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PROFESSOR: Welcome to Lecture 15 of 14.13.
Today we're going to talk about utility from beliefs.
Overall, lectures 15 and 16 are talking about utility
from beliefs and learning.
Well in the previous lecture, we talked
about attention and the idea that attention
might be a limited role-- so you might not have the capacity
to attend as much as we can.
And then thought a little bit about, what kinds of things
are people paying attention to?
And can it be that people systematically
attend to the wrong things and miss important things
in the world?
Today we talk about different deviations from, perhaps,
optimal belief or optimal information acquisition, which
is people might derive utility directly from beliefs that
therefore have potential incentives to deceive
themselves in certain ways.
Next time, we're going to talk more
about learning-- sort of deviations
or systematic deviations from Bayesian learning.
So to summarize today, we're going
to talk about the utility from beliefs.
People directly deriving utility from beliefs,
from what they think about the world,
about themselves, what's going to happen in the future
or how smart they are and so on.
On Monday, we're going to talk about non-Bayesian learning--
this idea that people essentially have
trouble being visual learners.
Being Bayesian is quite hard.
You may have taken probability theory and so on
and have learned quite a bit.
But even as a very smart and educated MIT student,
there will be Bayesian learning problems
that are way too hard once you have several variables, lots
of information.
It's just really hard to do these things in your head.
And people might just not be very good at it
and then sort of use heuristics and biases instead.
And then after that, we're going to talk about projection
and attribution bias, which essentially,
if people have trouble predicting
how they might feel in different states of the world--
if you're hungry, it might be hard for you
to not think about being hungry or think
about how it might feel.
But you're not hungry.
If you're sad, it might be very difficult
for you to understand how it feels
when you're happy and so on.
And so I should say, on Thursday and Friday,
tomorrow, you're going to talk in recitation about Bayesian
learning, which is sort of like, how
do economists or statisticians think you should optimally
learn?
What's the Bayesian benchmark here?
And we're going to talk then about-- on Monday--
deviations from that.
OK.
So the first big picture overview is like,
why might people miss information and fail to learn?
What are potential reasons?
Why might people do that?
And we talked about true potential issues
already last time.
One is, very broadly, attention is limited.
That's to say, there's so much information in the world that
we just cannot attend to everything.
Right?
And so one specific example was inattention to taxes.
But you could think about there's
lots of different prices in the world.
It's just way too much information in the world
for you to attend to everything.
And so one example that we talked about
was inattention to taxes.
It's saying that taxes that are not included in the sales price
might be easily missed by people.
And we have this very nice paper by Chetty et al.
that demonstrated that-- that people essentially
systematically under-estimate or under-appreciate taxes
that they are exposed to.
People pay more and more attention
to taxes that are directly included in the sales price
compared to taxes that are only added at the counter.
And of course, both of them you have to pay.
And so you really should not really
under-appreciate those taxes, because that's
just expensive for you.
We did not get much into why are people doing that,
but more like show the existence of people
seem to be missing those taxes.
Then we talked about reasons why people might systematically--
and even in the presence of lots of data in front of them--
not update properly, even if they are, in fact, Bayesians.
And the reason might be that they
might have the wrong theories of the world.
You might think that certain variables are just
not important for your well-being
or for any important things in the world,
and therefore, you have essentially--
since your attention is limited, you will only
collect some information.
You only focus your scarce attention
and memory to what you think is important things in the world.
And so now if you do that, you might systematically
miss or not collect data that would help you essentially
improve your theories and therefore,
even in the very long run, even when you get lots of data,
you will not update.
Notice that that's quite different
from rational inattention.
There is rational inattention theories would say,
well people's attention is limited,
but they focus attention to whatever
is most important for them.
So it can't really be that they have huge losses
from a lapse of attention, because if they were, then
they would direct their attention to something that
could be potentially important.
In contrast, the "Learning by Noticing"
paper, the theory paper by Hanna et al. that we discussed,
provides a reason why people might not
pay attention to stuff that's really important for them.
And so, again, if your theory says
that certain aspects or certain information is not helpful,
you would not pay attention to those pieces of information.
And if you don't pay attention to those pieces of information,
you will never update your own theories
and your own theory will essentially
persist for a long time, potentially forever.
We're going to talk now about two other reasons
for potentially wrong beliefs.
One is anticipatory utility.
This is, essentially, people like to look forward
to good things in the world.
Suppose you have a vacation coming up in six months
from now.
You might think about this positive event going forward.
Essentially, good or bad events in the future that might happen
and you might derive utility from those events already now.
Second, there's what people call ego utility, which
is, people derive utility from thinking that they are smart,
good-looking, and so on.
So essentially, they derive utility
from thinking positively about themselves.
Now for both of those kinds of pieces of utility,
people now potentially have some incentives to delude themselves
and to think that things are perhaps
better than they actually are, because that
will make them happier.
And so then often there is, at the end of the day,
there's some trade-off between having
overly positive or optimistic beliefs will
make people happier.
They feel good about themselves.
They feel about good things happening in the future.
But that may come at the cost of not preparing or taking
wrong actions because people are sort of overly optimistic.
Right?
So one example would be people might not
get tested for certain diseases because they want
to think that they're the healthy people
and want to be happy about the future
and look forward to a positive future.
But of course, if they were getting tested,
that would help them to take optimal actions-- potentially
medication or any other actions reacting
to the potential disease that they may have.
And for ego utility, for example,
if you always think that you are smarter than you actually are,
well that might make you happy.
But at the same time, that might have come at some cost
and you might not prepare properly
for some exams or interviews or other things.
You might just miss important things that
might hurt you along the way.
And then finally, the last reason
that we'll talk about next week is people might simply just
be bad at Bayesian learning.
Then there's no utility from beliefs or the like involved.
It's just a lot of the computational issues
that we ask people to do are just really hard
and people might be bad at that.
And therefore, people use heuristics and biases.
And then systematically, most of the time these heuristics
and biases are quite helpful and help people
making reasonable decisions.
But then often these heuristics and biases are, in some ways,
systematically wrong.
In some cases-- and we can then think
about some systematic errors and perhaps offer
some ways in which you can improve
people's decision-making by avoiding these errors.
Now let's talk about utility from beliefs.
So it's important to understand that economists typically
define utility functions over outcomes, such as money,
consumption, health.
Think of these things as things that people
consume one way or the other, or things that they can usually
measure at some point.
So you can look at it like, you have money.
Then if you have money, you will spend it on consumption goods.
