Education Signaling & Screening

Lent TermLecture 5

Dr. Radha Iyengar

The course so far…

Big differences in Wage Structure across groups & time periods

(lecture 1)

Skill biased changes increased returns to ed (lecture 2)

Group/Cohort specific differences unexplained by general skills (lectures 6-10)

Model of human acquisition (lecture 3)

Variation in marginal benefits

Variation in marginal costs (lecture 4)

Estimating returns to schooling

Credit Constraints

Education Production

Signaling/Screening Models (lecture 5)

Specific Capital

Discrimination

Illegal Labor Markets

Today Sorting Models (signaling and screening)

Signalling models as a way of revealing underlying variation in the cost parameter (e.g. ability)—Basic Spence Model

Such models may lead to multiple equilibria which

Are not necessarily socially optimal (e.g. lead to over-investment in schooling because of divergence between private returns and total returns)

Have very different welfare implications

Human Capital & Information

So far, we’ve had individuals investing in education as productivity enhancing

Employers know the value of that enhancement and it’s the same for everyone at that level of investment Don’t worry about underlying parameters that led

employees to choose that level of education The level of schooling perfectly describes the

productivity of all workers with that level of education

Heterogeneity There is some heterogeneity in the

underlying ability of individuals

This underlying variation may be directly related to productivity (e.g. better at producing cogs) or indirectly related (e.g. less likely to take sick days, shirk, etc.)

The variation in ability also varies the cost of education (the “signal”)

Imperfect Information Individuals know their own cost parameter

employers do not we will consider later whether the

econometrician studying the market can observe the parameter

Key Idea: some type of cost information which is negatively correlated with ability. This is a prerequisite for the an observable,

alterable characteristic to be a persistently informative signal in the market.

Screening (Stiglitz, 1975) What if employer required a “screening” criteria

(you have to take a test)

This “screen” is more costly for low ability types than high ability types

Employers want types to reveal themselves by having H types take the screen and L types not

Whether this actually happens on relative costs of screen (c) and fraction of H versus L types (λ)

Why? The screen costs cH for H types and cL for L

types if wH – c < λ wH + (1- λ) wL

High ability types have no incentive to screen because by they make more in the pooling equilibrium

Does this make sense as a sustainable equilibrium? (We’ll do this formally in a bit)

Some Big Points Education when used as a screening

mechanism (e.g. if education provides information as well as skills), it can actually lead to worse social conditions

Why? To begin note that: Private and public returns to schooling differ There is a region of tradeoff between firms and

workers Restrictions education as screening may just

shift screening and actually lead to worse conditions

Private-Public Returns differ Social returns to education differ from

private returns.

while screening has productivity returns, it will decrease equality.

For some regions there is a tradeoff between efficiency and distributional concerns.

Over-consumption There is also a region in which education

expenditure may both increase inequality and decrease net national income.

Overspending happens because the median voter does not pay the median share of education and thus has an incentive to over consume—especially in publicly funded schools

For these things to be true Highly stylized model and may not hold

without these assumptions The more able are better in every relevant

sense, so there is an unambiguous ranking of abilities

Labor supply is inelastic Individuals have perfect information there is not method of on-the-job screening the screening is accurate The information acquired is “general”, i.e. not

firm specific

The way the model works There is an information feedback loop.

As new market information comes into an employer (through either observation, hiring, etc.) they form beliefs on productive capabilities

These are related to observable signals and adjust their beliefs accordingly

To start consider a case where employers get 1 signal, pre-hiring, and then do not learn/adjust wages

Model Set-up Two types of workers

H: productivity level yH

L: productivity level yL

Fraction of H workers in the population is λ with the fraction of L workers then being (1 – λ)

Workers know their type, employers don’t

Education Investment Individuals can engage in education investment or not

so that the choose education level e Є {0, 1}

If choose e=1, there is a cost H: cH

L: cL

Education does not increase the productivity of either type of worker

After choosing e workers enter the labor market

Single Crossing Assumption Crucial assumption is that:

cL > cH

That is, education is more costly for low ability workers.

Makes sure that in the space of education and wages, the indifference curves of high and low types intersect only once.

All the Assumptions of the model

Assumptions: Ability is private information Absent information, all firms (which are risk

neutral) treat individuals the same Productivity of a single employee cannot bet

determined Single crossing of costs assumption

These together imply that: Hiring competitive among a large number of risk-

neutral firms workers will be paid their expected productivity

Defining an Equilibrium An equilibrium is when a set of employer

beliefs generate offered wage schedules, applicant signaling decisions, hiring and ultimately new market data over time that are consistent with the initial beliefs.

