Professor Ben Polak:
So today we're going to
study asymmetric information.
It's our last week,
and we're going to focus on
signaling today.
I'll spell it with one "L" here
as a concession to the
Americans.
So we're going to divide this
class into two parts.
And for the first part we're
going to focus on the case where
there is some verifiable
information in the problem.
So we'll see what this means in
a while, but let me just set up
an example and we'll see where
that takes us.
So I want to return to a game
we know well by this stage,
which is the Cournot game.
So there's two firms,
and they're competing in
Cournot--so they're competing in
quantities--and we'll call the
firms A and B.
Suppose that Firm B has
costs--so to be more formal,
these are constant marginal
costs--equal to cM,
where M means middle or medium
or something.
Firm A also has costs but those
costs could come in one of three
types.
It could be that Firm A has
high costs, and high costs are
equal to middle costs,
plus a little bit.
It could be that Firm A also
has medium costs.
And it could be that Firm A has
low costs, and the low costs are
just the medium costs minus a
little bit.
Now, before this competition's
going to take place,
before they're actually going
to play the Cournot game,
Firm A has an opportunity.
Firm A's opportunity is to
reveal its costs to Firm B.
So to make this more explicit,
initially, Firm B obviously
knows his own costs and,
since there is only one type,
Firm A obviously knows those
costs as well.
So Firm A and Firm B know what
Firm B's costs are.
But initially,
although Firm A knows her own
costs, Firm B does not know Firm
A's costs.
So let's write that up.
So Firm B knows only its costs,
and Firm A knows both costs.
But the key decision we're
going to focus on is that Firm A
has an opportunity to reveal its
true costs to Firm B.
Now, it can do so in a
verifiable way.
For example,
it could hire an accountant.
That accountant from a
reputable outside firm could
come in and do the accounts for
Firm A and then publish them in
The Wall Street Journal or
something.
So Firm A can do that,
and let's assume it's costless
for it to do that.
So Firm A can costlessly and
verifiably reveal its costs to
B.
The question is:
this is going to happen before
they play Cournot.
The question is:
should Firm A reveal those
costs or not?
Should Firm A publicize or give
away its informational
advantage, if you like,
to Firm B by telling Firm B
what its costs look like.
So what do people think?
Let me grab the mike and ask
people a little bit.
Imagine you're the manager of
Firm A.
Are you going to tell Firm B
what you're costs are or not?
Wave a hand in the air,
or should I just cold call
here?
Let me cold call,
so what's your name sir?
Student: Hugh.
Professor Ben Polak:
Hugh, and so suppose you're
the manager of Firm A,
would you reveal the
information or not?
Student: I would tell
them only if my costs were
lower.
Professor Ben Polak:
All right,
so Hugh says I would reveal the
information only if my costs
were lower.
Now why do you want to reveal
the costs if you have lower
costs?
Student: Because then my
firm will produce at a lower
cost so Firm B will produce less
because they know that we'll get
most of the market.
Professor Ben Polak:
Good.
It's Hugh, is that right?
Student: Yeah.
Professor Ben Polak:
So the point that Hugh is
making is there may be some
advantage in having the other
side know my costs if my costs
are low,
since that may induce the other
side to produce less.
Let's just fill out that
argument by putting in the
Cournot diagram.
So here's the Cournot diagram.
Here's the quantity for Firm A.
Here's the quantity for Firm B.
And here is the best response
or reaction curve for Firm B.
And in this picture there's
going to be three different
possible reaction curves for
Firm A, each one corresponding
to different costs.
So, for example,
this could be the reaction
curve or the best response for
Firm A in the case in which it's
medium.
But if it had lower costs what
would happen to that reaction
curve?
Would it shift in,
would it tilt,
what would happen to it?
Someone shout it out.
It would shift out.
If it had lower costs then it
would shift out so this would be
the best response for Firm A in
the low case,
and conversely,
this would be the best response
for Firm A in the high case.
So the point that Hugh is
making--or he should correct me
if this is unfairly paraphrasing
him--is if I have low costs then
I want the other side to know I
have low costs because that puts
us into the equilibrium in which
this is my best response curve
and this is the other side's
best response curve,
and Firm B ends up producing
less and ends up lowering its
production.
Is that right?
So the key idea here is that
this is a game--an idea we've
had often--this is a game of
strategic substitutes.
So if I have low costs,
I want the other side to know
that I have low costs because it
will cut back its production
which helps me.
On the other hand,
if I have high costs,
then I kind of like to remain
hidden.
I really don't want the other
side to know that I have high
costs, because if I have high
costs,
the other firm's actually going
to increase their production and
that's going to hurt me.
But notice I've twisted the
question a little bit.
The question I actually asked
you was: would you reveal the
information about your costs.
And I flipped that around to a
slightly easier question which
is: what would I like the other
side to know?
Now what would I like the other
side to know?
I'd like the other side to know
if I have low costs.
I'd like the other side not to
know if I have high costs,
but that's not quite the
question we asked.
The question we asked was would
you, given whatever your costs
are, reveal that information to
the other side?
I think what Hugh has told us
is--so to say exactly what he
said--Hugh said if I had low
costs I'm going to reveal it to
the other side.
Is that right?
So, so far what do we know?
So far we know that if I have
low costs then I will reveal it.
So far we know that.
But what if I don't have low
costs?
What if I have middling costs
or high costs?
Well let's take these in turn,
what about middling costs?
What should I do if I have
middle level costs?
So somebody's got their hand
up, let me go and take advantage
of that.
What's your name?
Student: Alec.
Professor Ben Polak:
Shout it out so people can
hear.
Student: I think you
should still reveal because they
know if you had low costs you
would reveal,
and so if you had middle costs
and you didn't reveal then they
could think you either had
middle costs or high costs and
it's better for you to just
reveal that you had middle
costs.
Professor Ben Polak:
Good, did people hear that?
Let me just repeat that.
So you might think that if I
have middle costs,
you might think that I could
reveal or not reveal,
depending on what the other
side thought.