It could be apples and bananas, of course.
It could be also like haircuts or other services or health,
for example.
And I can measure whether you have good or bad health.
Usually we think about some outcomes that
could be at levels of outcomes.
So essentially, like three apples or five apples or seven
apples are the arguments of utility function.
It could be also-- as we discussed when we talked about
reference-dependent utility--
it could be in part being deviations from some reference
point or changes over time.
But importantly, here, the arguments-- or goods
and services, essentially, are the arguments
of the utility function.
Instead, another source of utility
could be beliefs about such outcomes.
So now it's about what might happen either in the future
or what's happening right now.
And you might directly derive utility from such beliefs.
Now such utility from beliefs can be a very powerful source
of utility.
One example, for example, would be
a high-profile public speech.
Suppose you have to give a public speech in front
of the entire universe.
Now of course you might sort of derive utility
directly from that experience itself.
You might like it a lot.
You might find it very stressful.
So the 10, 20, 30, whatever minutes--
however long the speech is--
might give you positive or negative utility.
But perhaps the utility of that experience
itself might be or could be dwarfed
by the stress and anticipation derived beforehand
from anticipating it.
That is to say, you might think about it.
You might prepare about it.
You might worry about it.
You might not sleep at night.
So there might be lots of stress or positive excitement
and anticipation.
Every day-- if you give the speech sometime in September,
every day until September you're going
to think about it positively or negatively.
And you might derive positive or negative anticipatory utility
from it.
There's another part of utility that we're not
going to talk about.
It's utility from memories.
So you might afterwards look back and say, oh,
that was really nice.
And you have a video, and you're going to enjoy it, and so on.
We're going to not talk about that, but that's sort of--
backward-looking utility could be quite important as well.
Now when you think about utility from beliefs, one way to think
is that this is all in your head.
But it turns out the utility from beliefs
can actually even affect physical outcomes.
In particular, there's a large body
of research on placebo effects, which
is defined as a treatment that can help patients merely
because he or she believes it will.
That is to say, if you give people a placebo or a sugar
pill, something that essentially has no active ingredient,
and tell them that this is, in fact, an effective drug
for something, that drug itself, relative to control,
might have treatment effects.
Now that often is the case for things like pain medication.
Although usually we think pain medication-- if you give people
placebo pills, compared to actual pain medication,
these drugs are about a third as effective as pain medication.
Depends, of course, on the dosage.
So that's quite powerful, but then you might say,
well that's only in people's head,
and maybe people just say they're
happier or less in pain, when, in fact, they're not.
There's also some studies that have actually
found some physical symptoms.
So you give people a placebo pill and there's
actually physically, in some measurable ways--
hard measures, not just self reports-- people
are doing better.
So the placebo effect can be, in fact, quite powerful.
So when you now think overall about sources of utility,
it's hard to imagine, in fact, any source of utility
that's not influenced to some extent by beliefs.
Often it's about how you look forward to some things.
It's not just about going to a restaurant or a date
or having fun with friends.
A lot of it is also just the anticipation of all of that.
OK.
So now more specifically, what do we
mean by anticipatory utility?
So many emotions in particular are intimately
linked, related to what a person thinks about the future.
And you think about hope, fear, anxiety, savoring, et cetera--
a lot has to do with some stuff that
might happen in the future, some events that
might happen for sure, or some events that could happen
but we're just worried about, such as when
people are afraid and anxious about certain things.
Those are actually things that might happen, even
with a pretty low probability, yet people right now
might be for sure quite anxious or worried or afraid.
Now then how do we define and think
about anticipatory utility?
Well it's utility derived now from anticipating
in the future.
So there's stuff that, in the future,
enters your utility function directly.
And those events that will happen in the future
could be consumption, could be also
services, could be like bad shocks or any things that
will happen in the future.
Right now, in the current period,
you're already feeling good or bad about it.
Or something that will happen one or several periods
in the future.
And anticipatory utility is a prime example
of utility from beliefs.
Now how might anticipatory utility affect behaviors?
You can think about, broadly speaking,
two classes of implications that we are going to think about.
There are sort of other potential effects
that might be there.
So the first one is people, if they have anticipatory utility,
that might affect the choice of timing of certain outcomes.
That is to say, if you have the choice when you can experience
a certain good, you might want to delay that or not,
depending on your anticipatory utility.
For example, if I asked you, would you
like to go on a vacation next week or six months from now
or six weeks from now?
You might say, in fact, six months from now
is preferable because then you'll
have six months to look forward to that experience
and be really excited about it.
Instead if I say, it's only next week, well
then, it might be fun to go next week
and maybe if you're discounting, you'd
rather it earlier than later.
But then there's not very much time to look forward to it
and to savor and be excited about this experience.
So anticipatory utility might affect the choice
of timing of outcomes.
We're going to talk about this in a bit.
Second, and perhaps more consequentially,
anticipatory utility also may affect
people's beliefs and their information acquisition.
That is to say, if there is some things
that I like to look forward to in life-- for example,
if I think I'm a healthy person, I'm going to age really
happily, and I'm going to live until age 90
happily, for a long time, well then for example,
that anticipatory utility might then
depend a lot on the beliefs about my health status.
And now if there were tests or some information
that I could acquire about HIV, be it about cancer,
be it about Huntington's Disease and the like--
it's very serious potential diseases,
people might under-use or under-acquire such a type
of information because they want to maintain
overly positive beliefs about what's
going to happen in the future.
And that could be potentially quite important
because if people are not getting, for example, cancer
screening, well then some treatments that perhaps could
be done very early might get delayed,
and that could be potentially quite costly.
We're going to talk about this second.
OK.
Let me show you some motivating evidence
of anticipatory utility.
This is not so much to establish the existence of such utility
to you as like a very rigorous test and showing exactly
this is anticipatory utility and how much of that is there,
but rather to get you to start thinking
about the patterns of behavior generated by it.
So George Loewenstein ingeniously
asked undergrads about their hypothetical willingness
to pay now to obtain or avoid certain experiences.
So they asked them about the willingness
to pay as a function of the amount of time
until the experience occurs.
So all values are normalized relative to students'
willingness to pay to obtain the experience right away.
So you ask people about, like, how much
are you going to pay for right away and 24 hours from now
and three days from now, and a year from now, five years,
10 years from now?
And then the willingness to pay right now
is 1 by definition and everything is relative to that.
What are the experiences that you ask people about?
There's sort of both pleasant and unpleasant experiences.
