Models of Unemployment
Mankiw
Chapter 7
Learning Objectives
1. Unemployment is caused by real wage
rigidity
2. Unemployment can persist in the long run
if RWR persists. This is known as “the
natural rate of unemployment”
3. Possible causes of RWR include,
efficiency wages, search costs, union
action, min wages.
Real Wage Rigidity
S • Wages are real
W
• Wage at W1
• Excess supply of labour
W1
– Unemployment
W0
• Wage bid down to W0
– Eqm restored
D
L
• So unemployment will
occur if the wage does
not fall for some reason.
• Always ask why!
Temporary Unemployment
• We have already seen one source of
unemployment in the AS-AD framework
• There real wages can remain high in a
recession as workers fail to react to reduced
cost of living
• This will eventually go as economy returns
to equilibium
Natural Rate of Unemployment
• What determines the long run rate of
unemployment
– Location of LRAS and LRPC
• Persistent unemployment
• Why is it not zero?
– Why is the wage above the market clearing
wage rate?
– Competitive labour market has zero
unemployment.
• Defn: Involuntary Unemployment: Would accept
job at going wage rate if offered
– Not chairman of IBM
Sources of RWR
• What can generate RWR on a persistent
basis?
– Unions: Insider/outsider theory
– Min wage
• Size of this effect controversial
• Evidence unclear
• Cant be the whole story as wage is low
– Efficiency wages
– Search Theory
Efficiency Wages
• Efficiency Wages explain why wage will
not fall to market clearing level.
• Basic idea: wage influences productivity
– Firm won’t want to pay a low wage
– Labour is not like any other good and wage is
not like any other price
• Examples:
–
–
–
–
Nutrition
Turnover
Applicant pool
Monitoring
Shirking
• Look at the monitoring version of efficiency
wages in detail
– Shapiro & Stiglitz
• Assume workers exert effort equal to
– Zero – shirking
– e>0 – not shirking
– Think of effort as no. of units produced
• If shirking, firm does not earn revenue but
will still have to pay wage unless worker is
caught
– Need to eliminate shirking workers
Firm’s Policy
• Carrot and stick approach
• Stick: Institute a monitoring policy
– Catch shirker with probability p<1
– If caught sacked – get only unemployment
benefit
• Firm pays a wage high enough so that
worker doesn’t want to shirk
– W>b so that getting sacked hurts
– This is insufficient
No Shirking Condition
• How much does firm have to pay to
eliminate shirking
• Worker has three options
– Remain unemployed – collect benefits: b
– Work and shirk – get wage :w
• Risk loosing job with probability p
– Work and not shirk – get wage : w
• But exert effort: e
• Net gain of w-e
• Note w>w -e >b
– So in absence of threat of sack worker would
shirk
nonshirk  shirk
w  e  (1  p ) w  pb
e
w
b
p
e
w
b
p
Equilibrium
• Note that the NSC implies a wage which
will not equal the market clearing wage
except by coincidence.
• So there will be unemployment in
equilibrium
• Why doesn’t wage fall?
– Because lower wage would lead to shirking
– Even lower profits
• Post a bond?
– Commitment
– Open to abuse
– Pension schemes, salary scales, promotion
• As the quality of the monitoring procedure
improves
–
–
–
–
P rises
NSC shifts down
Wage down
Unemployment down
• As effort required rises
–
–
–
–
e up
NSC shifts up
Wage up
Unemployment up
S
W
NSC
W1
D
L
Unemployment as a Discipline Device
• The basic model model is incomplete
– Need to account for re-hires after being sacked
• unemployment low
– Easy to get job
– being sacked is not a severe punishment
• Need to pay even higher wage to avoid
shirking
– NSC curve slopes up
– Asymptotic to Supply curve
• Note if unemployment is zero wage is
infinite
• Unemployment is a
discipline device
• Enables the policy of
high wage plus
monitoring to work
• threat of sacking means
something
• So unemployment is
both cause and effect
– Effect: of high wage
– Cause: of effective
monitoring procedure
Search
• Unemployment is stock of those waiting for
a job
• Unemployment and unfilled vacancies can
co-exist
• matching unemployed workers and firms
with vacancies takes time and money
• Less socially damaging
Matching
• Central idea of search model is matching
function
– Another name for hiring function
• For a worker to be hired requires that an
unemployed worker meets a firm with a
vacancy.
• Number of successful matches
– Increases with U
– Increases with V
– h(U,V)
• Matching is not instantaneous
• There will exist U and V in any instant
• In a competitive labour market
– No U
– V infinite
– Matching immediate
Beveridge Curve
• What happens to U when V increases?