However, what Alec's arguing
correctly, is if I don't reveal
that I have middle costs,
the other side,
Firm B, knows that my costs are
not low.
So the only way they could
mistake me is they could think
I'm a high cost firm.
They know I'm not a low cost
firm.
How do they know I'm not a low
cost firm?
Because the low cost firm would
have revealed,
that was Hugh's argument.
So since low costs are firms
are revealing,
if I'm the middle cost firm,
if I don't reveal no one's in
any doubt I'm not a low cost
firm.
So all I could be is a middle
cost firm or a high cost firm.
All I could have is this
reaction curve,
which is the one I actually
have, or this reaction curve.
So if I don't reveal then the
other side might think that I
have high costs in which case
they're actually going to
increase their production and
hurt me.
So since the low cost firm is
going to reveal,
the medium cost wants to reveal
to ensure that no one thinks
it's high costs.
So low cost reveals and
therefore cM reveals as well to
prevent being mistaken for a
high cost firm.
Now there was a question,
let me come down and collect
the question.
Yeah?
Student: I was just
going to ask what if you have,
A reveals to both to the low
and middle class,
then they're obviously going to
know that he's a high cost,
which means that the concealing
doesn't do any good.
Professor Ben Polak:
Exactly,
and your name is?
Student: Bethany.
Professor Ben Polak:
So Bethany's pointing out
that once we know the low cost
type's going to reveal,
we know that the middle cost
type is also going to reveal so
as not to get mistaken for being
high cost,
which means,
if you're running a high cost
firm, it really doesn't matter
whether you reveal or not,
because you're going to be
revealed by the fact that you
didn't reveal.
Is that right?
Had you been low cost you would
have revealed.
Had you been middle cost you
would have revealed.
And therefore,
whether you choose to reveal or
not, everyone knows that you're
high cost.
So therefore, cH is revealed.
Everyone see that?
Okay, now notice that in this
argument we've just constructed
there were three types of firms
- high, middle,
low.
But I could have constructed
exactly the same argument,
albeit somewhat more tediously,
with a 100 types of firms.
Firms that had absolutely the
lowest costs,
firms that had the 99th highest
costs, 98th highest costs,
97th highest costs and so on.
And this argument would have
been exactly the same.
At each stage the firm that's
left in the analysis who has the
lowest cost, will want to reveal
to distinguish itself from those
who haven't revealed "yet,"
and therefore we'll get
unraveling.
We'll get information to be
revealed, and notice
interestingly,
we'll get information to be
revealed beyond the medium.
So the 51st highest cost firm
will reveal, therefore the 50th
highest cost firm will reveal,
therefore the 49th and so on.
In fact, the only firm who
won't explicitly,
actively reveal themselves is
the firm who has absolutely the
highest cost.
And as Bethany points out,
they're going to be revealed
anyway.
So this is an idea--this idea
is called "informational
unraveling."
And again, in keeping for my
American audience,
I'm going to put one "l" in
unraveling.
Is that right,
there's one "l" in America
right?
Someone should just check that
on Google or something,
I think that's correct.
What's the lesson here?
So one lesson is that this
happens.
We'll come back to that,
but another lesson,
perhaps a more important lesson
is: often the lack of
information,
the lack of somebody signaling
to you, the lack of somebody
trying to tell you something,
conveys information.
This was the point that Bethany
was making.
The fact that the high cost
firm doesn't in fact go out and
reveal information to you,
reveals something about what it
knows.
So Hugh's initial comment was
correct.
If I was the high cost firm I'd
like to remain hidden but I
can't remain hidden.
From your point of the view as
the receiver of the information,
there is information in the
lack of the attempt to convey
information.
So lesson: the lack of a
signal, the lack of an attempt
of a firm to signal you some
information, the lack of a
signal can be informative.
So this is an often forgotten
lesson.
It's a very simple idea,
but there's a natural tendency
when you're dealing with
information to focus on the
evidence that is there,
rather than the evidence that's
not there.
There's an expression that goes
with this.
The expression is "silence
speaks volumes."
You've all heard that
expression, silence speaks
volumes.
Let me give you one other
example.
So there's a Sherlock Holmes
story--by the way,
do you all know who Sherlock
Holmes is?
Good, so there's a Sherlock
Holmes story in which Sherlock
Holmes solves the murder.
He figures out who did the
murder.
And Dr.
Watson who's his sidekick is
trying to figure out how Holmes
could possibly have solved the
murder.
He says how did you solve the
murder?
Holmes says,
it's because of the barking
dog.
And Watson says,
what do you mean it's because
of the barking dog?
The dog didn't bark.
Holmes says,
that's exactly the point,
the fact that the dog didn't
bark, didn't make any sound
tells us who must have committed
the murder.
It's very easy to fall into the
trap of being Watson and to
ignore the thing that didn't
happen and focus on the things
that did happen.
Here, it's easy to forget that
actually the high cost firm is
revealed by doing nothing.
So this is the idea that
silence can speak volumes.
Every year I go back and try
and figure out what that
quotation is from and I can
never find it,
so anybody who finds it I will
give them a prize of some sort.
Originally I thought it must be
Shakespeare but it doesn't
appear to be.
So this is a little example
involving Cournot,
but I want to try and convince
you that this example is more
general.
Let's pick up the question;
sorry go ahead.
Student: Isn't it
possible that there's an
equilibrium where the costs of
remaining hidden as a middle
cost firm outweighs the benefit.
Professor Ben Polak:
Not if we take the model
literally.
Not if we take the model in
Cournot literally because,
suppose Firm B doesn't know
whether you're high or middle,
then he's going to think your
costs are somewhere in between
and relative to your costs being
middle he's going to produce
more,
that's the point here.
Now it's true that in a richer
model there may be some other
advantage in having information
hidden,
but that would have already
applied to the low cost firm.
Let me give you some other
examples and we'll see this in
other contexts,
and see that it might actually
ring true.
So one other example involves
resumes.
So this example requires some
explanation for the
non-Americans.
How many of you are
non-Americans here?