One of them is receiving monetary gain
or avoiding monetary losses.
There's obtaining a kiss from a movie
star of the student's choice.
And there is avoiding a non-lethal but very painful
electric shock.
And now you can think about why Loewenstein
asked about hypothetical willingness to pay,
because implementing that would be pretty tough to actually do.
Now when you think about these types of experiences,
you can think of it about like, what
would your hypothetical willingness to pay be?
And how would that look like as a function of the timing?
Would it go up or would it go down over time?
And there's going to be two forces at play.
There's going to be discounting at play.
And there's going to be anticipatory utility at play.
We talked about discounting already
a lot, which is, people like to have
positive stuff in the present--
or rather in the present than in the future.
People like to push negative stuff away to the future.
So if bad stuff is going to happen, like an electric shock,
you'd rather have that 10 years from now
rather than right away.
So then the question now is, how does anticipatory utility
affect those kinds of choices?
And I already gave you some of the situation to start with,
which is like, if you had a vacation that you potentially
can experience, would you rather have this right now?
Would you rather have it in a week from now,
six months from now, or 10 years from now?
Well that depends on your anticipatory utility.
You might prefer to have it in six months from now
because that allows you to look forward
to it for quite a long time.
You might not want to have it 10 years from now.
That might be good from the perspective
of anticipatory utility, but it's really, really far away
and you'd rather have things in the present than in the future.
So maybe if you take together anticipatory utility
and discounting, you'd rather have it in an immediate amount
of time from now, which gives you the sort of a form
of an inverse U-shape of valuations over time,
or valuations as a function of when--
right now of a function of what's
going to happen in the future.
Let me show you what I mean.
So when you look at Loewenstein's examples--
in particular, the kiss of the movie star
is an example of an inverse U, where
this is a pleasant experience.
And what seems to be the case is that some people
prefer that experience to happen in three hours, 24 hours, three
days, and one year from now, compared to immediately.
You see the values here are always
higher than 1, which is sort of what things are normalized to.
So let me back up for a second.
What does this graph show?
It shows the time delay on the x-axis, which is immediately,
three hours, 24 hours, three days, one year, 10 years
from now on the x-axis.
That's when the actual experience is happening.
And on the y-axis is the proportion
of the current value.
And it's normalized to 1, so the valuation immediately is 1.
Notice that these are willingness to pay
to receive the experience or willingness to pay to avoid it.
So everything is positive.
Now for the kiss now, we see that the delay
of three days from now seems to have the highest valuation.
So people like to delay this for a bit.
Notice that discounting would not generate you this pattern.
Discounting would say, you want it
right away because you really enjoy this experience.
So anticipatory utility would say, well three days from now
and even a year from now it's better, because now you
can savor it, really look forward to it,
be excited about it when that's happening.
However, 10 years from now, people
seem to like less than right now, presumably because it's
really, really far away.
So A-- I guess you're discounting
that a lot and the experience itself gets discounted a lot.
B-- even the anticipatory utility
might only kick in nine years from now
because it's really so far away that it's
hard to think about this because it's so far away.
And you might even experience anticipatory utility
nine years from now.
But you might discount that as well because it's really
far away in the future.
So it seems like people have some preference
for the present.
There is some discounting going on.
And there's sort of two forces at play-- discounting
versus anticipatory utility.
Now in contrast, when you look at the negative shock,
here it seems to be that people really
seem to dislike having that shock in 10 years or one year
from now, compared to having it right away.
What's going on here?
Well if you have the shock in one year, 10 years from now,
this is really an unpleasant thing
that hangs over your head.
So what, instead, people want is they'd rather sort of get it
over with right away and not have to think about it too much
overall.
Now and that's, again, sort of the opposite of discounting.
If you just had discounting, what you would say
is, well rather I'm willing to pay
to avoid it if it's right away.
It's really unpleasant right away.
It's not so bad if it's 10 years from now.
So what discounting would say is,
the function should be going down
as you see it for losing $4.
And why is that?
Well losing $4 seems to be like, people rather
do that in the future rather than in the present.
And it's not really a thing that you think about it.
You don't have a lot of anticipatory utility
about losing $4 in 10 years from now.
That's not such a hugely important thing.
However, if you get an electric shock 10 years from now,
that might be really unpleasant.
So you really don't want to have that in the year or 10 years
from now, having this hang over your head for a long time.
So you'd rather have it right away
to not have to suffer from any anticipatory utility, even
though from a discounting perspective, that's actually
sort of worse.
OK.
And so I already said all of this-- subjects
prefer a kiss from a movie star three days rather than now.
They also prefer to have a shock now rather
than in one year or 10 years.
Remember this is willingness to pay to avoid a situation,
so the willingness to pay right now for the shock right
now is lower than the willingness
to pay in one or 10 years.
So the curve is going up.
Now this contradicts discounting of any kind.
If you think about any discounting,
positive or negative discounting--
as in, you might have a preference for the present
or preference for the future--
you cannot generate these kinds of patterns.
In particular, a pattern that's really hard
to generate is a pattern where you
get sort of these hump-shaped cases
where, essentially, for inverse use,
because either you want something in the present
or really far away in the future.
But as I said before, if you had discounting, what you would get
is essentially things are either increasing or decreasing.
In the time horizon, positive things, you want right away.
Negative things you'd rather have in the future.
And this is not at all with Loewenstein finds.
Now what is the natural explanation?
People look forward to the kiss.
So they delay to enjoy anticipation.
And it's very unpleasant to anticipate the shock,
so they get it over with quickly.
Now why did Loewenstein choose the kiss example?
You can think about this for a second.
Well it is an experience with a high degree
of savorability-- something you can think about and look
forward to in the future.
Loewenstein tries to rule out alternative explanations
based on preparation.
You might sort of say, well kissing a movie star right away
might not be great because you want to get ready, shower,
sleep well, and tell all your friends about it,
and so on, or get some advice on which movie star to pick and so
on.
So there might be some reason that preparation might push you
in three days from now.
Similarly, if he had said a dinner at a restaurant instead,
you might say, well in a few days'
delay is perfectly reasonable even
without anticipatory utility.
You might want to make a time right away.
It might not be a good time.
You want to get a date, et cetera, for the dinner.
So choosing stuff later because of preparation
seems totally reasonable.
That's not what Loewenstein is talking about here.
He really is thinking about anticipatory utility.
And so he has some other examples,
but really, you can argue that really this is not
about preparation, but part of that
could be preparation as well.
