adverse selection,signaling, screening
DESCRIPTION
A presentation based on Chapter 13 of the Microeconomics Book from Winston, Mas-CollelTRANSCRIPT
Adverse Selection, Signaling, Screening
Adverse Selection, Signaling, Screening
Timo Grote
December 1, 2013
Adverse Selection, Signaling, Screening
1 Introduction
2 Adverse Selection
3 Signaling
4 Screening
5 Conclusion
Adverse Selection, Signaling, Screening
Introduction
Motivation
Where do we have perfect information in our daily life?
How important are information assymetries in buisnessand economics?
Typical Examples:
Second-hand markets (used car market)Labor marketinsurance marketcredit market in developing countries
Adverse Selection, Signaling, Screening
Introduction
Motivation
The economics of information were developed in the 70swith:
”The market of Lemons”(1970) by George AkerlofMichael 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 in2001
Adverse Selection, Signaling, Screening
Adverse Selection
The Model
Adverse Selection: exists whens information betweeninteracting units are assymetrically distributed and determinewelfare inefficient market outcomesAssumption of an enhanced Akerlof model (1970):
Many identical (potential) firms hiring workersIdentical constant returns to scale technology, with laboras the only input=output: θMaximization of profits under risk neutrality andpricetaking behaviourWorkers differ in productivity level θ ∈ (θ, θ) ⊂ R with0 ≤ θ < θ <∞Distribution function F (θ) associated with the continousdensity function f (θ) = F 8(θ) > 0Workers can earn r(θ) when they work at homeTotal number of workers: N
Adverse Selection, Signaling, Screening
Adverse Selection
The Model
Worker´s perspectiveare maximizing their profits facing a trade off betweenworking in a firm or at homeas productivity is publically observable workers work infirms for w ∗(θ) = θnumber of workers employed is {θ : r(θ) ≤ θ}The sum of aggregate surplus:∫ θ
θ
N[I (θ)θ + (1− I (θ))r(θ)]dF (θ) where I (θ) is either 0
or 1Sum of agregate surplus is maximized if:
I(θ)=
{1 if θ ≥ r(θ)0 otherwise
if the given condition holds an equilibrium is attained
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 imperfectinformation
Definition 13.B.1:In the competitive labor market model with unobservableworker productivity levels, a competitive equilibrium is a wagerate w ∗ and a set Θ∗ of worker types who accept employmentsuch that
Θ∗ = θ : r(θ) ≤ w ∗ Condition (13.B .4)
w ∗ = E [θ|θ ∈ Θ∗] Condition (13.B .4)
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 ocurringsituation is pareto inefficient
Adverse Selection, Signaling, Screening
Adverse Selection
Competitive equilibrium with adverse selection
Additional Assumption: r(θ) varies with θ and r 8 > 0
The result is a competitive equilibrium with adverseselection(Figure 13.B.1):
Adverse Selection, Signaling, Screening
Adverse Selection
Complete market failure
One extreme case of adverse selection is that just lowability workers are accepting w
The result is complete market failure(Figure 13.B.2):
Adverse Selection, Signaling, Screening
Adverse Selection
Multiple competitive equilibria
Another extreme case are multiple competitive equilibriaas the firm offers wages with a function E [θ|r(θ) ≤ w ]The slope of the function varies with the density ofworkers accepting the wage (Figure 13.B.3):
Adverse Selection, Signaling, Screening
Adverse Selection
Constrained Pareto Optima and Market
Intervention
The Constrained(Second-best) Pareto optimum is marketequilibrium that can not be improved by an external agent
Proposition 13.B.2: In the adverse selection labor marketmodel (where r(.) is strictly increasing with r(θ) ≤ θ for allθ ∈ [θ, θ] and F (.) has an associated density f(.) withf (θ) > 0 for all θ ∈ [θ, θ]), the highest-wage competitiveequilibrium is a constrained Pareto optimum
Adverse Selection, Signaling, Screening
Adverse Selection
Constrained Pareto Optima and Market
Intervention
Intuition:
If government could observe θ, it could implement a fullyPareto optimal equilibrium
If all workers accept employment in the highest wageequilibrium it is fully (and constrained)Pareto optimal
To move all workers to become employed in the highestwage equilibrium can implement w e = w ∗ = r(θ∗) andwu = 0
Aditionally the unemployed can be taxed to force them towork wu < 0 (which is not Pareto improving)
Adverse Selection, Signaling, Screening
Adverse Selection
Constrained Pareto Optima and Market
Intervention
As the Pareto Improvement is not possible, the aggregatesurplus can be increased by
scheduling that every worker accepts employment
firms pay wage w = E [θ]
which leads to the social welfare function:∫ θ
θ
N[I (θ)θ + (1− I (θ))r(θ)]dF (θ)
Whether an allocation is a constrained optimum dependon the point at which the welfare evaluation is conducted
Adverse Selection, Signaling, Screening
Signaling
Model
Signaling: is the idea that the better informed partycredibly conveys the other one of its quality underasymmetrical informationModel assumptions
Same assumptions as beforeBut only two types of workers:θH , θL with θH > θL > 0and λ = Prob(θ = θH ∈ (0, 1))Workers receive education level e for cost of c(e,θ) withc(0, θ) = 0, ce(e, θ) > 0, cee(e, θ) > 0, cθ(e, θ) <0 for alle > 0 and ce,θ < 0No human capital effectUtility:
u(w , e|θ) = w − c(e, θ)
Home production r(θ) = 0 for all θ
Adverse Selection, Signaling, Screening
Signaling
Worker allocation process with signaling
Allocation of workers works as follows
