MARCUS DITTRICH
Wage and employment effects
of non-binding minimum wages
Marcus Dittrich
TU Chemnitz & CESifo
Andreas Knabe
FU Berlin & CESifo
Social Choice and Welfare
Moscow, July 2010
MARCUS DITTRICH
MOTIVATION
• “The effects of the minimum wage on employment and the
distribution of income have been hotly debated policy
question for over 50 years.“ (Brown 1999)
•
– Pro: raising the wages of the lowest-paid would help
fighting poverty
– Contra: introducing such rigidities impedes allocative
role of flexible wages, causing more unemployment and
possibly even more poverty
One issue that most proponents and opponents agree on:
MW have to be binding to have any effect!
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MARCUS DITTRICH
MOTIVATION: SPILLOVER EFFECTS OF MW
•
•
But: Many studies report that raising the MW has spillover
effects (Katz/Krueger 1992, ILLR; Manning 2003, Neumark
et al. 2004, JHR).
Two important stylized facts:
1. Firms raise the wages of workers that used to earn less
than the new MW above the minimum level required.
2. Workers already earning wages above the new MW
receive wage raises as well.
• Possible explanation: Employers attempt to maintain their
internal wage hierarchy.
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MOTIVATION: SPILLOVER EFFECTS OF MW
Experimental evidence (Falk et al. 2006, QJE)
• excludes wage hierarchy effects or effort considerations
• similar to “ultimatum game”
• firm proposes a wage
• worker sets reservation wage
match if firm‘s offer ≥ res. wage
• main finding: introduction of MW increases wages above
the new minimum, because it drives up reservation wages
• Potential explanation: MW affects what people consider to
be a ”fair” compensation for their work.
• How can these findings be explained by theoretical models?
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OUTLINE
1. Motivation: spillover effects of MW
2. Model economy
3. Nash wage bargaining
4. Kalai-Smorodinsky wage bargaining
5. Conclusion
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MODEL ECONOMY
• economy with large number of sectors
• bargaining over wages (w ) between unions and firms
• representative firm’s profit: 1
 w  1
  w   L  wL  L   

• representative union’s utility:
V  w   wL   N  L  w0 , with L  N
• alternative income:
w0  ub  1  u  w
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NASH WAGE BARGAINING
Nash bargaining solution follows from four axioms (Nash 1950,
Econometrica):
1. Pareto efficiency
2. Invariance to equivalent utility representations
3. Symmetry
4. Independence of irrelevant alternatives
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NASH WAGE BARGAINING
• Nash bargaining solution:
max(v1  d1 )  (v2  d2 )
v1 ,v2 S
where vi = player i ’s utility, d i = conflict utility, S =
utility possibility set
• applied to wage bargaining problem:
max   V  w   V0     w 
w
 w
s.t. L   

1
1
 1  
 w Nash  w0  

 2 
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NASH WAGE BARGAINING
V
V(wmon)
A
V(())
V0
L(w)=N

(wmon)
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NASH WAGE BARGAINING
V
A
V(wNash )
B
const.
C
V0
(wNash )

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NASH WAGE BARGAINING
What do non-binding MW do?
1. sectoral level
• wmin  w Nash
• w0 exogenous
 Sectoral MW has no effect on bargained wage.
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NASH WAGE BARGAINING
V
A
V(wNash )
B
const.
C
V0
min
(wNash ) (w )

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NASH WAGE BARGAINING
What do non-binding MW do?
1. sectoral level
• wmin  w Nash
• w0 exogenous
 Sectoral MW has no effect on bargained wage if it is
non-binding.
2. national level
• wmin  wiNash i  no change in any wages
• hence, w0 unchanged
 National MW has no effect on bargained wage if it is
non-binding.
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KALAI-SMORODINSKY WAGE BARGAINING
• alternative axiomatic solution (Kalai/Smorodinsky 1975,
Econometrica)
• maintain first three axioms of Nash solution
• replaces IIA with “individual monotonicity” axiom
 a player must not suffer from an enlargement of the
bargaining set that leaves the maximum utility attainable
by the other player unchanged
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KALAI-SMORODINSKY WAGE BARGAINING
• both bargaining parties agree to a solution that equalizes
the relative utility gains ( ratio of the actual gains to
the maximum feasible gains)
• maximum feasible gain is determined by the payoff one
can secure by pushing the other party to the minimum
payoff it would just be willing to accept
• could be interpreted as “fairness” (McDonald / Solow
1981, AER)  if a player could have more (without
hurting the other player), he should have more
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KALAI-SMORODINSKY WAGE BARGAINING
• general KS solution: both parties make equal
proportional concessions from their respective favored
points  KS curve:
v1  d1 v2  d 2
 *
*
v1  d1 v2  d 2
• applied to wage bargaining problem:
v1  V (w), d1  V0
v2  ( w), d 2  0
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KALAI-SMORODINSKY WAGE BARGAINING
• “utopia points”:
v1*  arg max V ( w) s.t.   0
w
v  arg max ( w) s.t. V  V0
*
2
w
• bargained wage:
L( w)  w  w0 
L( w)  wL  w 


mon
mon
L( w )  w  w0  L( w0 )  w0 L  w0 
w0
KS
 w 
 1
1  1      
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KALAI-SMORODINSKY WAGE BARGAINING
V
V*
V(wKS)
utopia
point
A
D
C
V0
(wKS )
 (w0 )

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KALAI-SMORODINSKY WAGE BARGAINING
What do non-binding MW do?
• wmin  w0  change in utopia point:
v2*  arg max ( w) s.t. w  wmin  w0
w
• KS curve:
L( w)  w  w0 
L( w
mon
)  w
mon
 w0 
• bargained wage: w KS