But what you really think about is going on is,
really, this is about anticipatory utility.
When you think about, is preparation
problematic for the electric shock in particular?
Well the answer is no, because that
would induce subjects to prefer it later,
which is not what Loewenstein finds.
Remember, Loewenstein finds that people
would like to have the shock right away, as opposed
to a year or 10 years from now.
And so preparation would say, well, I
want it in three days and a year from now instead.
But that's not really what Loewenstein finds.
So maybe if you're not happy with the preparation
explanation for the kiss of the movie star,
preparation will not be able to explain to you
the electric shock example.
OK.
There's another example.
So Loewenstein has this funny thing
where he says, well getting electric shock has
been a little bit of a weird example.
So let me find something more realistic.
And then being an academic, what he comes up with
is cleaning hamster cages.
So he asked subjects how much they'd
have to be paid to clean 100 hamster cages.
I've never cleaned any hamster cages in my life.
I imagine it'd be quite unpleasant.
So you think about, what kinds of patterns
do you expect to see?
And what you expect to see is sort of something
similar to the electric shock.
So people might really not look forward
to cleaning hamster cages in a while from now
and would rather do it right away
to avoid anticipatory utility.
That would be the pattern.
So that willingness to pay for avoid it
right away or you'd have to pay them not so much
do it right away, compared to having
to do it in a while from now, because the anticipatory
utility makes things worse, as it did for the electric shock.
And this is what Loewenstein finds.
If the payment is now for cleaning
to be performed next week, it's going to be like $30.
But if the payment is now for cleaning
to be performed in a year from now,
the payment has to be higher.
It's $37.
And again, discounting preparation or the like
would create the opposite--
people would rather have it in the future
than in the present, which is not what Loewenstein finds.
Notice, again, these are willingness to pay
to have to do the experience.
So how much would I have to pay you to do it?
Now again there's two forces here at play--
there is discounting versus anticipation.
Now how do we think about discounting?
So we talked about discounting before.
And there are sort of three steps
to thinking about discounting that we talked about.
One was, there was a question like,
what determines a person's instantaneous utility
at each point in time?
We didn't talk about this very much during time preference.
We were just saying like, here's an instantaneous utility
function that determines how happy you are at each point
in time.
What we talked a lot about was, how
do people integrate or aggregate those utilities across time?
So you have some utility today, tomorrow, two days,
three days from now.
And we then talked about, how do you
aggregate, how much weight do you
put on the different periods?
And then we talked about, what does
the person predict about the future utility and behavior?
Which is sort of the question about sophistication
and naivete that we discussed as well.
So as I said, the discounting issues
you covered are about point number 2.
The sophistication versus naivete issues
are more about point number 3.
And here, people's prediction about the future utility
and behavior was only relevant to the extent
that it was helpful or harmful in helping
people make good decisions.
Right?
So people didn't derive utility from being sophisticated
or naive directly.
People only derive utility from their instantaneous utility
function and from depending on the weight they
put on those different instantaneous utilities.
But their prediction affected their choices,
and their choices, in turn, affected the utility.
But it was never the case that people's predictions,
their beliefs directly entered the utility function.
So instead, anticipatory utility is about point number 1.
It's about the instantaneous utility function-- what
goes into that, and perhaps people's beliefs
about the future might do that.
That's what we're talking about now.
Now notice that things like social preferences
or reference-dependent preferences,
those are also about number 1.
Again, time preferences so far that we talked about
were about items number 2 and 3.
Now what are the interactions between anticipation
and discounting?
We talked about this already.
So you can distinguish between pleasant and unpleasant
experiences.
So anticipatory utility is stronger for events
that are closer in time, right?
Something that's like 10 years from now,
you're not that worried about right now.
For something that's tomorrow or in two hours from now,
you might be really worried about.
Now for pleasant and savorable experiences,
some delay is optimal to have a few periods of anticipation.
So think about each hour, each day
as a period of anticipation.
So you'd rather have three days than two days than one day
of anticipation because each day counts
as the day of anticipation, and you may value each day.
But you don't want it to be too far away because then there's
also discounting.
You'd rather have things at the present or close to the present
than in the future.
You don't want stuff to be in a year or two years from now
because that's really far away, and then
you discount that experience very much.
Notice that you might also discount
the anticipatory utility.
That is to say, suppose you have only three days of anticipatory
utility of a nice restaurant or some nice experience.
Only two or three days before that
experience you're going to be excited about it.
Well then if that's in 10 years from now,
you're going to discount all of that.
And then that's really far away.
And if you really present bias or just discount a lot,
then you're also going to discount
the anticipatory utility.
So there's some trade-off for savorable, pleasant experiences
between discounting and anticipatory utility,
which might give you this inverse-U, hump shape power.
Instead or in contrast, for unpleasant, fearful
experiences, you want to either do it immediately
to eliminate periods of anticipation--
so you might just say, get it out of the way.
I don't want any anticipatory utility.
And getting it out of the way essentially minimizes
anticipatory utility because you get it over with.
Or you might put it off as much as possible for discounting
reasons and to weaken anticipation.
That's to say, let's just do it in 10 years from now.
I might not worry about it for quite a while.
I might also just discount any future anticipation.
And for discounting, if there's stuff in the future,
I'd rather have bad stuff happen in the future
than in the present because it essentially
discounts the future.
And it's good for me to discount bad stuff that's
happening in the future.
So far we talked about the implications
of anticipatory utility for the timing of consumption.
Right?
That is to say, when would you like a certain experience
to happen?
In the immediate present, in a few days, or further away
in the future?
But we took it as a given that something might happen
and then the question was just when.
You could think of some examples where that might be important.
Perhaps, more important overall for people's welfare decisions,
and perhaps also for policy is people's information-gathering
and beliefs.
That is to say, you might get a situation where anticipatory
or ego utility--
I'm going to show you--
might affect how much information people gather.
And they might not be as informed
as they could be otherwise because
of those anticipatory utility reasons.
So one question you might ask yourself is, well,
would an individual in a non-strategic setting
with no anticipatory utility ever strictly prefer
to refuse free information?
And it's actually hard to come up with some situations
where people just would refuse information if they're
perfectly neoclassical.
You might say, well people might be overwhelmed.
There's too much information available.
And you might not be able to attend to everything.
But in general, I think the assumption in economics
is, well the information could be useful for something.
You might not even know that right now,
but it might turn out that actually it's
quite interesting information.