1 Nature determines type of productivity2 Worker choosing e dependent on his type3 Firm makes offer conditional on e4 Worker chooses rationally the best offer
Result: Perfect Bayesian equilibrium
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 ahigh ability given e is a PBE
The worker´s strategy is optimal given the firm´sstrategyThe belief functionµ(e) is derived from the worker´sstrategy using Bayes ruleThe firms wage offers determined by e constitute a Nashequilibrium of the simulatenous-move wage offer game inwhich the propability of a high ability worker is µ(e)
Adverse Selection, Signaling, Screening
Signaling
The indifference curves cross once which is called thesingle crossing property
Firms offer a wage w(e) = µ(e)θH + (1− µ(e))θL
Adverse Selection, Signaling, Screening
Signaling
Seperating Equilibrium
Seperating equilibrium: Worker types choose differenteducation levels
Lemma 13.C.1:In any seperating perfect Bayesian equilibrium the optimalwages are:
w ∗(e∗(θH)) = θHw ∗(e∗(θL)) = θL
Adverse Selection, Signaling, Screening
Signaling
Lemma 13.C.2: In any seperating perfect Bayesian equilibriume∗(θL) = 0
Since education is shows productivity and is costlyL typ choose e = 0H type choose e > 0
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 availableIf they choose e=0, they expect to receive w = θLthen forbidding signaling activity is Pareto improving
If the fraction of productive workers λ increase thepropability that θL workers are worse off increases
Adverse Selection, Signaling, Screening
Signaling
In a pooling equilibrium all workers choose the same levelof education e∗(θH) = e∗(θL) = e∗
The optimal equilibrium wage isw ∗(e∗) = λθH + (1− λ)θL = E [θ]
Pooling equlibria with e > 0 are PBE but the Paretodominant education level is e=0
Adverse Selection, Signaling, Screening
Signaling
The intuitive criterion
Different types of equilibria can be sustained as PBE
Problem of the refinement, the ”Intuitive criterion” byCho and Kreps (1987):
The outcome of an equilibrium can only be Paretooptimal if low ability workers have no incentive to signalwronglyIf the ”Intuitive criterion” applies only the bestseperating equilibrium survives
Adverse Selection, Signaling, Screening
Signaling
Even the best seperating equilibrium can be paretodominated by a state without signaling activity
As high productive workers are better off, crosssubsidization in favor of low ability workers can paretoimprove the situation
Adverse Selection, Signaling, Screening
Screening
Screening: The uninformed side of the market takesobservations to reduce information assymmetryModel:
Same framework as in Screening chapter
No education signaling, but firms create jobs withdifferent task levelsTask levels do not affect output, but decrease workerutilityUtility 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
Adverse Selection, Signaling, Screening
Screening
The Situation is viewed as a two-stage game:
1 Two firms simultaneously offer a set of contracts(w,t)
2 The workers decide on whether and which contract toaccept
Proposition 13.D.1: In any SPNE of the screening game withobservable worker types a type θi worker accepts contract(w ∗
i , t∗i ) = (θi , 0) and firms earn zero profits
Implications:
if w ∗ > θi firms make losses
if w ∗ < θi firms gain profits
if (w ∗i , t
∗i ) = (θi , t
p) with t p > 0 the firm could deviateand underpay to gain positive profits
Adverse Selection, Signaling, Screening
Screening
Other Case: θ is unobservable for firms
Two types of equilibria:
pooling equilibriaseperating equilibria
Lemma 13.D.2 No pooling equilibria exit
In any pooling equilibrium workers of type θH would beunderpaid
Lemma 13.D.3 If (wL, tL) and (wH , tH) are the contractssigned by the low- and high-ability workers in a seperatingequilibrium, then both contracts yield zero profits; that is,wL=θL and wH=θH
Adverse Selection, Signaling, Screening
Screening
Lemma 13.D.3 If (wL, tL) and (wH , tH) are the contractssigned by the low- and high-ability workers in a seperatingequilibrium, then both contracts yield zero profits; that is,wL=θL and wH=θH
Adverse Selection, Signaling, Screening
Screening
Proposition 13.D.2 In any subgame perfect Nash equilibriumof the screening game, low-ability workers accept contract(θL,0) and high ability workers accept (θH , t
pH) where t pH
satisfies θH − c(t pH , θL) = θL − c(0, θL)
Adverse Selection, Signaling, Screening
Screening
Welfare considerations (only equilibrium cases):
By and large the same as for signalingL types are worse offH types are better off
Adverse Selection, Signaling, Screening
Conclusion
Adverse Selection:
market failure tendenciesθH workers often worse offstate intervention unrealistic
Signaling:
θH workers are better offintuitive criterion as a good instrument
Screening
θH workers are better offbut equilibrium in model can be undermined
Adverse Selection, Signaling, Screening
Conclusion
References
Akerlof,G.(1970). The market for lemons: Qualityuncertainty and the market mechanism.Quaterly Journalof Economics 89:488-500Macho-Stadler, Ines, and J. David Perez-Castrillo(2001).Introduction to the Economics of Information:Incentives and Contracts. Oxford: Oxford UniversityPress.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 incompetitive insurance markets: An essayy in theeconomics of imperfect information.Quarterly Journal ofEconomics 80:629-649Spence, A. M. (1974). Market Signaling.Cambridge,Mass: Harvard University Press.