To find an equilibrium: we guess a set of self-confirming beliefs and then check that they are indeed confirmed by the feedback loop.

The Equilibria In this type of game, we use the equilibrium

concept: Perfect Bayesian Equilibrium

The striking features are: there are an infinite number of equilibrium for a given level

of education that generates a maximum productivity that perfectly inform the employer

The equilibria are not equivalent in terms of welfare There are also equilibria that do not perfectly inform the

employer. The assumption of negative correlation between signal

cost and productivity is necessary but not sufficient for signaling. We need a significant number of signals

Two Classes of Equilibria In this case: two types of equilibria

Separating: High ability group chooses e = 1 and low ability choose e = 0. Two different contracts are offered wH and wL

Pooling: everyone chooses the same level of education e and everyone gets an average wage wavg

Separating Equilibria- 1 The basic idea: gain in earnings for high ability

people enough to justify costs of education, gain in earnings for low ability workers not enough given high costs of education

Condition for equilibria:yH – cH > yL > yH – cL

Possible since cH < cL

All high ability workers obtain education, and all low ability workers choose no education

Separating Equilibria-2 Wages (conditional on education) are:

w(e = 1) = yH

w (e = 0) = yL

Notice that these wages are conditioned on education, and not directly on ability, since ability is not observed by employers

Separating Equilibria - Firms Firms:

Given the strategies of workers, a worker with education has productivity yH while a worker with no education has productivity yL

Firms are competitive, so they must offer at most the marginal productivity of labor

Firms cannot offer less than this because rival firms will offer at least MPL

Thus firms cannot profitably deviate from this strategy

Separating Equilibria - Workers High ability worker deviates: choose no

education Will get w (e = 0) = yL

w(e = 1) – cH = yH – cH > yL

Low ability worker deviates: obtaining education e = 1 the market will treat as a high ability worker,

and pay the higher wage w (e = 1) = yH

But yH – cL < yL

Separating Equilibria Summary Education not productivity enhancing but a

signal of underlying inherent worker productivity

Education is thus valuable only as a signal

Firms can condition wages on this signal (not the underlying parameter) and if we have single crossing—we can distinguish types

Pooling Equilibria What if the reward to high workers or the cost of

low ability workers was too low. Then both low and high ability workers do not obtain education

Suppose the wage structure is w (e = 1) = (1 – λ)yL + λyH w (e = 0) = (1 – λ)yL + λyH

This can happen in the situation where: yH – cH > (1 – λ)yL + λyH yL > yH – cL

No incentive to deviate by either workers or firms

Does Pooling Make Sense? This equilibrium is being supported by the

belief that the worker who gets education is no better than a worker who doesn’t

But education is more costly for low ability workers, so they should be less likely to deviate to obtaining education

Intuitive Criterion-1 The underlying idea: if there exists a type

who will never benefit from taking a particular deviation, then the uninformed parties (e.g. firms) should deduce that this deviation is very unlikely to come from this type

The overall conclusion is that if education is a valuable signal, then is that separating equilibria may be more likely than pooling equilibria

Intuitive Criteria-2 This falls within the category of “forward induction”

Rather than solving the game simply backwards, we think about what type of inferences will others derive from a deviation.

Think of a relatively intuitive speech by the deviator along the following lines: you have to deduce that I must be the high type deviating

to choose e = 1 low types would never ever consider such a deviation

because it is not profitable even if they convince you they are the high type

I would find it profitable if I could convince you that I am indeed the high type even if I must bear the cost of the signal

Pooling Equilibria Refinement For low ability individuals: it really doesn’t

make sense to deviate because yL> yH – cL but they get

(1 – λ)yL+ λyH >yL

Thus any deviation to e = 1 will be by high ability workers ability workers

Firms know this so can offer a wage to those who deviate breaking the pooling equilibrium

Continuous Education Suppose education is continuous e Є [0,∞)

Cost functions for the high and low types are cH(e) and cL(e)

ci(.) is strictly increasing and convex for i = H, L

cH (0) = cL (0) = 0

New Single Crossing Property The single crossing property is now: cH’(e) < cL’(e) for all e Є [0,∞)

This implies that the marginal cost of an additional unit of education is always higher for low types than H types

This is constrains our cost functions to cross only once, at e = 0

Single crossing property Illustrated

Cost

Education

cL(e)

cH(e)