And in particular, usually, the assumption
is there's free disposal.
Right?
If the information is not useful, just forget about it.
Don't care about it.
Whatever.
Just write it down somewhere and whatever.
It might be important in the future.
But really, why bother whether or not to have it?
It's no problem.
So you would never refuse it directly.
You might not pay for it if you think it's useless,
but you would never refuse to actually get it for free.
In contrast, somebody with anticipatory feeling cannot
ignore information because that information affects his or her
emotions.
But if it's something that some piece of information
makes you really unhappy, well it's very hard, actually,
to forget about it and ignore it because once it's out there,
once you've heard it, it's really that you can't unhear it
and it's very hard to forget.
In particular, it's hard to forget stuff
that you really care about, that you're
upset about or anxious about.
And so it's really hard to do.
And so one quite interesting example
is Dr. House and Thirteen.
Thirteen is one of his employees.
She's called Thirteen because I think
he had 25 or something interns.
And I think he fired almost all of them
except for Thirteen who was number 13 of these interns.
He never-- at the beginning, at least--
bothered to learn people's names.
So he just gave them numbers.
So Thirteen was number 13.
She was an excellent doctor.
It turns out that her family had a history
of Huntington's disease.
And Thirteen had the prime example, in the show,
of information avoidance.
She did not want to learn about whether she had the disease
or not.
And so the Huntington's Disease is such
that, if your parents have the disease, your probability
of having the disease yourself is way higher than
in the general population.
It's about 50% overall if one of your parents have the disease.
And so then you might think it's quite valuable to learn about
whether you have disease or not, for a variety of decisions
that you might make in the future or that are relevant
for the future, ranging from when to retire,
how much to exercise, what education
to get, how much to save, whether you have children
or not.
And Dr. House was usually pretty irrational.
And there is choices or decisions
that he does, was in fact being very neoclassical here
and saying, you should get this information
because it would be very helpful for you.
He, in fact, went behind her back,
tested her, and sent her the results.
And but then, Thirteen, for at least for quite a while,
did not go to look at these results,
presumably because she wanted to make herself think that she
will be healthy and sort of delude herself in some ways
about being a healthy person and not having this disease,
even though she was not sure.
And so avoiding that information helps
you do that because once you're tested,
you're either positive or negative.
And it's very hard to ignore that information
once you have taken it.
But before you have been tested, you
could always sort of delude yourself
and make yourself think that you don't have the disease.
Now what is Huntington's Disease?
Let me be a little bit more specific.
It's a degenerative neurological disorder.
It's a very severe and heartbreaking disease.
Essentially, it affects the brain.
It sets on around age 40 and really makes
people very dysfunctional.
And life expectancy is around 60 for somebody
with Huntington's Disease compared to 80
or even higher for people who don't
have Huntington's Disease.
People with parents or a parent with Huntington's Disease
have about a 50% chance of developing Huntington's Disease
themselves.
Since the 1990s, there's a genetic blood test available.
And so you can provide at-risk individuals with certainty
about whether will develop it so you
know for sure either you will develop it or you will not.
And those lab tests cost about $200 to $300,
plus consulting and other costs.
The tests here are often covered by insurance,
but most tests are paid out of pocket.
Emily Oster and co-authors of the paper that
is on the reading list were arguing
that people were not doing that partially to keep
the test results private.
Importantly, there's no cure or nothing that we can actually
do to improve the disease.
So when you think about other diseases, such as HIV or other
like, usually there, there's a key motivation
to learn about whether somebody is positive or negative,
because then they can get antiretroviral treatment
or the like.
Here that's not the case.
So there's no actual cure or behaviors
that you could do to that could mitigate
the course of the disease.
However, there's other potential behaviors
that you could engage in--
so prepare you better and deal better with the disease
once it sets on.
So what are these reasons?
Why could such a test be valuable?
Think about this for a second.
There's a number of potential reasons
that you might think about.
I've listed a few.
There's a question about whether or not
you want to have a child.
There's issues about marriage.
Would you like to get married or find a partner?
Or do you want to tell your partner?
And so on.
There's questions about retirement.
When do you want to retire?
For example, if you wanted to travel a lot after retirement.
Well if the disease sets on at age 40,
you might want to do that a lot earlier.
Education-- usually we think that the returns to education
are high.
So it's good news for anybody who is studying.
But usually these returns are accrued
over a long period of time.
You're done with your education at the age 22 or 25.
You can then start working from age 25 to age 65
or the like or even longer.
And so that's a long time.
But if instead, you have Huntington's Disease,
you might only have until age 40 or 45 or the like.
So the returns to education are way lower.
You might also do things like participation
in clinical research.
Perhaps there's some chance that at some point
there might be a cure.
You maybe want to contribute to that.
So there's lots of potential benefits of knowing,
and that test could really be extremely valuable for you.
And surely the value could be higher than $200 or $300.
Now what of the paper by Oster et al?
So Oster et al. observe a sample of previously
untested at-risk individuals over the course of 10 years.
Why is it useful to have a sample of at-risk individuals?
Well because the base rate, the rate
of people who are not at risk, who
don't have any parents with Huntington's Disease,
that rate is quite low.
So not being tested is not so much a puzzle.
If your chance is like 0.00-something percent,
then it's really not that-- it's quite costly to do.
It's $200, $300, plus hassle cost and so on.
And there's many diseases one could have.
Why test for Huntington's?
It's perfectly reasonable to not test for it.
But here, there are people, these at-risk people,
their chance is 50% to start with.
So there's a lot to learn from.
You go from 50% to either 0% of having it or 100% of having it.
So there's huge changes in your beliefs, potentially.
While if you are a person who is not at risk,
your chance of getting it to start with is like
0.00-something percent, with very high chance you're going
to go to zero from that.
So that's almost no change at all anyway.
And there's only like a tiny, tiny chance
that you're actually positive, in which, of course,
you might want to change your behavior quite a bit.
But the weight on that should be quite low
because the probability of a positive test is really low.
So Oster et al find very low rates of this genetic testing.
Fewer than 10% of individuals pursue predictive testing
during the studies, over this long period of time.
Many individuals get tested to confirm the disease rather
than actually learning about whether they have it or not.
You might think, what's really important is for the reasons
that I mentioned here--
it's generating knowledge.
Right, you want to know, should you retire early or not?
For that, you want knowledge.
You want to reveal uncertainty.
So if your chance to have the disease to start with
is 50%, going from 50% to 0% or 50% to 100%,
that's huge potential knowledge that's being created.
