Review

1
Review

• Given the scenario below, the firm should hire
• A. High school educated workers
• B. College educated workers
• C. A mix of both

isoquant
Qhs
isocost
Qcollege
2
Chapter 2

• Recruitment

3
Opinion poll

• Do applicants to highly skilled jobs tend to be
  qualified for these jobs?
• A. Yes, almost always
• B. No, they are often not qualified

4
Opinion poll

• Do applicants to highly skilled jobs tend to be
  qualified for these jobs?
• A. Yes, almost always
• B. No, they are often not qualified
• CNN Article Many employers consider more than
  half of all applicants to be unqualified.
• Adverse Selection

5
Reading for next class

• http//www.bepress.com/cgi/viewcontent.cgi?article
  1097contextev
• Or
• http//www.econ.ucsb.edu/babcock/EconomitVoice.pd
  f

6
Chapter 2 Motivation and Themes

• In the last chapter, we looked at whether firms
  should hire high or low skill workers. But
• Say, the firm has decided it wants skilled
  workers
• How does it go about hiring them?
• Big problem Adverse selection

7
Hiring the Right People

• How do you find the most able people for a given
  job?
• High wages?
• Suppose worker prod in all firms is equal and
  they know productivity but firms do not
• Say firm pays the average wage
• Will it get workers who are
• A. Better than average
• B. Less than average
• C. Average

8
Adverse Selection

• If firm offers 20/hr then only workers with
  lt20/hr productivity are apt to apply
• This is called Adverse Selection

Distribution of Productivities
Density
W
9
Solutions

• Pay to screen workers
• Often impractical
• Offer probation wages
• Require credential

10
Probation wage

• If you cannot observe a workers true
  productivity, then
• Use low initial wage to keep low-productivity
  workers away.
• Offer big raise to those who are not fired after
  first period (to attract productive workers)

11
Model of Probation Wage

• Assume
• 2 periods, interest rate0.
• Unskilled wage (outside option) is WU
• Skilled wage (outside option) is WS WU G
• Your firm pays W1 in period 1, W2 in period 2
• How do you choose W1 and W2?

• Goal 1 Attract skilled
• Must offer SUM over 2 periods that at least
  matches what skilled worker could get elsewhere
• W1W2gt2WS
• For simplicity set W1W22WS
• Goal 2 Repel Unskilled
• W1ltWU
• For simplicity W1WU

12
Optimal Strategy

• Goal 1 Attract skilled
• Must offer SUM over 2 periods that at least
  matches what skilled worker could get elsewhere
• W1W2gt2WS
• For simplicity set W1W22WS
• Goal 2 Repel Unskilled
• W1ltWU
• For simplicity W1WU

• Just substitute in
• W1W22WS
• WUW22WS
• W22Ws-Wu
• W22(WuG) Wu
• W2Wu2G
• Proposition 1 As premium G earned by skilled
  workers in the general market rises, the gap
  between period 1 and period 2 wage must rise.

13
Graphical Representation

• In practice, could offer W1WU-e, W2Wu2G e

WSG
WS
WS-G WU
Period 1
Period 2
14
Extension

• Assume P prob unskilled worker doesnt get
  detected
• Goal 1 Attract skilled
• W1W22WS,
• Goal 2 Repel Unskilled
• W1PW2 (1-P) WUlt2WU
• Substitute in
• W12WS- W2
• (2Ws-W2)PW2(1-P) WUlt2WU
• (P-1) W2lt2WU-(1-P) WU- 2WS
• W2gt2WU-(1-P) WU- 2WS
• (P-1)
• W2gtWUPWU-2WS
• (P-1)

• W22WS-WU-PWU
• (1-P)
• GW2-W1
• GW2-(2WS- W2)
• G2W2-2WS
• G2 (2WS-WU-PWU) -2WS
• (1-P)
• G4WS-2WS(1-P)-2(1P) WU
• (1-P)
• G2WS2WSP-2(1P) WU
• (1-P)
• G2 (1P) (WS-WU)
• (1-P)

15
Interpretation

• G2 (1P) (WS-WU) (1-P)
• If P goes up what happens to G?
• A. G?
• B. G?
• C. Cant tell
• P??G?

16
Punchline

• P??G?
• Proposition 2
• As the probability that less productive workers
  will not be detected rises, the probationary wage
  must fall and the wage paid after the end of the
  probationary period must rise.
• Intuition
• If unskilled workers now have a CHANCE to get the
  W2 payoff, must reduce the wage they now would
  get for sure in period 1 and increase wage paid
  in period 2, to lower the overall expected
  payment they get. (Increase in period 2 wage is
  necessary to keep skilled workers happy).

17
Question 1

• I am hiring workers. Im paying a probation wage
  in the first period. I want only skilled workers
  to apply, but Im still getting some unskilled
  workers.
• Should I pay a lower probation or higher
  probation wage?
• A. Lower
• B. Higher

WSG
WS
WS-GWU
Period 1
Period 2
18
2) Education credential as signal

• Mechanism
• Find an observable trait tied to productivity,
  e.g. education
• Credential (or signal) should be harder for
  low-productivity workers to acquire
• If wage gap between those with and without the
  credential is small, only most able will find it
  worth the effort to obtain.

19
Hazing

• http//www.youtube.com/watch?v2BLV1vdqzxgfeature
  related

20
Opinion Poll

• If you had to choose, which would you rather
  have?
• A. All the knowledge you gained in college, but
  no college degree
• B. The college degree, but none of the knowledge
  you gained

21
Signaling

• Assumptions for Signaling Theory of Spence
• 2 ability types, high and low.
• VMPhigtVMPlo
• Asymmetric information
• Firms dont know ability type
• Workers do
• More able workers have lower costs of schooling
• Lower effort costs, enjoy school more, find it
  easier, have more time for work or other things

22
Equilibrium Notion

• Firms best-respond to workers, workers
  best-respond to firms.
• Both end up correct in their beliefs about what
  other will do.
• Example Equilibrium Demonstrations in former
  Soviet Union
• You get shot if you show up and no one else does.
  