So one thing you need to know
as non-Americans is the way in
which people write resumes in
America.
Everyone know what a resume is?
A CV, a resume, right?
So when you look at a typical
resume from an American
student--if you're not American,
for those of you who aren't
American--how should I put this
politely?
It has a tendency to make you
want to vomit.
So that's basically the polite
version of what I was going to
say about that.
So why does it have a tendency
to make you want to vomit?
Because Americans have a
tendency to put down everything
on their resume.
So if they were captain of the
chess team in third grade,
and there they are now,
they're forty and applying for
a job, it still says I was
captain of the chess team in
third grade.
And this is particularly true
when it comes to public service,
when it comes to sort of moral
acts.
So most people in Europe will
be a bit embarrassed about
writing their good deeds on
their resumes,
but Americans,
there's a little spot on their
resume which is about their good
deeds or their public service
and they put everything.
When I was eight I helped a
little old lady across the road
with her shopping basket,
and there it is on their
resume.
So why is it that Americans
reveal so much information on
their resume?
Well think about informational
unraveling, right?
So resumes are verifiable
information, it's hugely costly
to be caught cheating about your
resume.
So basically you're not going
to lie on your resume.
And imagine if I'm admitting
students, let's say to law
school, to Yale Law School,
and I'm reading the student's
resume and in the spot where I'm
expecting to see public service
there's nothing written there.
What do I assume about that
student?
I assume that the person did
nothing.
This person has been a self
serving "evil git" their entire
life, has never even helped a
little old lady across the road.
So people put down everything,
even these minimal things,
even these pretty shockingly
tiny acts of charity to reveal
themselves from those people who
did absolutely nothing,
that are basically the devil
incarnate.
So this is about resumes,
let's just take this a bit
further.
How many of you are from Los
Angeles?
So in Los Angeles I'm led to
believe, I'm told--you can
confirm this or not--there are
lots and lots of restaurants.
This is true, right?
Lots of restaurants and some of
these restaurants are good and
some of them are bad.
And, more to the point for
today's example,
some of these restaurants are
clean and some of them are not
so clean.
Is this true?
So it turns out that until the
late nineties,
the Los Angeles Municipality
rules,
local law, said that every
restaurant in Los Angeles
County, I think it was,
had to get visited by the
health inspector.
And the health inspector would
come around, I think it was
annually, and go to these
restaurants and they would issue
a certificate,
and this was a health
certificate and written on it
large letters--I think they were
red letters--was either A,
or B, or C.
There may even have been A- as
well, but for the purpose of the
story let's just call it A,
B, and C.
Now that was all the law said.
The law did not say that you
had to display your health
certificate anywhere.
So what does this model tell us
to expect about Los Angeles in
the mid-nineties?
Well if you're running a little
restaurant in Los Angeles and
you get an A health certificate
from the health inspector,
what are going to do with that
A certificate?
You're going to display it
prominently in the window,
right?
A health certificate.
So if you're running a slightly
less healthy restaurant,
maybe this is Ale's pizza chain
again,
and you still get a B
certificate from the Los Angeles
Health Inspector,
are you going to display it or
not?
You're going to display it
right, because why not?
We know the A's are going to
display.
These certificates are being
given to everybody,
so you're going to display even
a B certificate.
Now, I'm told,
from people who lived in Los
Angeles at the time,
that you could go around to the
greasiest spoon in Los Angeles
and look through these grease
smeared windows with the
cockroaches running all up and
down them,
and if you looked carefully
behind the cockroaches and the
grease you'd see a certificate
displayed that said C on it.
Presumably there was a D grade
as well: even the C's were
displaying.
So that's pretty dramatic
information unraveling.
Now, I'm exaggerating slightly
to make a separate point.
It turns out that in certain
areas of Los Angeles you'd
expect to see these health
certificates displayed,
even the C's,
and in other areas you wouldn't
expect to the see the C's
displayed.
Which areas would you expect
not to see people bothering
displaying their C or B-
certificate?
Any guesses?
The tourist areas.
Because for this story about
information unraveling to work,
the people who are the
receivers of the information
need to know that you got the
certificates.
So if you're a tourist in Los
Angeles, you don't know this
system is in place,
and therefore if you're a C
certificate right next to
Disneyland or something,
whatever it is,
you can still make some
tourists ill,
without having to tell them
you're about to do so.
So that's a second example,
let me give a third example,
a little bit closer to home.
At the last curriculum reform
at Yale, there was a big debate
about what to do with Credit
D/Fail.
And one of the proposals for
Credit D/Fail was to allow
students to take courses Credit
D/Fail,
but if they ended up getting an
A or a B, they could display the
A or the B on their resume.
So they take a Credit D/Fail,
but if they got a grade like an
A or B, or an A- or whatever,
then they could opt in and have
it put on their resume.
What's wrong with that?
This is a serious proposal.
I was on this committee.
This was seriously made.
I didn't make the proposal but
this was made.
What's wrong with this proposal?
What's wrong with the proposal?
What would displaying Credit on
your transcript come to mean?
It could come to mean C right,
it would come to mean C,
because all of the A's and the
B's would unravel that
information.
So if information is verifiable
and can be freely transmitted,
it has a way of coming out.
Let me give you one slightly
more serious example.
As you all know,
if you're arrested in the
U.S.--you should know this--you
have the right to remain silent.
I'm not saying you're all about
to get arrested,
but were you to be arrested,
you have the right to remain
silent.
That right was true in Britain
as well until recently,
when the government,
which isn't so big on civil
liberties, changed the rule
slightly.
So now you have the right to
remain silent in Britain,
but the Court has the right to
take into account as evidence if
you remain silent.
So what's that done to the
right to remain silent.
I'll leave it to you to figure
out what that's done to the
right to remain silent.
So this idea that information
unravels depended on certain key
parts and the most important
part was that the information
was verifiable.
It mattered that the
information was verifiable.
And to get full unraveling all
the way down,
in this case to the highest
cost firm,
you needed the people on the
receiving side of the
information to actually know
that that information was there.
So to get the full unraveling
you really need something like
common knowledge of the presence
of the information.
