2-SIDED SEARCH MODEL Flashcards

(45 cards)

1
Q

We use a simplified version of … model

A

DMP = Diamond, Mortensen and Pissarides.

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2
Q

How many consumers?

A

N

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3
Q

How many in LF?

A

Q

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4
Q

Consumers join the LF based on…

A

the expected payoff to searching for a job.

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5
Q

Supply curve =

A

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

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6
Q

Firms can only produce if…

A

They post and vacancy and hire 1 worker

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7
Q

Cost of posting vacancy =

A

K = in terms of final good

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8
Q

Number of firms posting vacancies =

A

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

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9
Q

Z =

A

Output produced by the worker / productivity of the worker.

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10
Q

Search frictions imply that

A

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.

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11
Q

Matching fucntion

A

M = em(Q, A)

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12
Q

e =

A

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

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13
Q

4 properties of m(Q, A)

A
  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.
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14
Q

Probability of consumers finding a job =

A

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

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15
Q

j =

A

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

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16
Q

High j =

A

Good for consumers

Bad for firms since lots of A but fewer Q

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17
Q

Expected consumer payoff from searching in equilibrium =

A
P(Q) = pcw + (1-pc)b
P(Q) = b + em(1, j)(w - b)
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18
Q

How does j affect P(Q)?

A

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

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19
Q

Probability of firms filling a vacancy

A

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

20
Q

What do we assume about firms?

A

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

21
Q

Firm free entry conditon

A

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

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

22
Q

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

A

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

23
Q

How is equilibrium wage determined?

A

According to Nash bargaining theory

24
Q

2 things the outcome of wage bargaining depends on

A
  1. relative bargaining power

2. next-best alternative

25
Worker, firm and total surplus from an agreement
worker surplus = w - b firm = z - w Total = z - b
26
What else does Nash assume about bargaining process?
That each part receives a fraction of total surplus. a = worker bargaining power.
27
SO: equilibrium wage =
W = az + (1-a)b
28
Supply-side equilibrium equation
P(Q) = b + em(1, j) a(z-b)
29
demand-side equilibrium equation
em(1/j, 1) = k/(1-a)(z-b)
30
Urate in equilibrium =
U = Q(1-pc)/Q = (1-pc) = 1 - em(1, j)
31
Vacancy rate in equilibrium =
V = A(1-Pf)/A = (1-pf) = 1 - em(1/j, 1)
32
Aggregate output
Y = Mz = Qem(1, j)z
33
How does a productivity shock affect demand side?
Higher z = higher firm surplus from posting vacancy. | To be kept indifferent, need Pf to fall = j rises = more labour market tightness.
34
How does a productivity shock affect supply side? (2)
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
35
SO how does productivity shock affect the economy?
LF participation increases pf falls = vacancy rate rises pc rises as j rises = u rate falls
36
does 2-sided model explain data well in productivity shock?
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.
37
How could we improve the 2 sided model to make fluctuations in unemployment more data consistent?
Include wage rigidity as well.
38
Impact of higher b demand-side
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.
39
Impact of higher b supply-side
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.
40
Hw does higher b affect vacancy rate?
V = 1 - pf = 1 - em(1/j, 1) | Higher b means j must fall as compensation = lower vacancy rate.
41
Hw does higher b affect urate?
U = 1 - pc = 1 - em(1, j) | j falls = U rises
42
Micro vs macro ways b increases unemployment
``` Micro = one-sided model = higher U due to higher reservation wage. Macro = 2 sided = higher U due to lower vacancies. ```
43
Micro evidence on impact of b on urate
Meyer 1990 Just before benefits about to expire, Pc rises = Moral hazard - look harder for job / accept lower offer when benefits about to expire.§
44
Macro evidence on impact of b on urate
Compare US states after Great recession as changes in b different, but other characteristics the same. b led to slow recovery of employment.
45
Why may higher b in a recession not actually be that harmful?
Because high U mainly due to few vacancies, not about search effort.