Wage Dispersion (3) Search Frictions

Question 1

In the following wage equation estimated in a series of papers, explain the key parameters/variables:

wit = βXit+ μi + ψj(i,t) + εit

Answer 1

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

Question 2

In the given wage equation below, in what case is there no wage dispersion?

wit = βXit+ μi + ψj(i,t) + εit

Answer 2

No wage dispersion if there is no variance in εit

Question 3

What is the conclusion of the theory under the perfectly competitive market framework?

(2 points)

Answer 3

There should be no wage dispersion amongst homogeneous workers because

Wage = Marginal Productivity (and this is the same for all workers)

Question 4

Under what circumstances does the theory of compensating differentials predict no wage dispersion?

Answer 4

Under perfect competition for homogeneous firms and workers

Question 5

What models predict possible wage dispersion?

What do these models assume?

Answer 5

Asymmetrical information models

Assume ex ante that there is heterogeneity among workers

Question 6

What is assumed for the search frictions model?

Answer 6

Workers and firms are homogeneous

Search frictions exist

Question 7

What is the setup for the search frictions model?

5 points

Answer 7

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

Question 8

How is the CDF denoted in the search frictions model?

What does it capture in equilibrium?

Answer 8

F

In equilibrium the CDF captures the distribution of wages posted by firms

Question 9

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?

Answer 9

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

Question 10

In terms of CDFs, in what case will there be wage dispersion in equilibrium?

Answer 10

Wage dispersion iff there are no mass points

Question 11

If there is a mass point in a CDF diagram then what can we conclude regarding wage dispersion in equilibrium?

Answer 11

There is no wage dispersion

Question 12

In the search frictions model, what must be the case for wage dispersion to exist?

Answer 12

There must be search frictions

Question 13

What does “search frictions” mean?

Answer 13

It means that firms/workers don’t instantaneously have access to all applicants/jobs

Question 14

What is the cost of searching?

Answer 14

The cost (c) that the worker must pay in order to be able to sample a job offer from distribution (F)

Question 15

What is the meaning of “non-directive search”?

Answer 15

Workers sampling of job offers is random - they cannot search only for high wage jobs

Question 16

If the worker samples (x) jobs from the distribution (F) then what cost do they pay?

Answer 16

Search costs = cx

Question 17

Summarise the steps of the search frictions model

Answer 17

1. Firms post wages
2. Worker samples a desired number of offers (all at once)
3. Workers decide which job to take

Question 18

What wage will firms post?

Answer 18

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

Question 19

Outline the CDF considering firms will post wages where

b≤w≤p

Explain each.

Answer 19

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

Question 20

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?

Answer 20

λ(1)

λ(n)

i.e. (n) denotes the total number of offers

Question 21

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)

Answer 21

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)

Question 22

Denote the probability that, when there are 2 firms involved, a worker accepts the offer (w) from a firm

Explain

Answer 22

F(w)

Because the probability of accepting = the probability that the other firm offers below (w)

Question 23

If there are 3 firms involved then what is the probability that the worker will accept the wage (w) of one firm?

Answer 23

F(w) x F(w)

= [F(w)]^2

Question 24

If there are 3 OTHER firms involved then what is the probability that the worker will accept the wage (w) of the firm?

Answer 24

F(w) x F(w) x F(w)

= [F(w)]^3

Question 25

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

Answer 25

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+⋯

Question 26

How can you relate profits to the CDF?

Answer 26

If the CDF is continuous then profits will be continuous. If the CDF has mass points then so too will profits

Question 27

Explain why there can be no mass points in equilibrium (consider mass point w̅)

(2 points)

Link this to wage dispersion

Answer 27

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

Question 28

What happens if we remove search frictions from this model?

Answer 28

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

Question 29

What will the wage be if search frictions are removed from the model?

Answer 29

Model reverts to the perfectly competitive model

Hence wage = productivity (p)

Question 30

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)

Answer 30

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