But often, the information that
you have--you have information,
you want to reveal that
information--but unfortunately
it's not so easily verifiable.
So what we're going to focus on
for the rest of today is
information that is not
verifiable.
Let's start with an example
that's pretty close to home.
A lot of you have been doing
job interviews recently.
How many of you have been going
out either doing interviews for
internships or jobs?
I know a lot of you are missing
class so I'm assuming charitably
that's what you were doing.
So when you go to these job
interviews you could imagine
that you're turning up for some
job interview,
let's say it's at Boring Bank
of Boston.
And you turn up at this
interview for Boring Bank of
Boston, and one of the things
that Boring Bank of Boston wants
to know is are you interested in
working for Boring Bank of
Boston.
That's a plus for them.
What they tend to do is they
ask you.
More or less they say,
are you interested in working
for Boring Bank?
Now by the way,
if you are asked the question,
and you're interviewing for
Boring Bank,
and you're asked the question
by them are you interested in
working for Boring Bank,
what answer should you give?
You should answer yes.
How much information is there
in the fact that you answer yes?
None at all,
right, because clearly you want
the option of working for this
bank, so you're going to answer
yes anyway.
Now you may think this is just
a fictional example,
it's not.
I talked to some recruiters
from a bank in Boston that we'll
refer to as Boring Bank of
Boston not so long ago,
and I asked them about hiring
Yale undergraduates and what
Yale undergraduates should do to
impress them.
And the recruiter,
who is a Yale graduate himself,
said to me that frankly Yale
undergraduates do less well in
these interviews than Harvard
undergraduates.
I said, shattered and
disappointed--I said why,
and he said,
well when we asked them if
they're interested in working
for Boring Bank of Boston the
Yale guys say things like,
well I don't know it sounds
kind of boring.
The Harvard guys,
what do they do?
They show up with The Wall
Street Journal folded over
conveniently on the page about
Boring Bank of Boston,
and sometimes they're wearing a
silly hat with I'm boring on it.
So I tried to persuade this guy
that despite this fact,
there's really no information
in the fact that the Harvard
guys are doing this,
and in fact you should hire the
Yale people because at least
they were honest,
and, hey, that might make the
bank less boring in the future.
This didn't work,
so I need to persuade you guys
to actually cough up and be
dishonest here.
There's a lesson here.
So one lesson is,
if you're asked by an
interviewer for a summer
internship or for a job later,
if you want to work for them,
the answer is yes.
It's one of the few questions
for which the answer is not
backward induction:
it's just yes.
There's a secondary lesson
here, which is,
if an interviewer for a bank is
asking you in the interview if
you'd like to work for them,
you probably will answer yes,
but you probably want to work
somewhere else.
If they're dumb enough to ask
you that question you probably
want to work for someone else.
But this is a real problem.
The problem is here you are.
You have some information you'd
like to convey.
Maybe you really are boring.
Maybe you really do want to
work for this bank.
You want to convey this
information, but it's hard for
you to persuade the employer
that this it is true because
anybody can say they want to
work for the bank.
More generally in life,
this isn't only about whether
you want to work for a
particular bank or whatever it
happens to be,
it's also about whether you are
a good worker or not.
So let's try and think about
this in the context of not only
workers being boring or not,
but workers being good or not.
So we're going to look at a
costly signaling model.
It's going to turn out,
this model's going to be about
costly signaling,
and just for the purpose of the
model we're going to assume that
there are two kinds of workers
in America.
There are good workers,
we'll call them G,
and there are bad workers and
we'll call them B.
We'll assume that the
productivity of a good worker,
if you work for this firm,
is going to be 50 and we can
assume this is $50,000 or
whatever but let's just forget
units for now and just call it
50.
A bad worker,
their productivity is only 30.
So clearly, all other things
being equal, the employer would
rather employ a good worker than
a bad worker.
All other things being equal is
important because then we have
to pay the good worker more.
Let's assume this is the U.S.
economy, so roughly 10% of the
economy are good workers and 90%
are bad workers,
something like that,
and these are the proportions
in the U.S.
Let's also assume that firms
are competitive.
So firms are flooding into the
Yale Careers Office,
or the Yale Careers Fair,
and they're just desperately
trying to hire these workers.
There's competitive hiring
going on.
So firms compete for workers.
So they're going to pay 50 to a
worker they identify as good.
They pay 50 to a worker,
they the firms identify as
good.
And they're going to pay 30 to
workers they identify as bad.
If you're bothered by this
being exact, think of it as 50
minus a penny,
and 30 minus a penny.
It's not going to make any
difference to the analysis.
So if they can't identify a
worker, they think the worker's
just the average worker,
how much will the competitive
wage be?
What will be the competitive
wage of the average worker in
this economy?
It's not a hard math question.
Everyone's scratching their
head down here.
So this is 50 x 10% and 30 x
90%, which averages out as?
32% all right.
So they'll pay the average
which is 32 to a worker they
cannot identify.
Now, clearly in this model,
much like in the high cost
firms we started with,
the good workers would like to
be identified because they get
paid more.
The bad workers do not want to
be identified,
they'd rather remain hidden.
The problem here,
however, is there typically
isn't a verifiable piece of
information.
It's hard to verifiably
communicate to the other side
that you're a good worker.
So you guys are all good
workers right.
You wouldn't be here otherwise,
we hope.
So you show up to this firm,
this firm is looking for good
workers, and you could tell the
firm: "I'm a good worker."
In fact I'm betting most of you
have tried doing that in your
job interviews:
"I'm a good worker."
You could even do this in a
costly manner.
You could humiliate yourself by
jumping up on the table and
dancing on one leg while singing
some song about how you're a
good worker,
which would be humiliating but
it wouldn't in fact communicate
to the firm that you're a good
worker.
Why is it that you're dancing
this beautiful jig on the table
of the interview room,
singing this beautiful song
about how you're a good worker,
why doesn't that convince the
firm that you're a good worker?
Who's been in job interviews
recently?
Has anyone tried this?