Output for workers Suppose that the output of the two types

as a function of their educations yH (e) and yL (e)

yH (e) > yL (e) for all e

Education may make you more productive in this model yH (e) > yH (e’) for e’ > e But return to education is the combination of

that productivity effect and the signaling effect

Finding an Equilibrium - 1 Once again there will be multiple Perfect

Bayesian Equilibria some fully separating (know each type) some pooling some semi-separating (get a little of wrong type but

mostly separate)

To narrow this down let’s first find the first-best education level for the low type in the perfect information case (called the “Riley Criterion”)yL’(eL* ) = cL’(el* )

Finding Equilibrium - 2 Then we can write the incentive compatibility

constraint for the low type Low type obtains education eL the low type does not try to mimic the high type.

yL(eL*) – cL(eL*) ≥ w(e) – cL(e) for all e

Let eH be the level of education for high type Remember we don’t want the low type to imitate the high

type That means this constraint holds as an equality

yL(eL ) – cL(eL ) = yH (eH) – cL(eH) That is: it is not profitable for type L to choose eH and

pretend to be an H type

Defining the Equilibrium The equilibrium is then a set of contracts

such that: yL(eL*) = w(eL)

yH(eH) = w(eH)

The characteristics are that: L types do first best H types over-invest in education

Why does this happen? It comes from the single-crossing property (SC) and

the incentive compatibility constraint (IC):

yH(eH) – cH(eH) = yH(eH) – cL(eH) – (cH(eH) – cL(eH))

> yH(eH) – cL(eH) – (cH(eL*) – cL(eL*))

= yL(eL* ) – cL(eL*) – (cH(eL*) – cL(eL*))

= yL (eL*) – cH (eL*)

High ability workers investing in schooling more than they would have done in the perfect information case Define yH’(eH* ) = cH’(eH* ) as the first best

Our equilibrium has eH > eH*

Diagram of Equilibrium Ed. Levels

e

UL*UH*

UH

yL(e)

yH(e)

Ui = w(e) – ci(e)

eL* eH* eH

When is there no separating equilibrium? The separating equilibrium may not exist in the

following cases: If there are self-employment opportunities that

can realize the same returns that would have been realized by accurate screening without the screening

If individuals are perfectly certain of their abilities and can demonstrate them on the job

If individuals are very risk averse and not perfectly certain of their abilities

The Social benefits from Sorting If signal/screen costs are low and labor

supply is elastic then everyone can be made better off from screening by using an appropriate redistributive tax to compensate the worse off.

If there are returns to group homogeneity, then matching with screening may produce better allocation of labor

General Conclusions from Theory there may be multiple equilibria The equilibria can be pareto ranked In both equilibria the presence of the lower type

decreases the distorts the investment/wages of the higher type while the presence of the high type gives the low type at least their marginal product and maybe more

Social returns to screening mechanisms (e.g. education) differ from private returns. Which causes a divergence between pareto optimality and equality.

Empirical Evidence of Sorting Models Different types of evidence:

Returns to GED? (Tyler, Munane, Willett) Do compulsory schooling laws affect schooling levels for

higher grades? (Lang and Kropp) Do degrees matter? (Bedard—class paper)

Some of these are more informative in distinguishing the signaling model from human capital Strong distinct predictions from models in both cases Note that education can be both a signal and productivity

enhancing If both models are operating, may be hard to identify

which is dominant all the time.

Returns to GED (Tyler, Murnane and Willett) Why is this approach useful?

Passing grades in the Graduate Equivalent Degree (GED) differ by state individual with the same grade in the GED exam will get a GED in one state, but not in another.

If the score in the exam is an unbiased measure of human capital, and there is no signaling, these two individuals should get the same wages

If the GED is a signal, and employers do not know where the individual took the GED exam, these two individuals should get different wages.

State Variation in Standards TMW use 3 (of the possible seven different

passing standards) that existed across the US in 1990. a minimum score of at least 40 or a mean

score of at least 45 a minimum score of at least 35 and a mean

score of at least 45 a minimum score of at least 40 and a mean

score of at least 45

Control and treatment groups

Pass in some states—fail in others

Designing the Experiments “Experiment 4” variation in GED status by state is in group 4

the treatment states are those states that award a GED in score groups 4 and higher

the comparison states are those that award a GED in score groups 5 and higher

“Experiment 3” variation in GED status by state is in group 3 the treatment states are those states that award a GED in score

groups 3 and higher the comparison states are those that award a GED in score groups

5 and higher

“Experiment 3*” variation in GED status by state is in group 3 the treatment states are those states that award a GED in score

groups 3 and higher the comparison states are those that award a GED in score groups

4 and higher.

