2-SIDED SEARCH MODEL Flashcards
We use a simplified version of … model
DMP = Diamond, Mortensen and Pissarides.
How many consumers?
N
How many in LF?
Q
Consumers join the LF based on…
the expected payoff to searching for a job.
Supply curve =
P(Q) = the expected payoff needed to induce Q consumers to search for a job. (i.e. be part of LF)
Firms can only produce if…
They post and vacancy and hire 1 worker
Cost of posting vacancy =
K = in terms of final good
Number of firms posting vacancies =
A = number of vacancies since each firm only posts 1.
Z =
Output produced by the worker / productivity of the worker.
Search frictions imply that
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.
Matching fucntion
M = em(Q, A)
e =
the efficiency of the matching process for given level of A and Q.
4 properties of m(Q, A)
- CRS
- 0 if any Q or A 0
- Increasing in Q and A
- Diminishing marginal products - increase in matches induced by extra Q/A larger if A/Q smaller.
Probability of consumers finding a job =
Pc = M / Q = em(Q, A) / Q = em(1, j) by CRS
j =
j = A / Q = labour market tightness from firm’s perspective.
High j =
Good for consumers
Bad for firms since lots of A but fewer Q
Expected consumer payoff from searching in equilibrium =
P(Q) = pcw + (1-pc)b P(Q) = b + em(1, j)(w - b)
How does j affect P(Q)?
higher j =easier for workers to find a job = higher P(Q) = higher Q i.e. LF participation.
Probability of firms filling a vacancy
Pf = M / A = em(Q, A) / A = em(1/j, 1) by CRS
What do we assume about firms?
FREE ENTRY –> firms post vacancies until expected payoff = 0 otherwise more firms would enter and post vacancies.
Firm free entry conditon
Pf(Z - W - K) = (1-Pf)K
em(1/j, 1) = k / (z - w)
Given that the free entry equality must hold, what happens if K rises?
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
How is equilibrium wage determined?
According to Nash bargaining theory
2 things the outcome of wage bargaining depends on
- relative bargaining power
2. next-best alternative
Worker, firm and total surplus from an agreement
worker surplus = w - b
firm = z - w
Total = z - b
What else does Nash assume about bargaining process?
That each part receives a fraction of total surplus. a = worker bargaining power.
SO: equilibrium wage =
W = az + (1-a)b
Supply-side equilibrium equation
P(Q) = b + em(1, j) a(z-b)
demand-side equilibrium equation
em(1/j, 1) = k/(1-a)(z-b)
Urate in equilibrium =
U = Q(1-pc)/Q = (1-pc) = 1 - em(1, j)
Vacancy rate in equilibrium =
V = A(1-Pf)/A = (1-pf) = 1 - em(1/j, 1)
Aggregate output
Y = Mz = Qem(1, j)z
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.
How does a productivity shock affect supply side? (2)
- Movement along P(Q): from firm’s response, j rises = move along P(Q) = Q rises
- P(Q) shifts up since higher z = bargain higher w = P(Q) rises for given level of j
SO how does productivity shock affect the economy?
LF participation increases
pf falls = vacancy rate rises
pc rises as j rises = u rate falls
does 2-sided model explain data well in productivity shock?
- LR: explains higher LF due to higher z, but not since 2000.
- explains BC changes in urate, vrate and LF qualitatively, but not quantitatively.
How could we improve the 2 sided model to make fluctuations in unemployment more data consistent?
Include wage rigidity as well.
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.
Impact of higher b supply-side
- j falls = Q contracts along curve in response to firm response as fewer vacancies
- 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.
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.
Hw does higher b affect urate?
U = 1 - pc = 1 - em(1, j)
j falls = U rises
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.
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.§
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.
Why may higher b in a recession not actually be that harmful?
Because high U mainly due to few vacancies, not about search effort.