Why is that not a successful
strategy?
Steven, is that right?
Student: Yes.
A bad worker could do that too.
Professor Ben Polak:
A bad worker could do that
too.
So it's true that it's costly
and humiliating to dance up on
the table on one leg and sing
you're a good worker,
but it's no more costly and
humiliating for you than it is
for a bad worker.
So if that worked,
a bad worker would do it too.
So merely a song and dance
isn't going to work.
It's going to be hard to signal
to the outside world that you're
a good worker.
That's going to be our starting
point.
So we need a way for good
workers to distinguish
themselves from bad workers.
We need a way for them to
signal, and what's key about
that signal is it has to be a
signal that they can make and a
bad worker cannot make,
or alternatively,
a signal that they will want to
make but a bad worker will not
want to make.
So dancing on the table doesn't
do it, and the reason it doesn't
do it is bad workers and good
workers are symmetric with
respect to the dishonor of
dancing on the table.
So we need a way for good
workers, you guys,
to distinguish yourself from
bad workers, us guys.
How in the American economy,
what's the main way in the
American economy in which good
workers signal the fact that
they're good,
that they manage to distinguish
themselves.
What's the main signal used in
the U.S.
economy?
Somebody?
Yes, education.
So the main signal in the U.S.,
not the only one by any means,
but the main signal is
education.
What's going to distinguish the
good workers from the bad
workers is the good workers are
going to have degrees,
more degrees,
better degrees,
more degrees,
whatever.
So what we're going to look at
today is a model some of you
have seen before but we'll do it
in a bit more detail perhaps.
It's a model due to a guy
called Spence,
Mike Spence,
who actually won the Nobel
Prize in large part for this
model.
The reason we know he won the
Nobel Prize in large part for
this model is he didn't write
practically anything else,
so it must have been for this
model.
So what we're going to do is
we're going to imagine that the
degree, the education that these
people are going to get,
that's going to distinguish
themselves and show that they're
good workers to the
employers--let's assume that the
employers once again are banks
or whatever--we're going to
assume that the extra piece of
education they're going to get
is an MBA.
Some of you out there are
getting an MBA.
Where's my MBA? There he is.
There's my MBA student up there.
So the good workers are going
to get an MBA,
and the way this is going to
work, it's going to work on the
costs of getting an MBA.
So to get to this to be a
successful signal,
to make this signal different
from merely dancing on the
table,
it's either got to be the case
that bad workers cannot get an
MBA or it's got to be the case
that it's so costly for bad
workers to get an MBA that they
won't bother.
So we're going to make the
difference in costs.
So we're going to suppose that
the cost per year of getting an
MBA, of being in business
school, MBA education,
is 5 units if you're a good
worker.
We're going to assume that the
cost per year of going to SOM
and getting an MBA is a little
bit over 10, so 10 and a penny
if you're a bad worker.
So notice I've assumed in this
model that it's more costly per
year to get an MBA at Yale say,
if you're a bad worker than a
good worker.
Now, what are those costs?
What are the costs of getting
an MBA?
What's causing that cost
difference?
Well let's be clear what it
isn't.
It can't be the fees.
The fees are a large part of
the costs.
What are the fees of getting an
MBA at Yale this year?
Way too much right.
So the costs per year in terms
of fees are enormous,
but the fees themselves are not
going to do a good job of
distinguishing between good and
bad workers.
Why?
Because they're the same for
both parties.
We want something which is
differently costly,
so this is not the fees.
It can't be the fees.
They're the same for both
parties.
What other costs are there to
getting an education?
There's opportunity costs right.
All of you are economists--or
half of you are economics
majors--so the first thing that
should spring to mind is
opportunity costs.
But actually opportunity costs
don't help me here much because
if anything you'd think that the
opportunity costs of going and
getting an MBA at Yale are
higher if you're a good worker
than if you're a bad worker.
After all, if you're a good
worker you could stay home,
not get an MBA,
farm your parent's garden,
and, since you're such a good
worker, you'd have a high yield
in carrots or whatever.
Whereas, the bad workers will
not produce anything,
right?
So this is not really about
opportunity costs,
in fact, we'll assume that
they're zero.
We'll assume there are no
opportunity costs.
So what is it that's driving
this cost difference between the
good worker at SOM and the bad
worker at SOM?
Was that a potential answer out
there?
Student: Is it the
present value of future wages
for a good worker?
Professor Ben Polak:
Okay, so there we're thinking
about the future.
No, let's just focus on the
cost side.
You're right there's going to
be different things going on in
the future, but let's focus on
the cost side.
I had you before so let's have
this guy.
Student: Mental effort.
Professor Ben Polak:
Mental effort,
right.
So where's my MBA student up
there.
Here he is--where is he,
up there.
It's pain and suffering,
is that right?
I can't see him yet.
He's nodding, good.
It's having--when you go to the
MBA class--of thinking my God,
thank goodness I escaped being
an undergraduate,
and you go back to the MBA
class and I'm there
again.
I'm assigning the same horrible
problem sets and you still can't
read my handwriting and you've
still got to deal with my
accent, right?
Good workers find it easier to
read my handwriting and deal
with my accent,
right?
So what it is?
It's the mental effort.
It's the pain and suffering.
It's the pain of the work.
The only thing that
distinguishes the costs of good
workers from bad workers in
education is it's so painful to
do the work.
If we went to a party school,
this wouldn't work.
That's why we can't just have
party schools.
We actually have to put you
through some pain in the
classroom.
I'm looking for some
confirmation from up there.
So the pain of the work is what
distinguishes these things.
Now I claim that we can have an
equilibrium in this society in
which there are good and bad
workers;
in which good workers cost per
year is less than bad workers
cost per year of getting,
in this case,
an MBA--we could do the same
for undergraduate education but
let's focus on the MBA for now.
I claim there's an equilibrium
in this society,
there could be an equilibrium
in which getting an MBA takes
three years.
So I claim there is an
equilibrium here in which what
happens?
In which there are three year
degrees, degrees take three
years--a three year MBA sounds a
bit frightening but never
mind--in which the good workers
all get MBA's and the bad
workers do not.
