation for the disutility of labor– An outside option which determines what the

worker would get outsidr the employment relationship (alternative wage = OC of labor)

– A rent which tells us how much he can grab beyond that

When is unemployment involuntary?

• If the employed are better-off than the unemployed, the latter would prefer to be employed

• Therefore, involuntary unemployment rent = 0

• Does that mean we are at the Walrasian equilibrium?

What is a Walrasian equilibrium?

• WE holds if outside option = flow of utility corresponding to a zero wage

• But Unemployment Benefits and Welfare Minima can raise OO above that level

• Unemployment is then voluntary but above the walrasian level

Do we need rents in the model?

• Assume no rent

• For h(u) to be downward sloping, unemployment must negatively affect the outside option

• This cannot be true if the employed are no better-off than the unemployed

• We thus have a flat h(u) curve and are back to the wage floor model

Three classes of models:

• Collective bargaining models rents come from the union’s monopoly on jobs

• Individual barganing models rents come from turnover costs

• Efficiency wage models rents come from informational issues + incomplete contracting

Collective bargaining models

• There are three of them:– Monopoly Union– Efficient Bargaining– Right-to-Manage

Monopoly Union

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1

)1()1(

1)1( s.t.

)(max

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u

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ww

wL

KAw

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What is going on?

• The union maximizes the total expected income of members

• It takes the LD curve as given• Wages = markup on OC of labor• Markup inversely related to elasticity• OC of labor reflects job finding prospects

goes down with u• If UB indexed on wages, natural rate only

depends on replacement ratio and elasticity

Membership effects

• Note that union membership N has no impact on the outcome

• We can get membershif effects by introducing nonlinearities

• Example: unions maximize the median members’ expected income

• His employment probability is nonlinear in L/N

Getting membership effects:

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')/(

)/(

)/()1( s.t.

))/(1()/(max

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NL

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Comments:

• If elasticity of φ falls, then lower membership => higher wages and more unemployment

• If membership depends on past employment => persistence mechanism

• Membership rules matter (encompassing unions vs. Guilds)

Efficient Bargaining

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LV

LU

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1

,

Comments:

• Employment is determined at the privately efficient level from the match’s point of view

• Absent institutional rigidities, employment would be at its walrasian level

• Wage bargaining only affects the way the surplus is split wages are a pure transfer, the true allocative price is the OCL

Right-to-manage:

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ww

VU

ww

L

KAw

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LwwU

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001

1

)1(1

)1(

)(

max

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Comments

• Generalization of monopoly union model

• Generates suboptimal employment

• The rent now depends on the workers’ bargaining power in addition to the elasticity of labor demand

Individual bargaining

• In collective models, the firms cannot hire workers competitively at the margin

• Nor can other firms in the same sector do so

• Under individual bargaining, the firm could drive the surplus of the match to zero by simply hiring more people

• Turnover costs are needed to create a positive surplus

The dynamic insider/outsider model

• A representative firm can hire as much as it wants from the pool of unemployed

• Once hired, people negotiate their wage

• The firms incurs a cost F upon separation due to disagreement

The plumbing:

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))(1()()()(

)()()()()(

))(/()1()(

)())()()(()(

)())()(()()(

tuNtL

tustuthtu

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tLKAtm

tVtVtVthwtrV

tVtVtVstwtrV

uueu

eeue

Wage formation

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ue

ue

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10

)(1

1 FOC

))()(ln()1())()(ln(max)(

The hold-up problem:

• The intertemporal rent is fixed

• It goes up with the turnover cost

• It goes up with the worker’s bargaining power

• The turnover cost is a specific investment which can be appropriated by the incumbent worker

• F could equivalently be a hiring cost

Deriving the steady state wage schedule

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srbw

sh

su

bwFhsrVVhsr ue

1)(

1)())((

Wage pressure goes up with

• Turnover costs

• Insider bargaining power

• Unemployment benefits

• Turnover

• Real interest rates

The shirking model

• Employee effort e imperfectly observable (flow probability q)

• Penalty upon shirking limited to dismissal• In equilibrium, employees must be paid

rents• Otherwise, no penalty from dismissal: a

job is found instantaneously• Thus, unemployment duration acts as a

discipline device

Same plumbing as the insider model

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))(1()()()(

)()()()()(

))(/()1()(

)())()()(()(

)())()(()()(

tuNtL

tustuthtu

tJtsJtwtmtrJ

tLKAtm

tVtVtVthbtrV

tVtVtVsetwtrV

uueu

eeue

Deterring shirking:

q

e

u

srbew

q

eVV

tVtV

tVtVtVqstwtrV

tVtVtVsetwtrV

ue

Se

SueS

eeue

)(

binding )()(

)())()()(()()(

)())()(()()(

Comments:

• The model is equivalent to I-O model

• Just replace rent by e/q

• Rent now depends on effort levels and on the monitoring probability

• Effects of s and r are the same