2. Economic Theories of Equilibrium Unemployment
• Classical Model of the Labor Market
• Hansen Model
• Beveridge Curve
• Battle-of-the-Markups Model (NAIRU)
• Stock-Flow Model
• Persistency
• Summary
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2.1. Classical Model of the Labor Market
Problems:
• Unemployment (U) does not exist in equilibrium.
• Unemployment and job vacancies (V) cannot co-exist.
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2.2. Hansen-Model
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Approach:
In reality, the labor market consists of a multitude of micro labor markets separated by mobility and information
barriers. Consequently and contrary to the classical model, unemployed and vacancies can indeed co-exist. The
so-called employment curve (EE in the diagram) captures
this fact.
Model Specification:
Et   D

t
S

1
  
t
where: E = employed
D = labor demand
S
= labor supply
1/
= degree of mismatch. The measure varies
from zero (perfect match) to infinity (perfect mismatch).
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Thee CES functional form of the employment curve results from the following assumptions (Lambert, 1988):
Demand in micro labor market i:
ln Di  d   iD
Supply in micro labor market i:
ln Si  s   iS
Employment in micro labor market i:
ln Ei  min  ln Di , ln Si 
D
S
Where  i ,  i ~ N 2  0,   .
Integrating over all n micro labor markets yields the formula for the employment function given above, where 
varies inversely to
Var    

D
S

1
2
.
From this it follows that the variance goes to 0 (∞) und 
to ∞ (0) if D and S are positively (negatively) correlated. Positive (negative) correlation implies a low (high)
degree of mismatch.
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Equilibrium unemployment:
The unemployment rate that arises in equilibrium (D=S):
UR* 
SE
1
 1 2 
S
Corresponds to the relative distance from E to S at the
point where the supply curve S intersects the demand
curve D.
Determinants of equilibrium unemployment:
• Opaqueness of the labor market and the amount of profile discrepancy between the unemployed and job vacancies ().
• Ability and willingness of market participants to overcome existing information and mobility barriers ().
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2.3. Beveridge Curve in Switzerland, 1970-2008
0.6%
0.5%
1989
Vakanzenquote
0.4%
1990
1999
1988
1998
1987
1980
1981
0.3%
2000
1986
1991
2008
2007
2001
2006
1997
1979
1978
1985
2005
1992
0.2%
1977
0.1%
2002
0.0%
0.0%
1993
1995
1983
1970
1972
1971
1973
1974
2003
1984
1982
2004
1996
1994
1976
1975
1.0%
2.0%
3.0%
4.0%
5.0%
6.0%
Arbeitslosenquote
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Approach:
Transformation of the Hansen diagram in a UV coordinate system
Model Specification:
URt  VRt  
where: UR = unemployment rate
VR = vacancy rate
 = positional parameter
 = curvature parameter (high values yield flatness)
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Equilibrium unemployment:
The unemployment rate yielded by the equality
URt  b VRt  , where b measures the degree to which
vacancies are not fully recorded.
UR    b 
*

1
1 
Determinants of equilibrium unemployment:
• Opaqueness of the labor market and the amount of profile discrepancy between the unemployed and job vacancies (, ).
• Ability and willingness of market participants to overcome existing information and mobility barriers (, ).
• Degree to which vacancies are not fully recorded (b).
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2.4. Battle-of-the-Markups Model (NAIRU)
Reallohn
(w-p )
AG
AN
0
NAIRU
1
UR
1
UR
Inflationsänderung
( p t -  p t-1 )
0
NAIRU
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Approach:
The driving forces in the model are the income demands
of the unions and employer associations, respectively,
and their determination to enforce them. Unemployment
serves here to coordinate the demands of both sides by
threatening the unions with job losses and employers
with sales losses thereby preventing the income demands
from leading to an inflationary spiral.
Model Specification:
Wage demands of the unions (AN):
wt   0  pte  1  URt   2  xt
Price demands of the employers (AG):
pt   0  wte  1  URt   2  zt
Small letters symbolize natural logarithms. The letter e
signifies expected or tolerated values.
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Where: w
p
UR
x,z
= log wage
= log price
= unemployment rate
= factors which also make claims on GDP
and thus limit the room for redistribution
(e.g. the state)
 = autonomous income demands
 = weights reflecting the mitigating effect of
unemployment on income demands
Equilibrium unemployment:
The unemployment rate which balances the income demands of workers and firms (pe=p and we=w), given an
absence of other income demands (x, z = 0).
NAIRU 
 0   0 autonomous income demands

