A presentation based on Chapter 13 of the Microeconomics Book from Winston, Mas-Collel

1. Adverse Selection, Signaling, Screening
Adverse Selection, Signaling, Screening
Timo Grote
December 1, 2013

2. Adverse Selection, Signaling, Screening
1 Introduction
2 Adverse Selection
3 Signaling
4 Screening
5 Conclusion

3. Adverse Selection, Signaling, Screening
Introduction
Motivation
Where do we have perfect information in our daily life?
How important are information assymetries in buisness
and economics?
Typical Examples:
Second-hand markets (used car market)
Labor market
insurance market
credit market in developing countries

4. Adverse Selection, Signaling, Screening
Introduction
Motivation
The economics of information were developed in the 70s
with:
”The market of Lemons”(1970) by George Akerlof
Michael Spence´s ”Job Market Signaling”(1972)
Joseph Stiglitz essay: ”The Theory of Screening,
Education and the Distribution of Income” (1975)
These Contributions were awarded with the nobel prize in
2001

5. Adverse Selection, Signaling, Screening
Adverse Selection
The Model
Adverse Selection: exists whens information between
interacting units are assymetrically distributed and determine
welfare inefficient market outcomes
Assumption of an enhanced Akerlof model (1970):
Many identical (potential) firms hiring workers
Identical constant returns to scale technology, with labor
as the only input=output: θ
Maximization of profits under risk neutrality and
pricetaking behaviour
Workers differ in productivity level θ ∈ (θ, θ) ⊂ R with
0≤θ<θ<∞
Distribution function F (θ) associated with the continous
density function f (θ) = F (θ) > 0
Workers can earn r (θ) when they work at home

6. Adverse Selection, Signaling, Screening
Adverse Selection
The Model
Worker´s perspective
are maximizing their profits facing a trade off between
working in a firm or at home
as productivity is publically observable workers work in
firms for w ∗ (θ) = θ
number of workers employed is {θ : r (θ) ≤ θ}
The sum of aggregate surplus:
θ
N[I (θ)θ + (1 − I (θ))r (θ)]dF (θ) where I (θ) is either 0
θ
or 1
Sum of agregate surplus is maximized if:
I(θ)=
1 if θ ≥ r (θ)
0 otherwise

7. Adverse Selection, Signaling, Screening
Adverse Selection
The Model
If worker productivity is not observable:
w(θ) = w irrespective of type θ
now firms are only hiring workers under imperfect
information
Definition 13.B.1:
In the competitive labor market model with unobservable
worker productivity levels, a competitive equilibrium is a wage
rate w ∗ and a set Θ∗ of worker types who accept employment
such that
Θ∗ = θ : r (θ) ≤ w ∗ Condition (13.B.4)
w ∗ = E [θ|θ ∈ Θ∗ ] Condition (13.B.4)

8. Adverse Selection, Signaling, Screening
Adverse Selection
Pareto Inefficiency
Assume that r (θ) = r and F (r )ε(0, 1)
In an equilibrium Θ∗ is either [θ, θ] for w≥r or 0 for w< r
As the allocation of workers is not distinctive the ocurring
situation is pareto inefficient

9. Adverse Selection, Signaling, Screening
Adverse Selection
Competitive equilibrium with adverse selection
Additional Assumption: r(θ) varies with θ and r > 0
The result is a competitive equilibrium with adverse
selection(Figure 13.B.1):

10. Adverse Selection, Signaling, Screening
Adverse Selection
Complete market failure
One extreme case of adverse selection is that just low
ability workers are accepting w
The result is complete market failure(Figure 13.B.2):

11. Adverse Selection, Signaling, Screening
Adverse Selection
Multiple competitive equilibria
Another extreme case are multiple competitive equilibria
as the firm offers wages with a function E [θ|r (θ) ≤ w ]
The slope of the function varies with the density of
workers accepting the wage (Figure 13.B.3):

12. Adverse Selection, Signaling, Screening
Adverse Selection
Constrained Pareto Optima and Market
Intervention
The Constrained(Second-best) Pareto optimum is market
equilibrium that can not be improved by an external agent
Proposition 13.B.2: In the adverse selection labor market
model (where r(.) is strictly increasing with r(θ) ≤ θ for all
θ ∈ [θ, θ] and F (.) has an associated density f(.) with
f (θ) > 0 for all θ ∈ [θ, θ]), the highest-wage competitive
equilibrium is a constrained Pareto optimum

