[SQUEAKING]
[RUSTLING]
[CLICKING]
PROFESSOR: So let me very briefly recap
what we discussed last time.
So we started off thinking about choices and risk.
How do people think about economic behavior
when things are uncertain, when there's risk involved?
I sort of discussed and showed you
sort of the main workhorse model that economists
use to study risk.
That's sort of the expected utility.
That is a very commonly extremely useful
model for many situations.
So it's like very widely used.
If you ask 100 economists randomly
which model explains choices [INAUDIBLE]
the majority will surely tell you expected
utility is what you should use.
It explains a wide range of phenomena in very useful ways.
You can think about lots of different things.
You can, for example, think about investment behavior,
finance.
When you think about what should you invest in,
if things become more risky, if assets are more volatile,
you need to have a higher return for that,
or you need to be offered a higher
return to invest in those assets and so on and so forth.
There's lots of useful applications in finance
using expected utility.
You can think of a range of different issues.
You can think about, for example, criminal behavior,
about sort of the risk of getting caught.
What happens when the risk of caught goes up?
People engage in less crime and so on and so forth.
There's lots of different behaviors
that you can think about and explain using expected utility.
So I do want you to sort of take away the expected utility model
is a very useful model for various applications.
What we're trying to do is trying
to understand are there some applications for which perhaps
the expected utility model has some limitation, perhaps
because of its simplicity or parsimony because there's
only one parameter in there?
Can we sort of alter that in some ways
and try to make it more realistic in some situations?
So the key parameter of interest when
you try to sort of estimate this model,
trying to sort of match the data in some ways,
the parameter that you'd estimate here is you
need to sort of assume some functional form.
This is what I did last time.
I can show you this.
So this here, one very commonly functional form
is the CRRA utility function that's very widely used
in a lot of range of settings.
The feature of that is it has a constant relative risk
aversion, and that has a bunch of useful properties
for estimating things or making predictions.
So what you then need to do is you
try to sort of estimate somebody's risk preferences.
How do people behave under risk?
What you need to do then sort of assume some functional
form, for example, this CRRA utility function.
And then the question is kind of like how
do we estimate gamma the risk aversion parameter?
That's the key parameter in this model.
Now, how do you do that?
I showed you some different choices [INAUDIBLE]..
Essentially we reveal preference.
Economists believe when we reveal preference,
I give you some choices that involve risk.
And depending what you choose, that
reveals what your gamma is.
So you can do like small scale gambles,
which is just like small choices between different options.
Some entail more risks than others,
and then you can essentially just
sort of estimate using those choices,
or people certainty equivalent for such choices,
what's people's gamma is.
Now, what we found is that when you have small-scale gambles,
people look or appear very risk-averse.
They'll often decline gambles with positive expected value,
which makes them appear quite risk-averse once you
sort of estimate this parameter gamma.
Gamma looks like gamma is above 10, above 20, above 30,
really, really high.
Now, at the same time, you can look at large-scale risk.
There, when you look at large-scale choices,
when you sort of think about what's a reasonable gamma,
people actually only appear moderately risk-averse.
It doesn't look like they're particularly risk-averse.
When you sort of think for those large-scale choices
and we look at finance or housing or other applications
that people have estimated such models,
you get like gamma sort of between 0 and 2 roughly.
Now, what that then implies is if your gamma is
between 0 and 2, that means essentially
for small-scale gambles you should
be essentially risk neutral.
You should not care about really small risks
that are about a dollar or two.
So that sort of poses a problem because now we
have sort of two contradicting answers.
We have for small-scale risk, it looks like people
are really risk-averse.
For a large-scale gamble it looks like people are not
so risk-averse.
Now, we only have like one parameter,
is this gamma, which is coming from the concavity
of the utility function.
And when we only have one parameter and sort
of two contradicting pieces of evidence,
we can't sort of match both, right?
Because if you match one, then essentially
you can match the other and vice versa.
