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.

W

L

S

D

Real Wage Rigidity

• Wages are real• Wage at W1

• Excess supply of labour– Unemployment

• Wage bid down to W0

– Eqm restored

• So unemployment will occur if the wage does not fall for some reason.

• Always ask why!

W1

W0

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

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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

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W1NSC

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

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VUh

fEU

UhEfu

hiresfiresu

V

U

BC

• 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– Any level of V now

associated with higher 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:

wpV

VUhcV

),(

• As U increases:– Matches (h) increase– Prob of filling Vacancy– Profitability of

vacancies increases– Issue more vacancies– Curve gives firms

response

• Note importance of– Cost of vacancies– Matching not

certain/instant

• Curve will shift – down if c rises– Up if p-w rises

V

U

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

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Vac

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),(:

VUh

fEUBC

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• 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

BC

Vac

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),(:

VUh

fEUBC

wpV

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– 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 – firm gets– reflects workers negotiating power

• Net wage is equal to min (reservation wage) + share of surplusW=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

BC

Vac

U

V

U

Vcbpbw

WA

WB

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