Intermediate Macroeconomics - Lecture 8 - Search and ...econ.sciences-po.fr/sites/default/files/file/barany/int_macro/... · Intermediate Macroeconomics Lecture 8 - Search and Unemployment

Intermediate MacroeconomicsLecture 8 - Search and Unemployment

Zsofia L. Barany

Sciences Po

2014 March

Roadmap

I labor market factsI Diamond-Mortensen-Pissarides model of search and

unemploymentI change in unemployment insurance benefitI change in productivityI change in matching efficiency

Labor market facts

Labor market measurement

I working age population (N) = in the labor force + not in thelabor force

I labor force (Q) = employed (Q − U) + unemployed (U)

I not in the labor force: not working and not looking for work

I unemployment rate = UQ : fraction of those in the labor force

who are not working, but are actively looking

I participation rate = QN : fraction of the working-age population

that is working or seeking work

I employment rate = Q−UN : fraction of the working-age

population that is working

The participation rate in the US

The participation rate for men and women in the US

Key labor market statistics US

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

20.0

50.0

52.0

54.0

56.0

58.0

60.0

62.0

64.0

66.0

68.0

70.0 Jan-‐48

Aug-‐49

Mar-‐51

Oct-‐52

May-‐54

Dec-‐55

Jul-‐5

7 Feb-‐59

Sep-‐60

Apr-‐62

Nov-‐63

Jun-‐65

Jan-‐67

Aug-‐68

Mar-‐70

Oct-‐71

May-‐73

Dec-‐74

Jul-‐7

6 Feb-‐78

Sep-‐79

Apr-‐81

Nov-‐82

Jun-‐84

Jan-‐86

Aug-‐87

Mar-‐89

Oct-‐90

May-‐92

Dec-‐93

Jul-‐9

5 Feb-‐97

Sep-‐98

Apr-‐00

Nov-‐01

Jun-‐03

Jan-‐05

Aug-‐06

Mar-‐08

Oct-‐09

May-‐11

Dec-‐12

employment-‐populaEon raEo (%)

labor force arEcipaEon rate (%)

unemployment rate (%, right scale)

Source: Bureau of Labor statistics, monthly, seasonally adjusted data

The unemployment rate and the GDP in the US

Participation rates in European countries

Slide #9

Participation RatesParticipation Rates

50

55

60

65

70

75

80

85

1960 1965 1970 1975 1980 1985 1990 1995 2000

France Germany Italy United Kingdom United States

Slide #10

Unemployment RatesUnemployment Rates

0

2

4

6

8

10

12

14

1960 1965 1970 1975 1980 1985 1990 1995 2000

France Germany ItalyUnited Kingdom United States

Unemployment rates in European countries

Slide #9

Participation RatesParticipation Rates

50

55

60

65

70

75

80

85

1960 1965 1970 1975 1980 1985 1990 1995 2000


Slide #10

Unemployment RatesUnemployment Rates

0

2

4

6

8

10

12

14

1960 1965 1970 1975 1980 1985 1990 1995 2000

France Germany ItalyUnited Kingdom United States

Employment rates in European countries

Slide #11

Employment RatesEmployment Rates

50

55

60

65

70

75

80

1960 1965 1970 1975 1980 1985 1990 1995 2000


Slide #12

Employment rates, Employment rates, all persons aged 15all persons aged 15--64, 200664, 2006

0102030405060708090

Sw

itze

rla

nd

De

nm

ark

No

rwa

yN

ZS

we

de

nC

an

ad

aU

KN

eth

erl

an

dA

ust

ralia US

Au

stri

aJa

pa

nF

inla

nd

Ire

lan

dP

ort

ug

al

Ge

rma

ny

Sp

ain

Cze

chK

ore

aF

ran

ceG

ree

ceM

exi

coB

elg

ium

Slo

vak

Italy

Hu

ng

ary

Po

lan

dT

urk

ey

Employment rates in 2006

Slide #11

Employment RatesEmployment Rates

50

55

60

65

70

75

80

1960 1965 1970 1975 1980 1985 1990 1995 2000


Slide #12

Employment rates, Employment rates, all persons aged 15all persons aged 15--64, 200664, 2006

0102030405060708090

Sw

itze

rla

nd

De

nm

ark

No

rwa

yN

ZS

we

de

nC

an

ad

aU

KN

eth

erl

an

dA

ust

ralia US

Au

stri

aJa

pa

nF

inla

nd

Ire

lan

dP

ort

ug

al

Ge

rma

ny

Sp

ain

Cze

chK

ore

aF

ran

ceG

ree

ceM

exi

coB

elg

ium

Slo

vak

Italy

Hu

ng

ary

Po

lan

dT

urk

ey

Vacancies and unemployment

I aggregate number of vacancies posted by firms (A)