Once you think the chances like 99% or 99.9%,
going from 99% to 100%, you actually don't learn that much.
And you shouldn't change your behavior very much
from confirming that you have the disease.
Similarly, actually, there's similar evidence
in studies on HIV, breast cancer,
and other types of testing.
People tend to systematically under-test
even if the chance of having certain diseases is quite high.
And what's somewhat different for HIV and cancer--
any cancer, particularly breast cancer testing,
there's at least some hope that if a disease gets
detected early, one can potentially
do something about it.
There's some recent controversies or discussions
on like, is cancer testing actually helpful?
And are we over-testing in the sense, is the test actually
helpful in detecting potential diseases?
But surely for HIV, it would be quite valuable
if you knew early on whether you have a disease
or not because then you could essentially
take ARV, antiretroviral treatment, to help you.
Now let me show you first who's getting tested.
So what you see on this graph is on the x-axis investigator
evaluation of symptoms at the last visit.
So on the left, these are people who are normal,
who don't show any symptoms.
On the right, people have like certain signs
of Huntington's Disease.
And everything else in between, this
is sort of in the middle of that.
So further to the right means people have more symptoms.
In particular, to the very right,
these are people have like certain symptoms
of Huntington's Disease.
And what we see is, on the y-axis,
whether people since their last visit
get tested-- so there are several visits over time.
And the raw means are what I wanted you to focus on.
This is the upper of those two lines.
And what we see is essentially that testing rates
are very, very low.
The largest are about 5% in this particular sample.
And that's essentially increasing in the symptoms
that people have.
So overall that fraction is high.
And in particular for people where
you think the value of testing would be quite high, these are
people who don't necessarily show any symptoms
and people who have some symptoms but not very
strong symptoms, you would think for them
it would be particularly helpful to get tested
because you could learn a lot.
But instead, those are, in fact, the people
who almost don't test at all.
The test rates are something like 1% to 3%.
Now as I said before, for people with certain signs
of Huntington's Disease, the objective knowledge
from the test is very low since there's no cure.
You're almost sure that you have it anyway, so in a way,
you just really don't learn very much.
If you have these certain signs of Huntington's Disease plus
you're genetically predisposed to have the disease,
the chance of actually having disease is almost one anyway.
So the test really does not give you a lot of information.
However, perhaps, it changes your utilities
from beliefs, which I'm going to talk about in a bit.
Notice that the perceived probabilities
of having the disease might be lower even for people
with certain symptoms.
So what I'm showing you here is the investigator evaluation.
This is essentially a doctor or neurologist actually looking
at the symptoms and looking at, objectively,
what's your chance of having the disease.
That's different from what people actually
think they have.
So I guess A-- and what we learned
here-- is the testing rates are quite low.
Second, people systematically under-predict
or are overoptimistic about not having a disease.
That is what I'm showing you here,
is a motor score, which essentially
is an assessment of how good are your motor skills.
And one unfortunate thing about Huntington's Disease
is that your motor skills are deteriorating a lot.
And so a high score means here, essentially--
if it's bad means essentially you're not doing well
and you're more likely to have Huntington's Disease.
And what you see in the upper limit on the y-axis,
is essentially the probability-- the objective
and subjective probabilities-- of having the disease.
The upper line here that you see at the top,
that line is the actual probability, the estimated
actual probability.
And you see that's essentially increasing in the motor scores.
So people who have almost no symptoms overall,
they have essentially a 50% chance of having the disease.
That's the risk to start with.
But then once people have more symptoms,
that chance increases.
And once you have a motor score in the 20s or 30s,
your objective probability of having the disease
is close to 1.
Now in contrast, the second line that you see here
in the middle, that is the people's perceived
probabilities.
Those perceived probabilities are vastly lower and far less
steep than the actual probabilities.
You see that people's perceived probabilities when
they have no symptoms are still actually reasonably high,
and they're pretty close to the truth.
They're about 40%, compared to like something like 50%, 55%.
So that's actually not that far off,
perhaps because it's very clear.
If you have a parent who has the disease,
everybody knows essentially, and particularly in this kind
of study, everybody knows that the probability of having
the disease is high, and so that perhaps, people can't really
lie to themselves and know that the chances are
pretty high if they have been untested.
But then people seem to be largely in denial when
it comes to these symptoms.
People have these symptoms, and when
you have scores of 20 to 30, their perceived probability
of having the disease is really only slightly higher.
It's about 50% or the like.
And so the people who are about here, well
their actual probability is much higher.
And people don't seem to update information that's
really unfavorable toward them in terms
of anticipatory utility because they seem
to be feeling bad about it.
Notice that there's actually a significant share of people
who persist and really thinks about our reports
saying that there's no chance of having the disease.
So there are some people who have a motor score of 20 to 30,
and 10% to 20% of people here seem to say,
I have a 0 chance of Huntington's Disease, which
really seems to be unfortunately delusional in some ways.
But really, these might be people who really just do not
want to think about it and are just
really worried and anxious.
And they'd rather rule out that possibility
of being sick for themselves.
Now one important question then is,
well do individuals adjust their behaviors?
Right?
So far, we talked about, are people getting tested?
And the answer is largely no.
Second, what are people's beliefs about the disease?
And people seem to essentially be overly optimistic.
Now there's a question, well, does that
translate into their behaviors?
And now this is another little bit complicated graph.
But essentially what the figure shows
is coefficients relative to those tested negative
for Huntington's Disease.
Let's focus on the black graphs to start with.
These are people who are certain to have the disease, compared
to people who are tested negative.
So what we're comparing here is people
who tested positive compared to people who tested negative.
And so the coefficients, if they're positive,
essentially means that people are
more likely to get divorced, more
likely to retire, more likely to change their finances recently
in their preparation.
They're also more likely to be pregnant.
So they change, essentially, their behavior
relative to being negative.
So this is essentially just comparing
positive and negative people.
I should have said already, this is a type
of setting where experiments are pretty difficult and ethically
difficult to do, because if people really derive utility
from information, providing people with information
could really make them worse off.
It's quite different from other sort of experiments involving
information [AUDIO OUT] wrong beliefs
or sort of biased information about certain outcomes.
Usually there, you would say, well let's
provide them with good information.
Maybe they improve their behavior.
So there if you provide people with correct information,
you could only make people better off.
Here, however, since people derive utility
from this information, telling them the truth about stuff
that they perhaps didn't know about
could really make them worse off and deeply unhappy.