13. Adverse Selection, Signaling, Screening
Adverse Selection
Constrained Pareto Optima and Market
Intervention
Intuition:
If government could observe θ, it could implement a fully
Pareto optimal equilibrium
If all workers accept employment in the highest wage
equilibrium it is fully (and constrained)Pareto optimal
To move all workers to become employed in the highest
wage equilibrium can implement w e = w ∗ = r (θ∗ ) and
wu = 0
Aditionally the unemployed can be taxed to force them to
work wu < 0 (which is not Pareto improving)

14. Adverse Selection, Signaling, Screening
Adverse Selection
Constrained Pareto Optima and Market
Intervention
As the Pareto Improvement is not possible, the aggregate
surplus can be increased by
scheduling that every worker accepts employment
firms pay wage w = E [θ]
which leads to the social welfare function:
θ
N[I (θ)θ + (1 − I (θ))r (θ)]dF (θ)
θ
Whether an allocation is a constrained optimum depend
on the point at which the welfare evaluation is conducted

15. Adverse Selection, Signaling, Screening
Signaling
Model
Signaling: is the idea that the better informed party
credibly conveys the other one of its quality under
asymmetrical information
Model assumptions
Same assumptions as before
But only two types of workers:θH , θL with θH > θL > 0
and λ = Prob(θ = θH ∈ (0, 1))
Workers receive education level e for cost of c(e,θ) with
c(0, θ) = 0, ce (e, θ) > 0, cee (e, θ) > 0, cθ (e, θ) <
0 for all
e > 0 and ce,θ < 0
No human capital effect
Utility:
u(w , e|θ) = w − c(e, θ)
Home production r(θ) = 0 for all θ

16. Adverse Selection, Signaling, Screening
Signaling
Worker allocation process with signaling
Allocation of workers works as follows
1
2
3
4
Nature determines type of productivity
Worker choosing e dependent on his type
Firm makes offer conditional on e
Worker chooses rationally the best offer
Result: Perfect Bayesian equilibrium

17. Adverse Selection, Signaling, Screening
Signaling
Result
A set of strategies and a belief function µ(e) ∈ [0, 1]
giving the propability assesment that the worker has a
high ability given e is a PBE
The worker´s strategy is optimal given the firm´s
strategy
The belief functionµ(e) is derived from the worker´s
strategy using Bayes rule
The firms wage offers determined by e constitute a Nash
equilibrium of the simulatenous-move wage offer game in
which the propability of a high ability worker is µ(e)

18. Adverse Selection, Signaling, Screening
Signaling
The indifference curves cross once which is called the
single crossing property
Firms offer a wage w (e) = µ(e)θH + (1 − µ(e))θL

19. Adverse Selection, Signaling, Screening
Signaling
Seperating Equilibrium
Seperating equilibrium: Worker types choose different
education levels
Lemma 13.C.1:
In any seperating perfect Bayesian equilibrium the optimal
wages are:
w ∗ (e ∗ (θH )) = θH
w ∗ (e ∗ (θL )) = θL

20. Adverse Selection, Signaling, Screening
Signaling
Lemma 13.C.2: In any seperating perfect Bayesian equilibrium
e ∗ (θL ) = 0
Since education is shows productivity and is costly
L typ choose e = 0
H type choose e > 0

21. Adverse Selection, Signaling, Screening
Signaling
Welfare implications
Firms always make zero profits
Workers with productivity θL are worse off
Wokers with productivity θH are either better or worse off
High ability workers are worse off if
In a seperating equilibrium (0,E [θ]) is no longer available
If they choose e=0, they expect to receive w = θL
then forbidding signaling activity is Pareto improving
If the fraction of productive workers λ increase the
propability that θL workers are worse off increases

22. Adverse Selection, Signaling, Screening
Signaling
In a pooling equilibrium all workers choose the same level
of education e ∗ (θH ) = e ∗ (θL ) = e ∗
The optimal equilibrium wage is
w ∗ (e ∗ ) = λθH + (1 − λ)θL = E [θ]
Pooling equlibria with e > 0 are PBE but the Pareto
dominant education level is e=0