willingness to concede
1  1
Determinants of equilibrium unemployment:
• autonomous income demands (0, 0)
• disciplining effect of rising unemployment (1, 1)
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Link to Phillips Curve (NAIRU)
The Phillips curve describes a negative relationship between unemployment and inflation. It is derived as follows:
According to the Battle-of-the-Markups Model:
( 0   0 )  ( w  we )  ( p  p e )
UR 
1  1
( w  we )  ( p  p e )
UR  UR*  
1  1
Assuming (w - we) = (p - pe) yields:
( p  pe )  
(1  1 )
 (URt  URt *)
2
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If inflation follows a random walk
 pt = pt-1 + t
then rational expectations with regard to (p - pe) imply:
 pt e or pt e  pt 1   pt 1
pt e  pt 1   pt 1
pt  pt e  pt  pt 1   pt 1
  pt   pt 1
It then follows that:
( pt   pt 1 )  
(1  1 )
 (URt  URt *)
2
Thus NAIRU (UR*) is that level of unemployment that is
consistent with a constant rate of inflation (pt - pt-1 =
0).
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Reasons for non-market-clearing wages:
Efficiency Wage Model
• Shirking approach
Non-market-clearing wages create unemployment
which acts as a threat to prevent shirking.
• Fluctuation approach
Non-market-clearing wages increase bind workers to
firms thus reducing a firm’s costs of recruiting and
training new workers.
• Positive selection
Non-market-clearing wages attract more productive
workers.
Insider-Outsider Model
Workers with jobs (insiders) are only interested in setting wages that ensure their own employment, but not
that of the jobless (outsiders). The power to do this
arises from the costs that firms would endure were they
to substitute insiders with outsiders.
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2.5. Stock-Flow Model
Approach:
The exclusive focus on stock levels in the previous models is broadened by the inclusion of the flows leading into
and out of the stock of unemployed, thereby bringing the
duration or permeability of unemployment into play.
Search theory provides the behavioral background.
Model Specification:
The following holds with respect to the stock of unemployed U in equilibrium:
Flows into U  Flows out of U
E * PEU  U * PUE
P
E*
 UE
U*
PEU
Definition of the unemployment rate:
UR 

U
E U
1
1
E
U
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Equilibrium unemployment
The above implies:
UR* 
1
P
1  UE
PEU
Search theory as the theoretical base:
PUE = ·[1 - F(w*)]
spell duration 
1
1

PUE   1  F ( w*)
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Determinants of the optimal reservation wage (wR):
Model assumptions:
• wage distribution is known to the unemployed
• generating a wage offer costs k
• jobs are retained for life
• no time preferences requiring discounting
The accepted wage of a job searcher is maximized if the
following holds:
expected wage gain  expected costs
E  w  wR w  wR   E costs w  wR 

  w  w  f  w dw 
wR
R
1  F  wR 
k
1  F  wR 

  w  w  f  w dw  k
wR
R
marginal wage gain  marginal cost
The reservation wage that fulfills the equilibrium requirement is the one that maximizes the accepted wage
w*.
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Search theory implies:
• a horizontal hazard function if
- the time horizon is infinite.
- the wage distribution f(w) remains constant.
- k remains constant.
• an increasing hazard function if
- the time horizon is finite.
- job search is selective instead of random.
- k increases with the duration of search.
• a decreasing hazard function if
- long-term unemployment stigmatizes.
- long-term unemployment weakens skills.
- long-term unemployment demoralizes.
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Determinants of equilibrium unemployment:
• duration of unemployment (1/PUE)
• risk of unemployment (PEU)
• composition of the stock of unemployed
• frequency of job offers 
• distribution of wage offers F(.)
• wage demands of the unemployed (w*)
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2.6. Persistency
Main claim or insight:
The level of equilibrium unemployment also depends on
the current level of unemployment.
Consequence:
Cyclical unemployment can mutate into structural unemployment. The original cause of unemployment may thus
not provide guidance with respect to the appropriate policy answer.
Causes of persistency:
• Insider-Outsider Model (see above)
• negative duration dependence
The prospects of finding a job decline with the duration
of unemployment, be it because skills deteriorate with
prolonged unemployment or be it because extended
unemployment signals real or imagined deficiencies to
potential employers.
• capital scarcity
A prolonged downturn encourages firms to lower capacity so that capacity and hence jobs are scarce when
an upswing finally arrives.
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Incorporation of Persistency in Various Models
NAIRU
If NAIRU t  ( 0   0 ) (1  1 )   URt 1   t then in the
case of persistency:
 0  0
NAIRU 
1  1 1   
and in the case of hysteresis:
URt  URt 1   t
Median Lag:
URm  UR0*
 0.5  1   m
*
*
UR1  UR0
Stock-Flow Model
The median duration (m) corresponds roughly to the
equilibrium share of long-term unemployed.
Beveridge Curve
 is specified as a function of the share of long-term unemployed.
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Overview of the Determinants of Unemployment
Hansen/Beveridge
Equilibrium
• barriers (information, • income demands
mobility)
• willingness and ability • willingness to concede
to overcome them
• high wages
Non-equilibrium
NAIRU
• business cycle
Stock-Flow
• unemployment
risk
• duration of unemployment
• supply and cost shocks • long-term unemployment
• business cycle
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