But to tell you this is an
equilibrium I need to do a
little bit more,
so let me tell you one other
thing.
So I claim there's an
equilibrium in which the degrees
take three years,
all the good workers get MBA's,
all the bad workers do not get
MBA's, and what?
The employers identify MBA's as
good workers.
To make this work it has to
convince the employers.
So to make it work I need:
and the employers identify MBA
equals good, and not-MBA equals
bad.
So that's what I claim is an
equilibrium here and what I want
to do is I want us to show that
this actually is an equilibrium.
Now then, this is a slightly
different kind of equilibrium to
anything we've seen in the class
so far,
so I'm going to be a little
slow and nerdy about what we
need to check to check that this
indeed is an equilibrium.
So I'm going to leave some
space on the board and you
should leave some space too.
So my claim is this is an
equilibrium.
And we're doing guess and check.
I did the guess for you and
we'll do the check together.
To check, I claim,
I need to check two things.
One, I need to check that no
type will deviate.
So what do I mean by a type?
I mean types of worker.
Neither the good types of
workers would want to deviate
nor the bad types of worker
would want to deviate.
So this isn't new.
When we've checked equilibrium
we've always checked that people
don't want to deviate.
The only slight difference here
is instead of checking that
people won't want to
deviate I'm checking that
types of people won't
want to deviate,
but basically the idea is the
same.
Is that right?
The idea's the same,
so this is not really new.
The new thing is I also need to
check--actually I'll give myself
a bit more room here--I also
need to check that the
employer's beliefs are
consistent with the equilibrium
behavior.
So let's just stop and pause at
that a second.
We've never written down a
condition like this for
equilibrium, but here I have to.
Here there was asymmetric
information in the model.
And, in this equilibrium,
one important party to the
equilibrium, namely the guys who
are going to employ you,
that's pretty important right?
All they really have to do in
this model, of any importance,
is form an inference based on
your actions.
They observe whether you get an
education or not and they
conclude whether or not you're a
good or bad worker.
So we're going to write down as
a condition of this being an
equilibrium that those
inferences "make sense."
By make sense I mean that
they're consistent with what
actually is happening in
equilibrium.
So before we get too nerdy
about that let's just think why
that's a sensible thing to
require.
Suppose, in fact,
suppose the world was like
this.
All good workers got MBA's,
all bad workers did not get
MBA's, and employers thought
that the people who got MBA's
were half good and half bad.
That just doesn't sound right,
right?
If in fact it's the case,
that it's the good workers who
are getting MBA's and the bad
workers who are not,
then the only belief that the
employers can have that's
consistent is the MBA's are in
fact the good workers and the
non-MBA's are the bad workers,
is that right?
So I'm not making any deep
point here, I'm just pointing
out that we need to make sure
that the beliefs that people
hold in this equilibrium are
consistent with what's actually
going on in the equilibrium.
But having said that,
there's no mystery here,
everything's fine.
In this particular claim of an
equilibrium, good workers are
the ones who got the MBA's;
bad workers are the ones who
didn't get the MBA's;
and the employers,
when they see an MBA,
indeed think they're good;
and, when they see a non-MBA,
they indeed think they're bad.
So these beliefs are in fact
consistent with behavior,
so we're okay.
Okay, so I've had to check that
but it wasn't a big deal.
Everyone okay about why I'm
checking it?
I don't want people to hold
silly beliefs at equilibrium,
that's basically what I'm
saying.
All right, now let's go back
and check the sort of bread and
butter thing.
The bread and butter thing is
we need to check that no type of
worker is going to want to
deviate in this equilibrium.
So there's two types of worker.
There's good workers--and good
workers, what are they doing in
equilibrium?
What are the good workers doing
in equilibrium?
They're getting an MBA.
So the good workers,
they become MBA's,
and what are the good workers
identified as?
Once they got an MBA what does
the employer identify them as?
Good workers, right?
They're identified as good.
They get MBA's.
They're identified as good,
and their payoff is what?
What's the payoff of the good
workers here?
So they get paid 50 which is
their productivity,
but it costs them three years
of putting up with my homeworks.
So it costs them 3 x 5,
five for each year.
So 50 - 3 x 5 is what?
35, good.
So they get a total payoff of
35, and let me just pause a
second.
I made an assumption here
without telling you it,
so I'm going to say it.
Just to make the math simple
we'll assume that once you get
employed you work for a year and
then you drop dead.
That's a slightly morbid and
unpleasant assumption,
but otherwise we have to do
kind of present discounted value
of your whole future income and
then it turns into an accounting
class.
So we'll just assume that
everybody lives for one year.
If you want to do a more
complicated model then that's
fine, the idea will be the same.
So they get paid 50,
it's cost them 3 x 5,
and they get a total payoff of
35.
How about if they deviate?
If they deviate that means they
don't get MBA's.
So they're not MBA's.
They're identified as what?
If they don't get an MBA,
what are they identified as?
What does the employer think
the non-MBA's are?
Bad.
So if they deviate then the
employers think they're bad.
Even if they dance on the table
and say they're good,
they're in fact bad--they're
identified as bad.
And so their payoff is what?
What are they going to get paid?
They're going to get paid 30.
And sure enough 35 is bigger
than 30, so they're not going to
want to deviate.
So that's good news.
What about the bad workers?
Let's check them.
So the bad workers,
in equilibrium,
they're not MBA's.
They don't get an MBA.
They're identified as bad.
And they're paid what?
What are they paid these bad
workers?
Somebody?
They're paid 30.
They're paid their productivity.
So their payoff is just 30.
They didn't get an education so
it was free.
They get 30 for free,
so their payoff is just 30.
If they deviate,
if the bad workers deviate,
then they get an MBA.
So here come the bad workers.
They find their way into my
class in SOM.
They have a miserable time.
(I have a miserable time
because they're having a
miserable time.) But at the end
of the day they're identified as
good workers and hence they're
paid 50.
And their payoff is 50 - 3 x
10.01 which is approximately 20.