I vacancy rate = AA+Q−U : the ratio of the number of vacancies

to vacancies plus the number of employed

can look at relationship between unemployment rate and vacancyrate

The vacancy rate and the unemployment rate in the US

The Beveridge curve in the US

and very similar pictures across OECD countries

Key labor market observations

I the unemployment rate is counter-cyclical

I the vacancy rate is pro-cyclical

I the unemployment rate and the vacancy rate are negativelycorrelatedthe Beveridge curve

I the Beveridge curve shifted out during the last recession

Diamond-Mortensen-Pissaridesmodel:

Search and Unemployment

Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel for 2010 to

Peter A. Diamond Massachusetts Institute of Technology, Cambridge, MA, USA,

Dale T. Mortensen Northwestern University, Evanston, IL, USA

Christopher A. Pissarides London School of Economics and Political Science, UK

"for their analysis of markets with search frictions"

Search model of unemployment: main idea

I unemployed workers and job openings do not instantaneouslyfind each other

I → there are frictions in the labor market→ there is a search process

I source of frictions:I heterogeneity of workers and firms

uncertainty about the skills, and quality of jobsI imperfect information: invest resources in locating firm/worker

it takes time for a worker to find an ’acceptable’ joband similarly for an employer to find an ’acceptable’ worker

I mobility costs

I unemployment is a stock variable that adjusts slowly as aresult of this job finding process

A (much) simplified DMP model

I one-period model

I N consumers who can all potentially enter the labor force→ N is the working age population

I number of (active) firms is endogenous

Households

I each of the N individuals chooses whether toI search for work in the marketI or to do home production (working outside the market)

I a consumer searches for work ifthe expected return to search > the value of home production

I expected return to search is the same for all consumers→ if it is higher, more people search

I assumption: the value of home production is heterogenousacross householdsthis value captures: value of leisure, home production activity

I let Q be the number of consumers who search for work→ in the labor force→ out of the labor force are N − Q

I denote by P(Q) the level of expected payoff to search whichinduces exactly Q workers to search→ the supply curve of searching workers

The supply curve of searching worker

Firms

I each firm needs a worker to produce output

I a firm cannot simply hire a worker

I a firm must post a vacancy in order to have a chance ofmatching with a worker

I posting a vacancy incurs a (real) cost k

I let A be the number of active firms→ number of firms posting vacancies

Matching

I a match is between one firm and one worker

I timeline of decisions: 1. search 2. match 3. produce

I search is costly/time-consuming due to search frictions (e.g.heterogeneity in skills and skills requirements in the presenceof incomplete information)

I the more workers search for work, the easier for a firm to finda worker

I the more vacancies posted, the easier for a worker to find a job

I relationship can be formalized by a matching function:

M = e ·m(Q,A)

I M is the aggregate number of matches formedI assumed to be a neoclassical production function: matches are

produced using the labor force (here = number of peoplesearching) (Q) and active firms (A)

I e is a parameter capturing the matching efficiency

Optimization by consumers

I a consumer who chooses to search for work will find a matchwith probability

pc =M

Q=

e ·m(Q,A)

Q

= e ·m(

1,A

Q

)= e ·m(1, j)

I labor market tightness j ≡ AQ

I if searching and matched, consumer receives wage w

I if searching but not matched, consumer receives a payoff bunemployment benefit, utility value ?

I expected payoff from searching is then

E [search] = pc ·w+(1−pc)·b = b+pc ·(w−b) = b+em(1, j)·(w−b)



pc =M

Q=

e ·m(Q,A)

Q= e ·m

(1,

A

Q

)

= e ·m(1, j)








pc =M

Q=

e ·m(Q,A)

Q= e ·m

(1,

A

Q

)= e ·m(1, j)








pc =M

Q=

e ·m(Q,A)

Q= e ·m

(1,

A

Q

)= e ·m(1, j)








pc =M

Q=

e ·m(Q,A)

Q= e ·m

(1,

A

Q

)= e ·m(1, j)






Marginal consumer

I expected payoff from searching is

E [search] = b + pc · (w − b) = b + em(1, j) · (w − b)

I note: the higher Q, the lower j , and the lower pc→ the more people are searching the lower is the probabilityfor each to find a job

I E [search] is an exogenous value from the perspective of aconsumer

I there is a marginal consumer who is indifferent between homeproduction and searching for workfor this consumer: E [search] = value of home production