Difference-in-Difference Estimates

Why might results for minorities differ? -1 Many minority men take GED while

incarcerated the stigma of incarceration may depress the

post-prison earnings of dropouts, and eliminate any positive signaling value of the GED credential.

Many dropouts who obtained a GED while incarcerated may have zero earnings five years later because they are still in prison.

Why might results for minorities differ? -2 Why get a GED

Group 1: value on the credential or they perceive that employers place a value on the credential.

Group 2: ‘‘quasi-compulsory’’ in a social program from which they are seeking benefits.

The GED may be a signal of productive attributes for group 1 and a signal of ‘‘government program participation’’ for group 2. Employers discount the value of the ‘‘incidental’’ GED

(group 2) the distributions of groups 1 and 2 differ by race Statistical discrimination of blacks and whites by

employers

Concerns about identification - 1 Those who get GEDs do so to qualify for

post-secondary school training programs Actually acquire other skills—we just don’t

observe them Signaling interpretation is really just from

requirements for admission to training program

Responses Still it’s signaling (to post-secondary schooling) Can test longer term wage gains

Trends in post-GED Earnings

Individual participation decisions Different passing standards influence

individual behavior in systematic ways the decision to attempt the test

Can’t test this Would likely upward bias the estimates

the decision to migrate to another state Test the effect on migration Should observe high standard low standard states Not much empirical evidence of this

the decision about how much effort to exert on the test

Illustration of sorting from standards Can model the type of sorting that might

happen

Can purge data of this and still get similar results

Compulsory Schooling Laws (Lang and Kropp) Why is this a useful test?

Compulsory schooling should have different effects on educational attendance depending on whether education is a tool for human capital accumulation or if it is a form of signaling

This all begins because there individuals who choose the level of compulsory schooling (Sc) as their optimal level of schooling will be observationally equivalent to those who would choose S < SC but are forced to stay

Distinguishing the models - 1 In a signaling model: the lowest ability

increase their educational attainment because of law some higher abilities must increase schooling

to distinguish themselves from the lowest type.

If laws imposes a certain minimum signal for the lowest type, then the signaling hypothesis suggests some individuals not bound by the law will still increase their educational attainment.

Distinguishing the models 2 In the human capital model, a change in

the law will not change the return to education uses the factor price equalization assumption Workers for whom the return to schooling

sufficiently low as to choose dropping out will be bound to stay in school if they are affected by the law

Idividuals who are not bound by the law should be unaffected.

Illustration of Distinguishing Models

Ability

Schooling

Desired Schooling Level

Compulsory Schooling Level

Signaling Model Schooling Level

Human Capital Model Schooling Level

What age is school Compulsory?

Results from Lang and Kropp To test this

Treatment Group: 16 year olds (affected by the law) Control Group: 17-18 year olds (unaffected by the law) To test this, they use a SUR with time and state fixed

effects

The educational attainment of non-affected groups (i.e. the 17-18 year olds for whom the law was non-binding) increased consistent with the signaling hypothesis.

Conclusions from Lang and Kropp A compulsory attendance law might affect

individuals it does not directly constrain having weaker students in class lowers the quality of

education if forcing people to go to school longer teaches them

that they are benefiting from higher level schooling.

Even with these alternative explanations of the results exist the findings presented in this paper are supportive of the sorting model. Different policy implications ex post reformulations of the theory in response to

empirical evidence that contradicts the original formulation.

Concerns/Issues Factor price equalization: It is not clear

that that this is operable wages are the same across states for the same

education-ability pair the return to education is the same in each

state If there is correlation between ability and

mobility the theorem will fall apart

Bottom line from Evidence There may be some of both going on:

There may be some value to the signal but there are also productivity gains

Pure human capital model would require some re-interpretation of what’s going on Might not be the case—signaling fits better If it’s all human capital, need to re-think how

policies affect individual decisions

General Conclusions on Evidence Some evidence of signaling value to

degrees/tests/qualifications

Often can think of human capital unobservables story that coincides with these tests

Can almost usually rule out pure signaling story Still there are welfare consequences of access to signal

varies with parent’s income (just like credit constraint) May now worry about quality of signal (rather than quality

of education production)

Some next steps The link between human capital, signaling,

and wages opens up three important questions Why can’t employers “learn” about workers

continuously (that is why is education the signal?)

If the signal is different for different groups, what happens (is this “discrimination”)?

If there is sorting across different types of occupations/sectors, what is the “signal” for each sector (example: illegal markets)

Next week Specific capital and on the job the

trainings Do workers get training while working?

Who pays for training?

How is this related to turnover and matching of employees to employers?