Is that right?
So they don't want to deviate
either and now I'm done,
I've shown it's an equilibrium.
So just to recap.
To show that this was an
equilibrium, I had to show that
the good workers happily self
select into education and don't
want to deviate and skip
business school.
I have to show that the bad
workers self select into not
getting an education and don't
want to deviate and become
MBA's.
And I have to show that the
employers infer from this what
they should infer from this,
which was fine.
So I'm done.
This is indeed an equilibrium.
So notice, in this equilibrium,
the good workers do manage to
distinguish themselves from the
bad workers,
and they do end up getting paid
more (albeit at the cost that
they're going to die a year
later).
So this is called a separating
equilibrium--which I can never
spell.
I'm probably spelling this
wrong.
It's a separating equilibrium.
Why is it called a separating
equilibrium?
It's called a separating
equilibrium because the types
manage to separate and get
identified.
That's slightly misleading.
The good types manage to
separate and get identified,
and the bad types,
they don't want to get
separated, but they do get
separated.
Now, how many of you have seen
some version of the Spence model
before?
Some of you,
let's go into this in a little
bit more detail to see if we've
really understood it.
So in particular could we get
away with a shorter degree?
Here we had people going to get
MBA's and it took them three
years each.
That seems an awful long time
to get an MBA.
So how about a one year MBA.
Some of you might think this is
a somewhat abstract example but
actually this is the kind of
thing you hear about all the
time.
If you listen to ads in the
education press you keep on
hearing schools,
perhaps schools who lack
Economics professors,
putting up the proposals for
one year MBA degrees.
I won't mention any schools by
name because I'll probably get
in trouble.
So how about a one year MBA?
Let's see if that will work.
And we'll allow good workers to
separate themselves from bad
workers.
Let's assume that the costs per
year are the same as they were
before.
And let's suppose that this
candidate equilibrium,
this putative equilibrium,
involves the good workers
getting the MBA's;
the bad workers not getting an
MBA;
and the employers,
just as before,
identifying MBA's as good and
non-MBA's as bad.
Question: is that an
equilibrium?
So who thinks yes?
Who thinks no?
So you can all tell my why then.
So the answer is no.
So why is that not an
equilibrium?
Somebody, anybody?
Someone who hasn't answered yet.
Your name is?
Student: Asman.
Professor Ben Polak:
Asman, so shout out.
Student: The bad workers
would also benefit from doing
the MBA because their payoff is
still greater.
Professor Ben Polak:
Good, so what's wrong in this
equilibrium, it's not the
employer's beliefs.
If in fact people did follow
this behavior then employers
would be right to identify MBA's
with good.
It's also not the good workers
problem.
If in fact, employers are going
to pay more to MBA's,
then the good workers are even
more so going to want to go
ahead and get MBA's.
The problem here--this is not
an equilibrium--and the problem
is the bad workers.
The bad workers' incentives are
wrong here.
Why?
Because if the bad workers do
what they're supposed to do in
this equilibrium--actually it
isn't an equilibrium,
but in this supposed
equilibrium--what they're
supposed to do is not get an MBA
and get a payoff of 30.
But if they went and got an
MBA, if they deviate and no one
else deviates,
just them deviating,
if they deviate they get an
MBA.
According to the equilibrium,
they're now identified as good
workers.
They're identified as good so
their payoff would be 50 minus
one year at approximately 10 for
a total payoff of 40.
But 40 is higher than 30 so
that's violated our equilibrium
condition.
Everyone see that?
So here the bad workers,
if it only took one year of
pain and suffering to get an
MBA, the bad workers would go
and get an MBA as well.
And that would be trouble
because now everyone gets an MBA
and its just like dancing on the
table again.
So how long must an MBA be?
In this model,
with this cost structure,
how many years must it take to
get an MBA?
Two years, right?
One year didn't work but you
can try at home and check that a
two year MBA will work.
Two years will be just enough
to put off the bad workers.
Leaving aside the numbers
though, what's the idea here?
The idea is that to work as a
successful signal,
the signal has to separate the
good workers from the bad
workers.
The workers have to choose to
be separated.
They have to self select into
being MBA's or not being MBA's,
and we need just enough pain
and suffering--and let's be
careful--just enough
difference in pain and
suffering for the workers to
select correctly.
So what we need,
we need enough difference in
cost for good workers to get the
degree and for bad workers not
to want to do so.
So one thing we could do is
have a two year degree.
If you absolutely insisted on
having a one year degree,
how could you create a
difference in cost that would
work?
Suppose you were employed to
advise some university out in
the west somewhere,
who wanted to have a one year
degree program.
What should you do in that one
year degree program to make it
work, to make it allow people to
separate?
Raising tuition isn't going to
work because that's the same for
good and bad workers.
You need a way to separate the
good and bad workers.
How are you going to do it?
You're going to make it really
hard.
If you want to have one year
degree program,
it's got to be really hard.
You've got to really jack up
the difference between the good
and the bad workers,
so you need to hire professors
who have really bad handwriting.
Let's try and take a step back
from this model and see what
we've learned here.
Let's just try and draw some
lessons off this.
I want to draw two kinds of
lessons.
I want to draw lessons in
general about what makes a
successful signal in society,
and then I want to draw lessons
about education.
So I want to start with some
nerdy lessons about Game Theory
if you like, and then I want to
want to talk about some more
specific lessons about the
education system.
So the key lesson here is the
lesson we just learned.
The key lesson is:
to be a successful signal,
to be able to separate types of
people, you need there to be
large differences in costs.
So the first lesson is a good
signal--it isn't that it has to
be costly--it has to be
differentially costly
across types.
The reason is you want the
types to self select,
so there better be differences
in costs.
Be a little bit careful here:
you could have differences in
benefits but we'll leave it as
cost for now.
That's one lesson.
Now what's that telling us in
this model?
That's telling us that if you
make it very,
very easy to obtain
qualifications in the U.S.
society, for example,
if you lower the standards that
you need to get a high school
degree and perhaps you lower the
standards to get a college
degree--I'm not saying that is
happening,
I don't want to take a
political position on this.