And so one wants to be very careful with that.
And therefore, there are not a lot of experiments
in this space, at least for now.
So the study here that I'm showing you
is essentially observational data.
And in this case, comparing people
who have tested positive, compared
to people who tested negative.
If you look at people who are just tested recently,
arguably, these two types of people
are not that different because when
they made the choice of being tested, they didn't, of course,
know whether they were positive or negative.
So that comparison really shows that people
do adjust their behavior.
So people who have been tested positive
are more likely to change their lives in pretty dramatic ways.
For example, people are more likely to get divorced,
more likely retire, and so on.
People are also more likely to have a pregnancy.
I think this might be for women only
or for couples with their spouse.
And that seems like an interesting result, in a sense.
That's not what I would have expected.
Now that could be in part-- so the authors in the paper itself
say that the sample that's used to look at pregnancies
is relatively small.
So maybe in some sense one needs to be a little cautious
in interpreting those results.
It could be that people try to get pregnant or have
a child when they know about the disease
because they want to have a child early on.
There seem to be some technologies where
people can, in fact, avoid that their child had the disease.
So you could make sure that doesn't happen.
And there might be some couples who might say, well,
even if it's the case that one of the parents
will die early on, if the person was like 20 years old or the
like, they might want to have the child early so they can
spend sufficiently much time with the child
before the onset of the disease.
But anyway, it seems to be that people--
the black lines are relatively clearly above zero.
These are coefficients that compare essentially the black
versus the group that's negative,
which is the positive versus negative tested people.
Now when you look at the uncertain people,
these are people who, essentially,
with some probability, are positive
and with some probability are negative.
What we would sort of expect is that those people
are somewhere in between the positive
and the negative people.
So you would expect that the gray lines are also positive
perhaps not as big as the black lines.
Instead, you see essentially-- except for the pregnancy
result, and that doesn't seem to be significant perhaps
because the sample is small--
the gray lines are essentially pretty close to zero.
So essentially, people who are uncertain about the disease
behave very similarly to people who are tested negative.
So essentially, people who have not been tested
or who are uncertain about the disease,
they behave as if they were tested negatively
and likely because they essentially delude themselves
in some ways, thinking they are negative when there's no action
that they need to take.
So that really shows, or the authors
argue that, essentially the lack of testing
really changes people's behavior.
Notice that it's very hard for us to think about welfare--
are people better or worse off because of that?
Because of course, it's a choice to do so.
And you might say, well, I really
value thinking about I'm pretty healthy
and life is going to be good.
And that's really valuable to people.
And they take into account that changes in their finance
and so on would be valuable, but they're not doing this
because if they were doing it, they
would have to acknowledge to themselves that they are,
potentially at least, sick.
OK.
So how should we think about these beliefs and behaviors?
Let me summarize what we have seen.
So many people don't get tested, despite arguably good reasons
to do so.
People are often overoptimistic about the probability
of not having the disease, despite often fairly
clear signs that they have it.
And that really seems to be very much consistent
with anticipatory utility.
People want to feel good about themselves
and about the future.
And therefore, they're not getting tested
and therefore they're overly optimistic.
Such over-optimism then translates into behavior.
So people react less to the signs
of likely having the disease than they arguably should.
In particular, people who are not tested,
they look a lot in their behavior
similar to people who have been tested negative.
And that's to say, perhaps if they were tested positively,
they would change their behavior in ways
that could be useful for them, at least along the road.
Now what models can explain such behaviors?
It's important to understand neoclassical models would not
generate these facts, because you would say, well,
you should be tested because that would be useful.
And utility is just not--
there's essentially no utility from beliefs.
So why would you not get tested?
Let's say, well it's kind of expensive.
But arguably, the value of doing so should be quite high.
And the insurance would also pay for it
if you were not able to afford it.
Now let me write down or show you a simple model.
There will be a problem set, a question on this model
for you to understand it a little better.
So the model is extremely simple.
It has two periods.
And the relevant outcomes occur in Period 2.
In Period 2, the decision-maker will either
be negative with probability p.
So that positive person essentially
would be healthy, with probably p of not having the disease.
And that person will be positive with probability 1-p.
The instantaneous utilities in Period 2, how they will feel.
Think about Period 2 as being everything in the future.
So Period 1 is the period when you
think about potentially getting tested, which is right now
or this month or the like.
And Period 2 now is, say, next year,
everything starting from all of the future.
Now the instantaneous utility of this long future period
are u-minus and u-plus.
u-minus is if you're negative so u-minus is the good case.
And u-plus is if you're positive.
You sort of think that u-minus is larger than u-plus.
It's better to be negative than positive in that disease
or in general.
In Period 1, we're going to look at, now, people's choices.
We can assume no discounting whatsoever.
That's just for simplicity.
We also assume, for now at least,
that nothing can be done about the person's condition.
So A-- there's no cure.
B-- there's also no financial or other adjustment
that the person might be able to take to mitigate
the onset of the disease.
For now we're going to just rule that out.
This is just about, do you want to find out or not?
And why or why not?
Now what would I expect the utility theory to say?
Here what is expected utility?
Well it's very simple.
It's essentially, there's no anticipatory utility.
Expected utility is just what's going to happen in the future.
The probability p, you get u-minus, which
is the person is negative.
With probability 1 minus p, the person
is positive and then recedes utility u-plus.
Notice again, there's no discounting.
This is in Period 2.
But then since no discounting, delta or beta
are essentially just 1.
Now let's add anticipatory utility to this model.
Notice that this type of utility can only
depend on the person's beliefs about
whether she will have the disease or not, not on what
actually happens.
Right?
So the anticipatory utility depends
on the probability of having the disease,
and not on the actual consequences of the disease.
And since the person in Period 1 has this anticipatory utility,
doesn't know for sure whether she is going to have it or not,
the anticipatory utility will only depend on the beliefs,
on the probability p for perceived probability
p of having the disease.
Now we're going to make two extreme assumptions
about the formation of beliefs.
Number one is beliefs are correct,
in the sense that the decision-maker will always
optimally update their beliefs.
And once you've given the decision-maker a test,
the person cannot just make up their beliefs in certain ways.
If the test is positive, the person knows they're positive.
It's negative, a person knows that they're negative.
So p is either 1 or 0 once they have the test.
Or p is correct in the sense that the person knows it's p
and there's no wrong information or beliefs about it.
Second, the decision-maker can choose
to manipulate her beliefs.
