Wage Dispersion (3) Search Frictions Flashcards
In the following wage equation estimated in a series of papers, explain the key parameters/variables:
wit = βXit+ μi + ψj(i,t) + εit
For worker (i) and firm (j) at time (t)
Xit = individual HH characteristics
μi = worker effect (effect of the same worker across different firms)
ψj(i,t) = firm effect (effect of same firm across different workers
εit = unexplained element, once worker and firm effects are controlled for
In the given wage equation below, in what case is there no wage dispersion?
wit = βXit+ μi + ψj(i,t) + εit
No wage dispersion if there is no variance in εit
What is the conclusion of the theory under the perfectly competitive market framework?
(2 points)
There should be no wage dispersion amongst homogeneous workers because
Wage = Marginal Productivity (and this is the same for all workers)
Under what circumstances does the theory of compensating differentials predict no wage dispersion?
Under perfect competition for homogeneous firms and workers
What models predict possible wage dispersion?
What do these models assume?
Asymmetrical information models
Assume ex ante that there is heterogeneity among workers
What is assumed for the search frictions model?
Workers and firms are homogeneous
Search frictions exist
What is the setup for the search frictions model?
5 points
Continuum of homogeneous firms and workers
Firms post wage offers
Workers sample offers and decide which to accept
If worker takes the job then they produce (p) // If they don’t take the job then they receive benefits (b)
Assumes constant returns to scale
How is the CDF denoted in the search frictions model?
What does it capture in equilibrium?
F
In equilibrium the CDF captures the distribution of wages posted by firms
What does a “mass point” look like on a CDF diagram? (y-axis = wage, x-axis = proportion)
What about if there are multiple mass points?
If there is a mass point at (w1) then there will be a vertical line at that point
There will be a “step” pattern, with a vertical line at each mass point
In terms of CDFs, in what case will there be wage dispersion in equilibrium?
Wage dispersion iff there are no mass points
If there is a mass point in a CDF diagram then what can we conclude regarding wage dispersion in equilibrium?
There is no wage dispersion
In the search frictions model, what must be the case for wage dispersion to exist?
There must be search frictions
What does “search frictions” mean?
It means that firms/workers don’t instantaneously have access to all applicants/jobs
What is the cost of searching?
The cost (c) that the worker must pay in order to be able to sample a job offer from distribution (F)
What is the meaning of “non-directive search”?
Workers sampling of job offers is random - they cannot search only for high wage jobs
If the worker samples (x) jobs from the distribution (F) then what cost do they pay?
Search costs = cx
Summarise the steps of the search frictions model
- Firms post wages
- Worker samples a desired number of offers (all at once)
- Workers decide which job to take
What wage will firms post?
Nothing above prod level (p) as this would cause profits to be negative
Nothing below (b) as workers would not participate
Posted wage will be a best response given workers search behaviour
Outline the CDF considering firms will post wages where
b≤w≤p
Explain each.
CDF at (b) = 0 i.e. F(b) = 0 because no one earns below this
CDF at (p) = 1 i.e. F(p) = 1 because it would be unprofitable for firms to offer wages above this
Denote the probability that:
i) The worker is sampling only 1 offer
ii) The firm competes with (n-1) other firms from which the worker has sampled offers
What does (n) denote?
λ(1)
λ(n)
i.e. (n) denotes the total number of offers
If a worker samples two offers, from firms A and B, under what circumstances will they accept an offer from A?
Hence verbally explain the probability that the worker accepts As offer (wA)
The worker will accept As offer (wA) if the offered wage is higher than the wage offered by B (wB)
Probabililty of accepting As offer = the probability that Bs offer is below (wA)
Denote the probability that, when there are 2 firms involved, a worker accepts the offer (w) from a firm
Explain
F(w)
Because the probability of accepting = the probability that the other firm offers below (w)
If there are 3 firms involved then what is the probability that the worker will accept the wage (w) of one firm?
F(w) x F(w)
= [F(w)]^2
If there are 3 OTHER firms involved then what is the probability that the worker will accept the wage (w) of the firm?
F(w) x F(w) x F(w)
= [F(w)]^3
Give the general form of the probability that the firm offering (w) eventually hires a worker
Explain
Give the expansion of this up to n=3
H(w)= ∑(n=1)^∞ λ(n) [F(w)]^(n-1)
i.e. the sum of the probability of there being (n) firms competing in total * the probability of the worker accepting this firm over all of the others
H(w) = λ(1)+ λ(2)F(w)+ λ(3) [F(w)]^2+⋯
How can you relate profits to the CDF?
If the CDF is continuous then profits will be continuous. If the CDF has mass points then so too will profits
Explain why there can be no mass points in equilibrium (consider mass point w̅)
(2 points)
Link this to wage dispersion
If there is a mass point at w̅ then any firm that posts a wage above it (w̅+ε) can poach some extra workers, i.e its probability of hiring (H(w)) will increase a bit H(w̅+ε)
Because of the existence of this incentive, it must be that in an equilibrium, mass points do not exist.
Hence there must be wage dispersion (where there is a continuum of wages) in equilibrium
What happens if we remove search frictions from this model?
No frictions => no costs => c=0
Workers can sample all job offers
=> Any firm that offers less than other firms has zero chance of hiring
=> Firms will outbid eachother to zero profits i.e. we revert back to the perfectly competitive model
What will the wage be if search frictions are removed from the model?
Model reverts to the perfectly competitive model
Hence wage = productivity (p)
What happens to firms wage offers if search costs are very high?
Why might the worker not search at all in this case?
(3 points in total)
Firms know that they are the only offer being viewed so can offer the lowest possible wage: (b)
Workers won’t search if the wage = (b) because their benefit from searching and getting a job = b - c ; whereas their benefit from not searching = b (unemployment benefit)
b > b - c => no incentive to search