I for everyone with value of home production ≤ E [search] it isoptimal to search→ the supply curve of searching workers (Q)

P(Q) = b + em(1, j) · (w − b)

Optimization by firmsI a firm posting a vacancy will find a match with probability

pf =M

A=

e ·m(Q,A)

A= e ·m

(Q

A, 1

)

= e ·m(

1

j, 1

)I labor market tightness j = A

QI to post the vacancy the firm bears cost kI when a firm is matched with a worker, they produce output z

and pay wages wI when a firm is not matched, they do not produceI the payoff to a firm posting a vacancy is therefore z − w − k

when forming a match, and −k when they do not find amatch

I the expected payoff from posting a vacancy is then

E [vacancy ] = pf (z − w − k) + (1− pf )(−k) = −k + pf (z − w)

= −k + em

(1

j, 1

)(z − w)


pf =M

A=

e ·m(Q,A)

A= e ·m

(Q

A, 1

)= e ·m

(1

j, 1


Q

I to post the vacancy the firm bears cost kI when a firm is matched with a worker, they produce output z





= −k + em

(1

j, 1

)(z − w)


pf =M

A=

e ·m(Q,A)

A= e ·m

(Q

A, 1

)= e ·m

(1

j, 1







= −k + em

(1

j, 1

)(z − w)


pf =M

A=

e ·m(Q,A)

A= e ·m

(Q

A, 1

)= e ·m

(1

j, 1







= −k + em

(1

j, 1

)(z − w)


pf =M

A=

e ·m(Q,A)

A= e ·m

(Q

A, 1

)= e ·m

(1

j, 1







= −k + em

(1

j, 1

)(z − w)

Free Entry of firm

E [vacancy ] = −k + em

(1

j, 1

)(z − w)

I note: the higher A, the higher j , and the lower pf→ the more vacancies are posted the lower the chance foreach of being filled

I free entry of firms competes away all expected profits fromposting vacancies⇒ E [vacancy ] = 0⇒

em

(1

j, 1

)=

k

z − w

I firms post vacancies up to the point where the probability ofmatching (LHS) is equal to the ratio of the cost of posting avacancy to the profits from a successful match (RHS)

I this free-entry condition pins down labor market tightness j asa function of the wage rate w

Vacancies posted – Labor demand

Wage determination

I we have seen already labor supply and demand as a functionof labor market tightness, at a given level of wages

I to close the model, we need to specify how wages aredetermined

I note: workers are not paid their marginal product, as there arefrictions, which implies a kind of monopoly power from beingin a match

I assumption: wages are determined through bilateralbargaining, between a firm and a worker when they form thematch

I bargaining takes place when firm and worker meetI the outside option of each party is not to form the match:

firm would not produce; worker would receive UI benefitI firm has bargaining power since worker has only one offerI worker has bargaining power since firm has only one offer

Nash Bargaining

I Nash Bargaining: each party receives a share of the totalsurplus determined by their bargaining weight

I surpluses from forming a match:I for the worker: w − bI for the firm: z − wI → total surplus: z − b

I as long as z − b > 0, it is beneficial for the firm and theworker to form the match

I then Nash bargaining determines a wage w that splits thetotal surplus according to the bargaining weights

I let the worker’s relative bargaining weight be a, and the firm’sis then 1− a

I outcome of Nash Bargaining:

w − b = a(z − b)

Nash Bargaining







w − b = a(z − b)

Nash Bargaining







w − b = a(z − b)

Summary of the equilibrium conditions

I from Nash Bargaining: w = b + a(z − b)

I the searching worker’s supply condition:

P(Q) = b + em(1, j) · (w − b) = b + em(1, j) · (a(z − b))

I free entry condition of firms – job creation:

em

(1

j, 1

)=

k

z − w=

k

(1− a)(z − b)

I these two equations characterize the equilibrium of theMortenson-Pissarides model

Equilibrium

Equilibrium outcomes

I unemployment rate:

u =Q(1− pc)

Q= (1− pc) = 1− em(1, j)

I vacancy rate:

v =A(1− pf )

A= (1− pf ) = 1− em

(1

j, 1

)I aggregate output:

Y = em(Q,A)z = Qem(1, j)z

I recall that j = AQ is labor market tightness

Application 1: An increase in UI benefits, b

I reduces the total surplus of the match, z − b

I improves the worker’s outside option⇒ increases the wage, w = b + a(z − b), as Nash Bargainingnow allocates more resources to the worker