• Focus on steady state i.e. equilibrium
• Accounting rule for the flows in labour
market
–
–
–
–
U: stock of unemployed
E: stock of employed
H: hiring or matching rate
F: firing rate
u  fires  hires
u  f * E  h *U
fE
U
h(U ,V )
• Beveridge curve
slopes down
• As V rises, number of
hires increase
• For fixed firing rate,
this reduces U
• If f rose then curve
shift to right
V
– Any level of V now
associated with higher
U
BC
U
Vacancies Curve
• How will the number of V issued be
affected by U?
• Firms issue vacancies in order to maximise
profits
• Cost of issuing a vacancy: c
– Competitive labour market c=0
– C>0 implies V<infinity
• Benefit of vacancy: may fill it an earn
profits
• Profit per filled job: p-w
– One worker produces one unit: sell for p
• Vacancy once issued will not automatically
be filled
– Worker and firm have to be matched
– Crucial element
• Probability of filling a vacancy =h/V
• Net Profit from V:
h(U , V )
 p  w
  cV 
V
• As U increases:
– Matches (h) increase
– Prob of filling Vacancy
– Profitability of
vacancies increases
– Issue more vacancies
– Curve gives firms
response
V
• Note importance of
– Cost of vacancies
– Matching not
certain/instant
• Curve will shift
U
– down if c rises
– Up if p-w rises
Equilibrium
• Put both curves together
– Intersection gives eqm
– Natural rate of unemployment
– Eqm level of vacancies
• Where would competitive labour market be?
• What happens to equilibrium as parameters
change?
• c up:
–
–
–
–
–
Vac curve shifts (because c is in vac)
more costly to issue vacancies
So for any given U firms will isuues lower V
i.e. vac curve shifts down
Higher eqm U and lower V
• Firing rate rises
– Perhaps due to change in law -- or US vs EU
– BC shifts (because f is in BC)
• at any level of V, there are more fires, so stock of
unemployed will be higher
• i.e. BC shifts to right
– New eqm with higher U and higher V
– Why higher V?
• Higher unemployment makes it easier to fill
vacancies
• So firms issue more vacancies
• Shift along the V curve
h(U , V )
 p  w
VAC :   cV 
V
fE
BC : U 
h(U , V )
Vac
V
BC
U
• New Matching technology
– e.g. gov. scheme to help unemployed search for
jobs
– h increases for any given U and V
– This affects both curve (h in both equations)
– Vac Curve:
• H up implies prob of filling a vacancy increases
• Issue more vacancies at every level of U
• Vac curve shifts up
– BC:
• H up implies flows out of unemployment increase at
every V
• U falls for all V
• BC shifts left
h(U , V )
 p  w
VAC :   cV 
V
fE
BC : U 
h(U , V )
Vac
V
BC
U
– New Eqm ist at B
– U will fall
• The rationale for these schemes
– V may increase or decrease depend on size of
shift in each curve. Why?
•
•
•
•
•
H up tends to increase V directly
But there indirect effect
U falling makes more difficult to fill V
So it depends which is greater
Crucial parameter is H/V. Is this rising or falling?
Wages
• what determines w?
• Intuitively expect w to increase with V and
decrease with U
• Min wage = b (unemployment benefits)
• Max profits: p-b+cV/U
– Hiring now saves cost of vacancy in future
• Firm will not be able to pay just b
– Workers will demand some premium
– Firm will give premium because afraid of loosing profit
– Because matching is not instantaneous
• Assume they split the surplus
– worker gets b
– firm gets 1b
– b reflects workers negotiating power
• Net wage is equal to min (reservation wage)
+ share of surplus
W=b+b(p-b+cV/U)
• W is increasing in V and decreasing in U
– Note effect of c
• We can see W on diagram by drawing line
from origin
WA
V

w  b bp bc 
U

V
Vac
WB
BC
U
Final Test
• For all models of Unemployment ask the question:
– Why don’t unemployed workers offer to work
for less?
– W falls, labour market clears, U=0
• Answer:matching is not instantaneous
– still may not physically meet an employer
– Still have stock of people waiting for job i.e.
U>0
– When they do they have incentive to take
advantage and negotiate a higher wage
• Firm does not want to turn them away
Conclusions
1. Unemployment is caused by real wage
rigidity both in the short term and long
term
2. The natural rate of unemployment occurs
because RWR persists in the long term
Conclusions
3. Sources of RWR & Natural
Unemployment include
– efficiency wages: quality of workers
– search costs: cost of matching workers and
employers
– union action
– Min wages