In England that's happening.
I can do that.
In England that seems to be
happening.
So you lower the standards it
takes to get a high school
certificate in England,
and then you perhaps lower the
standards to get a college
degree, what are you going to
see happen?
You're going to see
qualification inflation.
If you make it easy for
everybody to get the first
degree, the good workers are
going to go on and have to get a
second degree.
If you make it easy to get the
second degree,
they're going to go on and get
the third degree.
So what this model predicts is
if you get rid of this cost
difference then workers will
find a new way to raise the cost
difference again.
The way that takes place,
at least in some economies,
is you start seeing
qualification inflation.
By qualification inflation I
mean that, pretty soon,
even to drive a dump truck you
need to have a university
degree.
Okay, now what are the lessons
here for education more
generally?
This is a pretty sparse model
of education but all of you,
and more immediately me,
are involved in the education
system.
So we should care about it a
bit.
It's probably the most famous
model of education.
As I say, it won somebody the
Nobel Prize.
What is it telling us about
education?
So the first thing I claim,
I claim that this is a rather
pessimistic model of education.
Why is this a pessimistic model
of education?
What's pessimistic about this
model?
Let's talk about that a bit.
Anybody, some hands up?
Some different hands?
Why is this a pessimistic model
of education?
Way over there,
a hand in another part of the
room, that will give the camera
a work out anyway.
Student: You won't learn
anything as a rule,
as that school has absolutely
no value for education.
Professor Ben Polak:
Good, so shout it into the
microphone, but that was right.
Student: You don't learn
anything at school in this
model.
Professor Ben Polak:
Right, this is a model with no
learning.
There's no learning in this
model.
In fact, people in this model
go in with their productivities
at 50 and 30 and they come out
with their productivities at 50
and 30.
Nothing you do at school
enriches you or makes you more
productive.
That's a pretty pessimistic
lesson.
Here we are in Lecture #23 or
something.
And the message of this model
is, you guys haven't learned
anything: you've just had a lot
of pain and suffering.
So there's no learning in this
model.
Now I hope that's not true as a
model of education.
I hope it's not true that we
only have pain,
but nevertheless,
let's pretend it's true at
least for now and see where it
takes us.
So a second observation of this
model, if we believe this model
of education in which you don't
learn anything,
education is just being used by
those people who are good anyway
to separate from those people
who were bad anyway,
then education in this model is
socially wasteful.
Why is education socially
wasteful in this model?
In what sense is it socially
wasteful?
Think of it from the point of
view of an economist?
In this model,
the productivity of the workers
doesn't change because of
education,
but some resources were used by
the good workers to get an
education.
At the end of the day,
the good workers are better
off.
The bad workers are worse off
and employers are the same as
they would have been otherwise,
but that's just redistribution.
There's no product from
education but resources were
wasted in education.
Does that make sense?
So in particular,
in our two year equilibrium,
or in our three equilibrium,
it was the good workers who
went to college,
or in this case went to
business school and they wasted
three years at five a piece.
So there's a waste of 15--a
waste of 10 in the two year
model.
According to this model,
education is socially wasteful.
How do we actually visualize
that waste in society?
So let's take the model
seriously, where is that waste
manifested in society?
Where is that waste manifested?
So you guys aren't working,
and where else is it
manifested?
You guys sitting here is part
of the waste.
You should be out doing
something else,
and where else is the waste?
Me.
You should take all your Yale
professors, stop using them as
Yale professors and wasting
those resources,
and have us go out and till the
fields or drive taxis or
something.
So there's a social waste here
and what we should do is,
according to this model,
is we should send the
professors to drive taxis or
dump trucks I guess.
I'm not claiming we'd be good
at driving dump trucks.
Our comparative advantage is
certainly in teaching classes
rather than driving dump trucks.
But it turns out that,
in this model,
teaching classes is completely
a waste of time,
and therefore you're better off
using those resources to drive
dump trucks.
Third, notice that in this
model the result of education is
what?
It's good for the good workers,
you guys managed to separate
yourselves and get paid high
wages.
That's nice for the Yale
graduates here,
but who were the losers in this
model?
Who were the losers?
The bad workers,
the 90% of workers in this
economy who aren't naturally
gifted, who aren't going to find
education easy.
They, in this model,
end up being paid 30.,
Without the education system
how much would they have been
paid?
32.
So in this model education
increases inequality,
and it doesn't increase
inequality in a benign way just
by making the rich richer.
It increases inequality by
making the poor poorer.
Education, in this model
increases inequality.
In this model it actually hurts
the poor.
Now, that strikes me as a
pretty important lesson
actually.
Again, I don't think we should
take this model too literally.
In the real world,
I at least hope that some of
you are learning something at
Yale.
You're looking extremely
doubtful that you could possibly
learn anything at Yale,
so maybe you're not,
I don't know.
But, in the real world,
I'd like to believe people are
learning here at Yale.
But one of the things that's
going on in education in
addition to learning,
one of the things is that you
guys are separating yourselves
and signaling to employers that
you're going to be good workers
for them.
As a consequence,
that's great for you but
someone else is being paid less.
This strikes me as an important
lesson to hear in an election
year.
In every election year in
America--I've been in a few
election years in America
now--there are two things that
all politicians agree on,
whether they're far right or
far left.
All politicians agree on two
things.
They agree that two things are
good.
One: kissing babies.
Two: they all want to be "the
education President," is that
right?
All of them, is that right?
Now, as a parent of some
babies, I'm not sure I want to
have politicians' kissing babies
but that's for another day.
The point here is what we're
learning--don't go yet
guys--what we're learning here
is that if education hurts the
poor maybe we shouldn't be so
keen to decide that we should
subsidize the education sector
itself.
Although, as an educator,
I hope you don't tell that to
anybody.
What's the take away message of
this model then?
The take away message is for
education to work as a signaling
device, for education to
generate a separating
equilibrium,
some children have to be left
behind.
We'll talk about that more on
Wednesday.