L( w)  wL  w 
L( wmin )  wmin L  wmin 
w0

 1 
min
1  1      w w0 
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KALAI-SMORODINSKY WAGE BARGAINING
What do non-binding MW do?
1. sectoral level
• wmin  wKS , but wmin  w0
• w0 exogenous
• bargained wage raises to a level above the former wage
• implication: MW is non-binding, but effective!
 Sectoral MW reduces the firm‘s utopia payoff and
hence drives up the wage.
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KALAI-SMORODINSKY WAGE BARGAINING
V
utopia
point
A
E
D
V0
C
(wmin )
(w0 )

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KALAI-SMORODINSKY WAGE BARGAINING
What do non-binding MW do?
1. sectoral level
min
KS
min
• w  w , but w  w0
• w0 exogenous
 Sectoral MWreduces the firm‘s utopia payoff and hence
drives up the wage.
2. national level
• direct effect in each sector if wmin  w0
• plus: changes in w0 affect wages in other sectors
 National MW does not have to be binding, but is
effective
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CONCLUSION
• Empirical evidence suggests that MW have real effects even if
they are not binding.
• Implications for economic theory:
KS solution is able to describe these effects, Nash solution is
not.
• Implications for public policy:
Even relatively low MW might have negative employment
effects  policy implications depend on whether union-firmbargaining follows Nash or KS solution.
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Thank you very much!
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MOTIVATION: SPILLOVER EFFECTS OF MW
Empirical evidence
• Katz and Krueger (1992, ILRR): Texan fast-food restaurants
– one-third “maintained their wage hierarchy” (workers who earned
more than the old MW will also earn more than the new minimum)
– 60% of restaurants who had starting wages already above new
minimum still increased their wages
• Manning (2003): US data 1979-2000
 spillovers for wages up to 150% of the MW
• Neumark et al. (2004, JHR): US data 1979-1997
 spillovers for wages up to twice the MW
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MARCUS DITTRICH
MOTIVATION: SPILLOVER EFFECTS OF MW
• Three popular theoretical explanations
1.
Substitution effects (Pettengill 1981)
•
2.
increase in demand for above-minimum wage workers raises their
wages, too
Monopsonistic firm behavior (Manning 2003)
•
•
some firms pay high wages to attract workers from low-wage firms
if low-wage firms pay more, also high-wage firms have to raise
their wages
Efficiency wages (Grossman 1983, JHR)
3.
•
smaller wage differential between skilled and unskilled workers has
to be compensated to keep up effort of skilled workers
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EXPERIMENTAL EVIDENCE
• Falk, Fehr & Zehnder (2006, QJE) conduct a laboratory
experiment in which a rent is distributed between
“workers” and a “firm”.
• In the experiment’s first step, workers state their
reservation wages, which are not observed by the firm.
• Then, the firm makes a wage offer and workers with
reservation wages below this wage offer are hired.
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EXPERIMENTAL EVIDENCE
• The introduction of a minimum wage raises workers’
reservation wages: Before its introduction, 91% of workers
stated a reservation wage below the later minimum wage.
• After it had been introduced, 59% reported that their
reservation wage was equal to the new minimum wage, and
the other 41% said that their reservation wage was even
larger than the new minimum wage.
• Result: minimum wages affect the wage level that people
are willing to accept even if they are not directly affected by
the new minimum wage.
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MODEL ECONOMY: MONOPOLY UNION
• reference scenario: monopolistic union sets the wage,
firms set employment
• monopoly union behavior:
max V  w   wL   N  L  w0
w
 w
mon
 w
s.t. L   

1
1
w0


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MODEL ECONOMY: MONOPOLY UNION
w
wmon
V(w)
w0
0
Lmon
L(w0)
L
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MODEL ECONOMY: MONOPOLY UNION
V
V(wmon )
A
V( ())
V0
L(w)=N

(wmon )
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MODEL ECONOMY: MONOPOLY UNION & MW
What do non-binding MW do?
1. sectoral level
• wmin  wmon
• w0 exogenous
 Sectoral MW has no effect on monopoly union‘s
desired wage.
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MODEL ECONOMY: MONOPOLY UNION & MW
V
V(wmon )
A
V0
L(w)=N
(wmon )
(wmin )

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MARCUS DITTRICH
MODEL ECONOMY: MONOPOLY UNION & MW
What do non-binding MW do?
1. sectoral level
• wmin  wmon
• w0 exogenous
 Sectoral MW has no effect on monopoly union‘s
desired wage.
2. national level
min
mon
• w  wi i  no change in wages
• w0 unchanged
 National MW has no effect on monopoly union‘s
desired wage if it is non-binding.
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NASH‘S AXIOMS
Find a bargaining solution that satisfies the following four
axioms:
1. Pareto efficiency (PAR)
2. Invariance to equivalent utility representations (INV)
3. Symmetry (SYM): symmetric utility functions should
ensure symmetric payoffs
4. Independence of irrelevant alternatives (IIA):
If S is the Nash bargaining solution for a bargaining set X,
then for any subset Y of X containing S, S continues to be
the Nash bargaining solution.
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KS‘S AXIOMS
Find a bargaining solution that satisfies the following four
axioms:
1. Pareto efficiency (PAR)
2. Invariance to equivalent utility representations (INV)
3. Symmetry (SYM): symmetric utility functions should
ensure symmetric payoffs
4. Individual monotonicity (MON):
If the bargaining set is enlarged such that the maximum
utilities of the players remain unchanged, then neither of
the players must not suffer from it.
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