Now, I showed you a little bit Matthew Rabin's--
what he calls the calibration theorem, which essentially
is sort of calibrating, showing in a fairly compelling way
that, in fact, you can formally show it's
not about sort of assumptions of a specific utility
function or the like.
For these very sort of minimal assumptions, which
is just the utility function is weakly concave,
you can essentially show that declining small-scale gambles
with positive expected value implies
that people make absurd choices when the gambles become larger.
The recitation will discuss this a bit
in more detail and sort of walking you exactly,
in somewhat slower speeds, through the specific example.
Now then, where we started then last time
was thinking about insurance choices.
This is a very nice paper by Justin Sydnor,
and one very nice feature of this paper
is that it involves real-world choices.
So it's not like some lab experiments
with some experiments.
Of course, some people care a lot about undergrads.
Some people might say, well, what
are these undergrads choosing anyway?
What does this have to do with real-world choices?
I think undergrads are great.
But one might wonder, like, if you recruit people
into some experiments and you see some choices, like what
do these choices really reveal?
Like, do we really find that these choices are predictive
of real-world behaviors?
So one answer to that is, well, let's
find some data from the real world.
Let's look at real choices that people
have made in real-world settings,
and this is exactly what Sydnor does.
So what he does is he has this data set of from a large home
insurance provider.
This is sort of 50,000 standard policies
that are sort of like representative of what
people choose overall.
And the key outcome of interest in this study
is like people's deductible choices.
What's a deductible?
Again, these are expenses paid out-of-pocket
before the insurer pays any expenses.
So you have like a deductibles of $500,
you have a damage of like $200, you
have to pay it all yourself.
If you have a damage of $1,000, you pay the 500
and then the insurer pays the rest.
And so what he has is he has choices
of a menu of four deductibles for each customer or client.
So you can see both people's choice sets,
and you can see people's preferred options.
And that allows them to sort of say, well,
if you have four options, you picked one of them.
That means you preferred that one over all three others.
So we can sort of essentially put some bounds
on people's risk aversion.
And so we looked at this already.
This is kind of what this roughly looks like.
There are different deductibles, which is essentially, again,
like how much how much you have to pay yourself
in case of damage until the insurance payments kick in.
You have the premium, which is like how much for sure
you have to pay every year.
And then there is the premium relative to the $1,000 policy.
How much more expensive is it?
That's in the third column.
How much more expensive is it to choose a lower deductible
relative to the $1,000 premium?
And then we have people's choices which is, in this case,
I guess, policyholder one shows a deductible of $250.
It was a premium of $661, which is
$157 more expensive than the $1,000 deductible option.
OK?
And for each policyholder, the company
was, in fact, sort of providing individual prices.
So essentially they were looking at where
do they live, what's the housing value, and so on and so forth.
Sydnor knows all of that.
So he knows the full set of options
that people had available and their actual choices,
and the options available vary by person.
How do we learn now about risk aversion?
Well, so the losses to the customers
are capped by the deductible, right?
So any loss you have from any damage that you get,
the losses are only up to the deductible.
So if you have a deductible of $500,
the most you can lose or have to pay in any case
if any loss occurs is $500.
So choosing a lower deductible then,
what it does it amounts to essentially reducing
that loss in case you have a damage.
So if you have a deductible of $500
and decide to instead choose a deductible of $250, that
means essentially in case there's
a damage, in case you have to pay something,
you don't have to pay 500.
You have to only pay 250.
But of course, if you lower your deductible,
the price of your insurance goes up, the premium goes up,
and the premium you have to pay for sure.
So the way you can think about this then
is like, if you choose a lower deductible, for sure
you have to pay more money.
But in case there's some damage to you
with some probability that happens,
if you have some claims, you have
to like pay less because your deductible is now lower.
OK?
So now what info do we actually need?
We need the available deductibles.
Like, essentially what are the deductibles for each choice?
We need the premium for each option.
We need the claim probabilities and people's wealth levels
because you have a utility function where
there's wealth in there.
I'll talk about this in one second.
Any questions so far?
OK.
So now one important feature in this I think
was asked like last time about like, well,
what about the claim rates?