I ⇒ makes firms worse off, and therefore reduces job creation⇒ fewer vacancies posted, A ↓, less tight labor market, j ↓

I unemployment rate rise,s u = 1− em(1, j), vacancy rate falls,

v = 1− em(1j , 1

)I overall effect on labor force is ambiguous, since:

1. higher wages increase return to job search → Q ↑2. lower labor market tightness (fewer vacancies relative to labor

force) reduces chances to find a job → Q ↓I effect on aggregate output is ambiguous too, Y = Qem(1, j)z

Higher unemployment benefits

Application 2: An increase in productivity, zI increases the total surplus of the match, z − bI does not affect the outside options of firms or workers

I according to Nash Bargaining, wages do increase,w = b + a(z − b)

I but also the surplus of the firm increases,z − w = (1− a)(z − b)

I → both the surplus of the worker and of the firm increase bythe same factor as (z − b)

I → the higher surplus boosts firm entry and job creation⇒ more vacancies posted, A ↑, tighter labor market, j ↑

I unemployment rate falls, u = 1− em(1, j), vacancy rate rises,

v = 1− em(1j , 1

)I labor force increases, since:

1. higher wages increase return to job search → Q ↑2. tighter labor markets improve workers chances of finding a job→ Q ↑

I aggregate output is rises too, Y = Qem(1, j)z

I the behavior of u and v is consistent with the Beveridge curve

Application 2: An increase in productivity, zI increases the total surplus of the match, z − bI does not affect the outside options of firms or workers

I according to Nash Bargaining, wages do increase,w = b + a(z − b)

I but also the surplus of the firm increases,z − w = (1− a)(z − b)

I → both the surplus of the worker and of the firm increase bythe same factor as (z − b)

I → the higher surplus boosts firm entry and job creation⇒ more vacancies posted, A ↑, tighter labor market, j ↑

I unemployment rate falls, u = 1− em(1, j), vacancy rate rises,

v = 1− em(1j , 1

)I labor force increases, since:

1. higher wages increase return to job search → Q ↑2. tighter labor markets improve workers chances of finding a job→ Q ↑

I aggregate output is rises too, Y = Qem(1, j)zI the behavior of u and v is consistent with the Beveridge curve

Higher productivity

Application 3: A decrease in matching efficiency, e

I no change in the total surplus of the match, z − b

I no change in outside options or wages, w = b + a(z − b)

I lower e reduces chances of forming a match

I → the lower chances of finding a worker reduce job creation,i.e. fewer vacancies posted, A ↓, less tight labor market, j ↓

I → the lower chances of finding a job reduces the number ofpeople searching for work⇒ reduces the labor force, Q ↓

I unemployment rate increases, u = 1− em(1, j)

I aggregate output falls, Y = Qem(1, j)z

I vacancy rate in equilibrium constanttwo opposing effects: e ↓→ v ↑ and j ↓→ v ↓

v = 1− em

(1

j, 1

)= 1− k

(1− a)(z − b)

Lower matching efficiency

Decrease in matching efficiency in the great recession?

I a decrease in matching efficiency implies a rightward shift ofthe Beveridge curve, a decrease in the labor force, higherunemployment, and lower aggregate output

I just as experienced in the recent recessionI what can be the cause of a decrease in matching efficiency?

I worse information about vacancies and searching workers→ not a very plausible explanation for the labor marketoutcome of this recession

I mismatch between skills firms needed and skills workers possess→ possibly if there are sectoral shocks, and workers leavingdeclining industries do not have skills required by growingindustries

I mismatch between locations of vacancies posted and whereworkers search→ quite relevant for financial crises: many workers are notselling their ’underwater’ houses to move to differentgeographical area

Decrease in matching efficiency in the great recession?

I a decrease in matching efficiency implies a rightward shift ofthe Beveridge curve, a decrease in the labor force, higherunemployment, and lower aggregate output

I just as experienced in the recent recessionI what can be the cause of a decrease in matching efficiency?

I worse information about vacancies and searching workers→ not a very plausible explanation for the labor marketoutcome of this recession

I mismatch between skills firms needed and skills workers possess→ possibly if there are sectoral shocks, and workers leavingdeclining industries do not have skills required by growingindustries

I mismatch between locations of vacancies posted and whereworkers search→ quite relevant for financial crises: many workers are notselling their ’underwater’ houses to move to differentgeographical area

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Intermediate Macroeconomics - Lecture 8 - Search and ...econ.sciences-po.fr/sites/default/files/file/barany/int_macro/... · Intermediate Macroeconomics Lecture 8 - Search and Unemployment