We're going to start with one, which
is essentially the assumption that beliefs are correct.
Let the anticipatory utility in Period 1 be f of p.
And recall that p is the probability of being negative.
Now let's assume that, which is obvious in some ways
and uncontroversial that u-minus is larger than u-plus.
So essentially, again, remember u-minus is the probability
of being negative.
So utility is higher in the second period
if you're negative than when you're positive.
And then f of p, f is increasing in p.
That's actually not so obvious in the sense it's not obvious
that going from a certain percentage
to a higher one, the anticipatory utility
always increases.
It's a reasonable assumption, but one
might be arguing about it.
But for now, we're going to just assume that f of p
is increasing in p.
Now does the person want to know her status?
Well let's think about this.
So if she doesn't find out her status,
her utility is f of p, which is her probability.
Or without finding anything else is p.
So f of p is just her anticipatory utility,
plus the term that we had before,
which is just the expected utility in the future in Period
2, which is p times u-minus, plus 1 minus p, times u-plus.
Now if she finds out her status, she
might find out that she's either negative or positive.
If she's negative, that's with probability p,
her utility is the anticipatory part.
If she's negative, she just gets f of 1.
She knows for sure that she's negative.
So there she is f of 1, plus u-minus in the second period.
All that, again, is with probability p.
If she's positive, her utility is f of 0.
So her probability of being negative is 0.
And then in the second period, you have u-plus.
Again, that is probability 1 minus p.
So now her expected utility, putting these things together,
is the part here in the back, which is p times u-minus,
plus 1 minus p, times u-plus.
That's what we already had above.
That's just the expected utility of Period 2.
And p times a negative test, which is f of 1,
plus 1 minus p, a positive test, which is f of 0.
OK.
And so now, if you want to figure out,
does she want to get tested?
We just have to compare 1 versus 2--
or 2 minus 1 if you want, if that's the value of getting
tested.
Notice that the expected utility part,
what's going to happen in the future,
will always be the same.
We have p u-minus, plus 1 minus p, u-plus.
We have that here as well.
The reason for that is because we assumed previously that we
cannot change the outcome.
Right?
So that's going to cancel out if we subtract 2 minus 1.
So what we're going to be left with is essentially
an expression that depends on f of p.
p times f of 1, plus 1 minus p, f of 0.
When does she reject or seek information?
Well she's information-averse if p times f of 1,
plus 1 minus p, times f of 0 is smaller than f of p.
That's exactly-- if you thought that's the case,
it's exactly like the concavity condition.
If f is concave, that's in fact the definition of concavity.
So if f is steeper for lower values,
then the person will be information-averse.
So if the person really dislikes any suspicion of bad news,
for example, due to anxiety, there's not
much value-added certainty, then the person
will not get tested and not seek information.
In contrast, that function is convex,
that is to say, if it's steeper for higher value,
than the person really likes certainty.
So some suspicion of bad news is not so painful.
That is to say, so essentially, when
you think about p starting with something like 50%, what you
want to compare is going from 50% to 100%, versus some 50%
to 0.
And going from 50% to 100% is more valuable.
It improves your anticipatory utility more than going
from 50% to 0% is sort of damaging of p of p-negative.
It's a little confusing notation.
Then essentially the person will seek information.
And it's the opposite if the person really dislikes
any suspicion of bad news.
And there's not much added value of certainty.
Now that is essentially just a question of,
what does this f function look like?
And we're going to try to figure out or try
to estimate that function.
Notice that it's a very simple example here, where essentially
the person has to always--
there's no self-delusion of self-deception.
The person always had to adhere to the truth.
Now consider instead the possibility
that the person can manipulate their beliefs
to make yourself feel better.
Now one question you might ask yourself as well
in the above framework, would you
want to hold correct beliefs?
Is there any good reason to hold correct beliefs?
And the answer is clearly no.
Well there's no instrumental reason of beliefs.
There's no cure.
You can't really make anything better.
You can't really adjust your behavior by assumption
currently.
So why you would you ever think that you
have to do this if you can make yourself feel better
by increasing your p?
So if she could believe that she's HD-negative, for sure she
would get higher utility for whatever happens later,
which is f of 1 is larger than f of 0, or f of 1
is larger than any f of p.
Right?
Essentially f of p is maximized.
We assume that it's increasing.
It's maximized that p equals 1.
So really in the model that I showed you so far,
if you could choose your beliefs,
there's really no reason whatsoever
of not choosing f of 1.
When there's a question, well why might you
not want to choose f 1 anyway?
And of course, the answer is, well
that's because there might be instrumental reason.
There might be actually some action
that you might be able to take to adjust your beliefs.
So in particular, incorrect beliefs
can lead to mistaken decisions.
You can essentially make worse decisions
if you have incorrect beliefs.
So then there's a trade-off.
Right?
There's a trade-off between, on the one hand,
if you have incorrect beliefs, if you're overly optimistic,
you feel good about it.
And you're happier than you would be otherwise
because you get to enjoy anticipatory utility.
But of course, that might come at the cost
of making wrong decisions.
So in that trade-off in general, decision-making
with anticipatory utility, it's like overoptimism leads
to higher utility than realism.
That is to say that if you're fully optimizing to start with,
some overoptimism would make you better off because essentially
you get the value of overoptimism
and then you're not going to distort your behavior very
much if you were optimizing to start with.
So generally you can show that slight optimism, in many cases,
in fact, an optimal thing to do, even if it comes at some cost.
And of course, the intuition here
is that the person wants to believe that she's healthy,
and it makes her feel better.
So she convinced herself that that's, in fact, the case.
Now optimal expectations, essentially, as I said,
trade-off-- anticipatory utility versus the value of knowledge
for making correct choices.
And then, as I said, overly positive beliefs
are an economic important implication
of utility from beliefs.
So once you assume or think about that there
might be utility from beliefs, then one corollary is
that people tend to have overly positive beliefs,
because you explained that with utility from beliefs--
because really people have incentives
to be overly optimistic even if that
comes at the cost of potentially making worse choices.
Next I'm going to show you some other evidence
of overly optimistic beliefs.
And then in particular, we're going
to talk about heuristics and biases, which is again the idea
that people might be not good patients,
in the sense that they might not be good at understanding
probabilities and how to update probabilities accordingly.
Remember, recitation on Thursday and on Friday
is going to talk about Bayesian learning.
So if you want a refresher on that,
that'll be quite helpful because on Monday we're
going to talk about deviations from Bayesian learning.
Thank you very much.