Well if the claim rates are really high
or if people think the claim rates are really
high, in some sense then, having very low deductibles
makes a lot of sense because then--
and very often it happens that you have to pay.
Then it makes lots of sense to have like lower deductibles.
But it turns out claims rates are actually very low.
So you can see overall--
this is like the full sample, this
is everybody-- people's claim rates is 4.2%.
These are yearly claim rates.
This is like out of 100 customers, 4.2 per year
actually claim any damage.
And then it varies a little bit also by choice of deductible.
So there's the people who happened
to choose in the end like $1,000, $500, $250, and $100.
But for each of them essentially, the claim rate
is below 5%.
So it's very low.
OK?
The second factor from this data is that reducing the deductible
is very expensive.
So for example, this is the full sample again.
On average, purchasing the insurance
where the deductible of $1,000 cost $615,
we can't say very much about that choice
because who knows how much the actual damages are and so on.
In some sense, that's sort of irrelevant for us
what that number is.
What we're interested in is like what
are the differences in costs of different deductibles?
How much do you have to pay to lower your deductible
to like $500, $250, and so on?
Now what you see here is like on average,
reducing the deductible from $1,000 to $500,
which is sort of what this column shows that's shown
in red, costs $999.91.
So if you choose then like $500, is this
is a risk-averse choice or not?
How do we think about that?
Suppose your claim rate is like, say, 5%.
Yes.
AUDIENCE: Well, I think it would be a risk-averse decision
because you're paying $100 more and your deductible
has gone down by $500.
So claim rate for that back of the envelope calculation
would need to be about 20.
PROFESSOR: Exactly.
So what you're saying is you're reducing the deductible
from $1,000 to $500.
Now, if you think that happens with a 5% chance, on average
you're going to reduce your payments by $25.
So 5% times $500, which is a $25.
But people are willing to pay about $100 for that.
So for sure they're paying $100, and the benefit that they get
is with 5% chance, at least the average customer,
with 5% chance they're going to pay $500 less in case
there's some damage.
That looks already pretty risk-averse.
Because as Ben says, surely you're
not risk-neutral, because then you would not do that.
You would choose the $1,000.
It looks fairly risk-averse.
Now if you go down then, if you go to like from $250 to $200,
there's an additional $133.22.
So that's to say reducing your deductible by another $150,
from $250 to $100, makes you for sure you have to pay $133.
And now if your chance is like 5% of getting like essentially
a damage, that is for a 5% chance of saving $150,
people are willing to pay $133 for sure.
OK?
So now if you try to calibrate this, what we already
know from this, the simple example
is that people look extremely risk-averse.
OK?
So that's kind of like the exercise that Sydnor is doing,
just saying, look, let's take these choices very seriously.
Let's look what people have done in real-world situations.
These are repeat customers, people
who have done this for a long time and so on.
What are people choosing?
And if you sort of assume expected utility, what would
people's gamma need to look like to be
able to explain this data?
And we can do this customer-- this is like the average rates.
They can do this sort of customer by customer.
Now, what he then finds is the majority of people
choose small deductibles.
Lots of people choose $250, $500.
Very few people choose $1,000, even among people,
and this is on the x-axis, who have been at the company
for 15-plus years.
You would say like the first time you do this,
maybe you don't understand your claim rate,
you don't understand what's going on or whatever.
But there's people who have been at this company for 15 years.
They should kind of know at some point
that claim rates are pretty low, at least on average.
And so like if you have 15 years at this company,
it's hard to believe that you'd still think that your claim
rate is, say, about 10% or the like
since it just doesn't happen very often.
OK.
Now, how do we think about people choosing a deductible?
Again, what you need is like the following parameter.
You need to have the yearly premium.
You need to have the deductible D. You're
assuming no other risks to lifetime wealth, which
is a bit of a distraction, but essentially you
can diversify risk and so on and so forth.
You also can assume that's at most one risk per year.
This is, again, sort of simplification
and doesn't really matter very much for the probability pi.
