2-SIDED SEARCH MODEL

Question 1

We use a simplified version of … model

Answer 1

DMP = Diamond, Mortensen and Pissarides.

Question 2

How many consumers?

Answer 2

N

Question 3

How many in LF?

Answer 3

Q

Question 4

Consumers join the LF based on…

Answer 4

the expected payoff to searching for a job.

Question 5

Supply curve =

Answer 5

P(Q) = the expected payoff needed to induce Q consumers to search for a job. (i.e. be part of LF)

Question 6

Firms can only produce if…

Answer 6

They post and vacancy and hire 1 worker

Question 7

Cost of posting vacancy =

Answer 7

K = in terms of final good

Question 8

Number of firms posting vacancies =

Answer 8

A = number of vacancies since each firm only posts 1.

Question 9

Z =

Answer 9

Output produced by the worker / productivity of the worker.

Question 10

Search frictions imply that

Answer 10

Not all workers searching for a job will find one, and not all firms searching for a worker will find one = can have unemployed workers & vacancies at the same time.

Question 11

Matching fucntion

Answer 11

M = em(Q, A)

Question 12

e =

Answer 12

the efficiency of the matching process for given level of A and Q.

Question 13

4 properties of m(Q, A)

Answer 13

1. CRS
2. 0 if any Q or A 0
3. Increasing in Q and A
4. Diminishing marginal products - increase in matches induced by extra Q/A larger if A/Q smaller.

Question 14

Probability of consumers finding a job =

Answer 14

Pc = M / Q = em(Q, A) / Q = em(1, j) by CRS

Question 15

j =

Answer 15

j = A / Q = labour market tightness from firm’s perspective.

Question 16

High j =

Answer 16

Good for consumers

Bad for firms since lots of A but fewer Q

Question 17

Expected consumer payoff from searching in equilibrium =

Answer 17

P(Q) = pcw + (1-pc)b
P(Q) = b + em(1, j)(w - b)

Question 18

How does j affect P(Q)?

Answer 18

higher j =easier for workers to find a job = higher P(Q) = higher Q i.e. LF participation.

Question 19

Probability of firms filling a vacancy

Answer 19

Pf = M / A = em(Q, A) / A = em(1/j, 1) by CRS

Question 20

What do we assume about firms?

Answer 20

FREE ENTRY –> firms post vacancies until expected payoff = 0 otherwise more firms would enter and post vacancies.

Question 21

Firm free entry conditon

Answer 21

Pf(Z - W - K) = (1-Pf)K

em(1/j, 1) = k / (z - w)

Question 22

Given that the free entry equality must hold, what happens if K rises?

Answer 22

K rises = higher cost to post vacancy = RHS rises

For firm to still be indifferent, need LHS rise too = lower j = easier to find workers

Question 23

How is equilibrium wage determined?

Answer 23

According to Nash bargaining theory

Question 24

2 things the outcome of wage bargaining depends on

Answer 24

1. relative bargaining power

2. next-best alternative

Question 25

Worker, firm and total surplus from an agreement

Answer 25

worker surplus = w - b
firm = z - w
Total = z - b

Question 26

What else does Nash assume about bargaining process?

Answer 26

That each part receives a fraction of total surplus. a = worker bargaining power.

Question 27

SO: equilibrium wage =

Answer 27

W = az + (1-a)b

Question 28

Supply-side equilibrium equation

Answer 28

P(Q) = b + em(1, j) a(z-b)

Question 29

demand-side equilibrium equation

Answer 29

em(1/j, 1) = k/(1-a)(z-b)

Question 30

Urate in equilibrium =

Answer 30

U = Q(1-pc)/Q = (1-pc) = 1 - em(1, j)

Question 31

Vacancy rate in equilibrium =

Answer 31

V = A(1-Pf)/A = (1-pf) = 1 - em(1/j, 1)

Question 32

Aggregate output

Answer 32

Y = Mz = Qem(1, j)z

Question 33

How does a productivity shock affect demand side?

Answer 33

Higher z = higher firm surplus from posting vacancy.

To be kept indifferent, need Pf to fall = j rises = more labour market tightness.

Question 34

How does a productivity shock affect supply side? (2)

Answer 34

1. Movement along P(Q): from firm’s response, j rises = move along P(Q) = Q rises
2. P(Q) shifts up since higher z = bargain higher w = P(Q) rises for given level of j

Question 35

SO how does productivity shock affect the economy?

Answer 35

LF participation increases
pf falls = vacancy rate rises
pc rises as j rises = u rate falls

Question 36

does 2-sided model explain data well in productivity shock?

Answer 36

1. LR: explains higher LF due to higher z, but not since 2000.
2. explains BC changes in urate, vrate and LF qualitatively, but not quantitatively.

Question 37

How could we improve the 2 sided model to make fluctuations in unemployment more data consistent?

Answer 37

Include wage rigidity as well.

Question 38

Impact of higher b demand-side

Answer 38

Higher b = workers can bargain higher wages = less attractive to open vacancies. To keep firms indifferent, need pf to rise = j falls so it’s easier to find workers.

Question 39

Impact of higher b supply-side

Answer 39

1. j falls = Q contracts along curve in response to firm response as fewer vacancies
2. But shift up as higher b = greater incentive to be in LF, plus can negotiate higher wages = Q rises
   So overall effect on LF and GDP ambiguous.

Question 40

Hw does higher b affect vacancy rate?

Answer 40

V = 1 - pf = 1 - em(1/j, 1)

Higher b means j must fall as compensation = lower vacancy rate.

Question 41

Hw does higher b affect urate?

Answer 41

U = 1 - pc = 1 - em(1, j)

j falls = U rises

Question 42

Micro vs macro ways b increases unemployment

Answer 42

Micro = one-sided model = higher U due to higher reservation wage.
Macro = 2 sided = higher U due to lower vacancies.

Question 43

Micro evidence on impact of b on urate

Answer 43

Meyer 1990
Just before benefits about to expire, Pc rises = Moral hazard - look harder for job / accept lower offer when benefits about to expire.§

Question 44

Macro evidence on impact of b on urate

Answer 44

Compare US states after Great recession as changes in b different, but other characteristics the same. b led to slow recovery of employment.

Question 45

Why may higher b in a recession not actually be that harmful?

Answer 45

Because high U mainly due to few vacancies, not about search effort.