• You overthrow the government if everyone shows
  up.
• I believe no one else will show up, so I dont
  show up.
• Everyone else believes no one will show up
• No one shows up.
• Equilibrium. Beliefs are not falsified
• Example Not an equilibrium Roommates
• I believe you will do the dishes, so I dont do
  them
• You believe I will do the dishes, so you dont do
  them
• No one does the dishes
• Not self-sustaining. Beliefs will be falsified

23
Spence Signaling Equilibrium - Graphically

• Firm strategy
• Pay VMPH to those who get s yrs of schooling
• Belief these will be high types
• Pay VMPL to those who dont
• Belief these will be low types
• Workers strategy
• Get s yrs if high type
• Get 0 yrs if low type
• Belief firms will pay VMPH to those with s yrs,
  VMPL to others

• CHltCL
• VMPHProd of high types
• VMPLProd of low types

CL
VMPH
CH
VMPL
s
24
Spence Signaling Equilibrium - Graphically

• Is there s that makes both workers and firms
  strategies a best choice, and their beliefs
  correct?

• CHltCL
• VMPHProd of high types
• VMPLProd of low types

CL
VMPH
CH
VMPL
s
s
25
Spence Signaling Equilibrium - Graphically

• Why does s work?
• Low types get
• VMPL-0 if no schooling
• VMPH-C0 if s years
• These values are equal
• Deters low skill types from s yrs (degree)
• High types get
• VMPL-0 if no schooling
• VMPH-C1 if s years
• VMPH-C1gtVMPL
• So high types get s yrs
• Firm is right. Workers are right. Beliefs not
  falsified

• This is called a separating equilibrium.

CL
VMPH
CH
C0
VMPL
C1
s
s
26
Spence Signaling Equilibrium - Graphically

• Not an equilibrium, because firms beliefs
  falsified

• What if s chosen as cut-off by firms?
• Do low types choose to get s years of schooling?
• A. Yes
• B. No
• C. Cant tell
• Yes, because get more utility than from VMPL.
• Effort cost not high enough to deter them
• Firm would end up paying low types VMPH
• But their prod is VMPL
• Firm loses money, goes out of business

CL
VMPH
CH
VMPL
s
S
27
Spence Signaling Equilibrium - Graphically

• What if s is chosen as cut-off by firms?
• Do low types choose to get s years of
  schooling?
• A. Yes
• B. No
• C. Cant tell
• No -- get more utility from VMPL.
• Do high types get s years of schooling?
• Yes -- get more utility from (VMPH-effort cost).
• Many equilibria exist
• S was the lowest s that still resulted in a
  separating equilibrium

CL
VMPH
CH
VMPL
s
S
28
Spence Signaling Equilibrium - Graphically

• What if s is chosen as cut-off by firms?
• Do low types choose to get s years of
  schooling?
• No, because get more utility from VMPL.
• Do high types s years of schooling?
• A. Yes
• B. No
• C. Cant tell
• No, because get more utility from VMPL.
• Nobody gets schooling
• Pooling Equilibrium
• (Uninteresting case)

CL
VMPH
CH
VMPL
s
S
29
Notes - Spence Signaling Equilibrium

• Here, schooling does not increase productivity
• Only gives evidence of pre-existing ability
• Schools as social evil
• Expensive signal. Resources thrown away.
• Is there a better way?
• Should we outlaw discrimination on the basis of
  education?

CL
VMPH
CH
VMPL
s
s
30
Is Schooling Only a Signal?

• Counterarguments
• Vocational aspects of education increase
  productivity
• Surgeon
• Engineer.
• Wouldnt firms/workers both be better off with
  contingent contract?
• Worker accepts lower wage in period 1, firm
  agrees to raise wage if worker high ability
• Cheaper for everyone than wasting 4 years in
  college!

CL
VMPH
CH
VMPL
s
s
31
Empirical Evidence

• Goes both ways
• Wolpin
• Self-employed acquire just as much ed as
  employees.
• Why, unless it increases prod?
• Who do they impress??
• Weiss
• Found dropouts and high school grads equally
  productive, but lower quit rates for grads.
• Implies signaling.

CL
VMPH
CH
VMPL
s
s
32
When is education more likely to raise prody?

• When specific skills taught map closely and very
  directly to skills used on the job
• Engineering
• Law
• Medicine
• MBA

33
Question

• In which setting is college degree more apt to
  capture productivity gains achieved through
  education and less apt to be purely a signal of
  pre-existing ability?
• A. Brain surgeon
• B. Car salesman

34
Signaling Extenions Fraternities and Hazing

• Frats provide benefits
• But need members to provide public goods
• Participate enthusiastically
• Organize parties, etc.
• Worry about free-riders
• Cant tell if applicants are free-riders (F) or
  committed (C)
• Use hazing H to get applicants to reveal types
• CFgtCC

CF
VMPC
CC
VMPF
H
H
35
Signaling Extensions - Gangsters

• Your run a crime gang
• Two types Mob types and FBI informants
• Potential gangsters know their types but you do
  not
• Cost of committing violent crime higher for FBI
  types
• Require v violence before you will hire worker

CFBI
VMPM
CM
VMPFBI
V
V
36
How many years of schooling above should firms
require for the high wage job?
Clo

VMPhi
Chi
VMPlo
s
1
2
3
4
5

• A. 1 B. 2 C. 3 D. 4 E. 5