lecture ii: constructing a theory of equilibrium unemployment microeconomic foundations of the wage...
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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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NLNL
NL
NL
wNL
NLw
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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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LwwNwLNwwLU
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)1(
0)()1()( :FOCs
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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
wLLAKV
LwwU
VUw
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:
))(1()(
))(1()()()(
)()()()()(
))(/()1()(
)())()()(()(
)())()(()()(
tuNtL
tustuthtu
tJtsJtwtmtrJ
tLKAtm
tVtVtVthwtrV
tVtVtVstwtrV
uueu
eeue
Wage formation
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FJVV
FtJtVtV
ue
ue
ue
uetw
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
Fu
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
))(1()(
))(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