23. Adverse Selection, Signaling, Screening
Signaling
The intuitive criterion
Different types of equilibria can be sustained as PBE
Problem of the refinement, the ”Intuitive criterion” by
Cho and Kreps (1987):
The outcome of an equilibrium can only be Pareto
optimal if low ability workers have no incentive to signal
wrongly
If the ”Intuitive criterion” applies only the best
seperating equilibrium survives

24. Adverse Selection, Signaling, Screening
Signaling
Even the best seperating equilibrium can be pareto
dominated by a state without signaling activity
As high productive workers are better off, cross
subsidization in favor of low ability workers can pareto
improve the situation

25. Adverse Selection, Signaling, Screening
Screening
Screening: The uninformed side of the market takes
observations to reduce information assymmetry
Model:
Same framework as in Screening chapter
No education signaling, but firms create jobs with
different task levels
Task levels do not affect output, but decrease worker
utility
Utility function of θ:
u(w , t|θ) = w − c(t, θ)
with c(0, θ) = 0, ct > 0, ctt > 0, cθ < 0 and ctθ < 0

26. Adverse Selection, Signaling, Screening
Screening
The Situation is viewed as a two-stage game:
1
2
Two firms simultaneously offer a set of contracts(w,t)
The workers decide on whether and which contract to
accept
Proposition 13.D.1: In any SPNE of the screening game with
observable worker types a type θi worker accepts contract
(wi∗ , ti∗ ) = (θi , 0) and firms earn zero profits
Implications:
if w ∗ > θi firms make losses
if w ∗ < θi firms gain profits
if (wi∗ , ti∗ ) = (θi , t ) with t > 0 the firm could deviate
and underpay to gain positive profits

27. Adverse Selection, Signaling, Screening
Screening
Other Case: θ is unobservable for firms
Two types of equilibria:
pooling equilibria
seperating equilibria
Lemma 13.D.2 No pooling equilibria exit
In any pooling equilibrium workers of type θH would be
underpaid
Lemma 13.D.3 If (wL , tL ) and (wH , tH ) are the contracts
signed by the low- and high-ability workers in a seperating
equilibrium, then both contracts yield zero profits; that is,
wL =θL and wH =θH

28. Adverse Selection, Signaling, Screening
Screening
Lemma 13.D.3 If (wL , tL ) and (wH , tH ) are the contracts
signed by the low- and high-ability workers in a seperating
equilibrium, then both contracts yield zero profits; that is,
wL =θL and wH =θH

29. Adverse Selection, Signaling, Screening
Screening
Proposition 13.D.2 In any subgame perfect Nash equilibrium
of the screening game, low-ability workers accept contract
(θL ,0) and high ability workers accept (θH , tH ) where tH
satisfies θH − c(tH , θL ) = θL − c(0, θL )

30. Adverse Selection, Signaling, Screening
Screening
Welfare considerations (only equilibrium cases):
By and large the same as for signaling
L types are worse off
H types are better off

31. Adverse Selection, Signaling, Screening
Conclusion
Adverse Selection:
market failure tendencies
θH workers often worse off
state intervention unrealistic
Signaling:
θH workers are better off
intuitive criterion as a good instrument
Screening
θH workers are better off
but equilibrium in model can be undermined

32. Adverse Selection, Signaling, Screening
Conclusion
References
Akerlof,G.(1970). The market for lemons: Quality
uncertainty and the market mechanism.Quaterly Journal
of Economics 89:488-500
Macho-Stadler, In´s, and J. David P´rez-Castrillo
e
e
(2001).Introduction to the Economics of Information:
Incentives and Contracts. Oxford: Oxford University
Press.
Mas-Colell, Andreu, Michael D. Whinston, and Jerry R.
Green (1995). Microeconomic Theory. New York, NY:
Oxford University Press.
Rothschild, M. and J. E. Stiglitz. (1976). Equilibrium in
competitive insurance markets: An essayy in the
economics of imperfect information.Quarterly Journal of
Economics 80:629-649