And then for now at least, we assume
accurate, subjective beliefs about the likelihood of a loss.
Now then, what is then the indirect utility function
of wealth?
What does the utility function look
like depending on these parameters?
Can somebody explain this what I'm showing here?
What is this equation?
Yes.
AUDIENCE: The first part says pi [INAUDIBLE] w
minus P minus D. The w minus P minus D
is your wealth if something happens.
[INAUDIBLE] pi.
And the 1 minus pi is on your utility of your wealth
if nothing bad happens.
[INAUDIBLE]
PROFESSOR: Exactly.
So for sure, so with probability 1 minus pi, nothing happens.
You have your wealth W that you had before.
You have to pay the premium for sure.
So in that case, you also have to pay the premium.
So you're going to end up with W minus P, the premium.
And then with probability pi, you also
have to pay the premium, which is W minus P,
but also you have to pay the deductible
because some damage occurred.
All right.
And then your indirect utility-- your expected utility
for that year is essentially then
the weighted average of these things.
And pi is essentially the weight on that,
which is the subjective or, in this case,
assumed actual probability of a damage occurring.
Now, I sort of said the indirect utility function,
utility of wealth function, what is that?
What's A, an indirect utility function?
And B, why is there wealth in it and not consumption?
Usually we think people eat stuff
and there should be like consumption here.
Why do we have wealth in here?
What is this?
Yes.
AUDIENCE: I think they might be like assuming [INAUDIBLE]
PROFESSOR: Exactly.
What is the indirect utility function?
AUDIENCE: [INAUDIBLE]
PROFESSOR: Exactly.
So usually you think what you do is if you go back
to like 14.01 notes or what was done in the first
I think recitation, usually what you
do is you maximize consumption with several goods
or one good or whatever over time,
and usually there's a budget constraint
and wealth is usually in your budget constraint, right?
You can only consume as much as how much money you have.
Could be like your income or your wealth
if it's over your lifetime.
Now when you do that and maximize it,
then you end up at an optimum.
What you can then do is like essentially express
the optimum.
Assuming that you have chosen optimally,
your consumption is saying you already
chose whether you wanted apples or bananas or whatever.
If we assume that you optimize, I can then essentially just say
assuming that you're optimizing, what
is your optimized utility for different levels of wealth?
And usually it's a function of wealth and prices,
and that's what the indirect utility function is.
We can very briefly also go over that in recitation.
But if you go back to your 1401 or other notes,
you will see essentially that it's
the outcome of a maximization problem.
Usually it's like for two goods or whatever.
Like, it's like income.
In this case, it's wealth because it's like over--
Yeah, it's wealth, but it could be available income
as well if you wanted.
Now, what the person is then going to do
is like each contract gives you an expected utility in terms
of how much do you expect your utility to be if you choose
that specific contract.
And now the maximization problem is now
you choose the contract J that maximizes the expected
utility or the expected indirect utility as a function
of these parameters.
Any questions on this?
So for each contract, we can write down what's
the indirect utility function.
It depends on people's wealth.
So we have to make some assumption
of how wealthy people are.
And it depends on these other parameters.
It depends on the premium, it depends on the deductible,
and it depends on the subjective probability of a claim
occurring in that year.
We assume that there's only one claim per year.
OK.
So now what we can do is then we can back out the implied risk
aversion from people's choices.
And in fact, what we can do is we
can get upper and lower bounds on people's risk aversion
from what they have chosen.
Let me sort of give you an example for that.
Suppose a person chooses a $100 deductible.
What does this mean?
Well, this means essentially that he or she preferred
the $100 deductible over all the other deductibles that
were available.
Right?
So essentially, if you choose the 100,
you get three inequalities.
You get like the $100 deductible is better
than the $250 deductible, the $100
is better than $500 deductible, and $100 is
better than $1,000 deductibles.
Now, this gives us a bound on people's risk aversion.
Is it the lower or an upper bound and why?
Yes.
AUDIENCE: I think it's a lower bound because $100 [INAUDIBLE]
is like the lowest you can go in a lower deductible
can cause more risk-aversion.
