Models of Unemployment
Natural Rate of Unemployment
• What determines the long run rate of
unemployment
– Location of LRAS and LRPC
• Why is it not zero?
• Or 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
S
W
• Wages are real
• Wage at W1
• Excess supply of
labour
– Unemployment
W1
• 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!
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
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
• 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:
• 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
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
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