PROFESSOR: Right, exactly.
Sort of like a corner solution.
So like, if the person who chooses $100--
that's the person that I just showed you previously.
This is the example that I showed you here.
Where was it?
This is a person who looks extremely risk-averse, right?
This is a person essentially saying
like, I'm choosing the lowest possible deductible.
I'm for sure paying quite a bit of money
compared to all these other options, 4% or 5% chance
of not having a damage.
So this person will look very risk-averse.
It's the lowest possible option.
So maybe the person, if there had been a $50 or zero dollars
option, would have even chosen that option.
We don't know because that's not available.
What you can then do is, however, you
can just write down these inequalities.
And so if you choose the $100 deductible
compared to the $250 deductible, it
will be the case that if you solve for gamma,
this gives you a lower bound for or gamma.
So what does that mean?
We know that gamma is at least as high
as the solution of this inequality will tell us,
but in fact, their gamma could be even higher.
We just don't know it because we don't have additional choices.
Now, if you choose the $1,000 deductible on the other hand,
you'll get like an upper bound.
The reasoning is exactly the same.
Essentially, if you choose the $1,000 deductible,
that's like the riskiest option you
can choose because essentially you're
choosing something you will choose not
to reduce your risk in any way.
So you're not willing to pay to do that.
It's kind of like accepting a gamble
and not choosing the safe options.
But we don't know whether this person would
have chosen like $1,000 on one deductible,
or $2,000, or $5,000, what deductible would
have been chosen because there's no other options
of deductibles.
And then in between, we have essentially lower
and upper bounds, because essentially we
know that if you choose 500, we know
that you didn't choose 1,000, and we know also
that you didn't choose 250.
So your gamma must be in between those options whatsoever
as implied by those two options.
There's a previous problem set that we posted that sort
of walks you through that.
We'll also go through that in recitation
to go through the mechanics of that.
Any questions on this?
Yes.
AUDIENCE: [INAUDIBLE]
PROFESSOR: I think that's not a problem because it's just
sort of flipped.
So we have the gamma--
that's why you have the gamma in the denominator as well.
So you get a problem if your gamma is 1,
because in dividing by 1, usually people
use a log utility for that.
Yeah.
AUDIENCE: [INAUDIBLE]
PROFESSOR: Yes, that's a great question.
So I'll get to this in a second.
So what I have done right now, and this
is the typical way economists think about these things,
is sort of say, let's take a model very seriously.
Here's the model that I'm using to try
to explain people's choices, and I'm essentially
assuming everything else away.
I'm essentially assuming that the person optimizes.
Those no mistakes.
There's no framing of facts.
There's no other stuff going on, liquidity constraints
and so on.
And I'm taking this very seriously.
I'm estimating gamma.
Now, the typical-- and this is section four of the paper,
in fact--
the typical thing then that happens
is other people are going to say like, well,
what about if people don't understand what they're doing?
What about people misperceiving the risk?
What about people framing effects in terms of the way
you present the choices?
People like to not choose extremes, but like to choose
and the middle.
Can that explain the results?
There's some concerns about that.
I think one thing that your explanation, for example,
would be able perhaps to explain is people choosing $500 over
like $1,000.
It's hard for the framing effects
to explain why people are choosing 250.
So if you look at this figure in particular, the people who
are in the company for 15 years, lots of people
choose deductibles of 250.
It's a little bit harder to explain with framing effects.
Why wouldn't you choose like 500 as opposed to 250?
Sydnor argues that's really not what's going on.
I think at the end of the day, probably
it's the case that people do not want these extremes
and, to some degree, I think some
of what's going on in this perhaps
at least contributed by some form of framing effect, maybe
marketing.
People who sell the insurance choices really want people--
they get paid presumably if they sell essentially
these low deductibles because that's how the company makes
a lot of money.
What Sydnor says there is like, well, it's
actually hard to sell people on stuff that they don't like.
It seems like people really seem to want these things,
and maybe some of that is sort of sales pressure, but probably
not everything.
So I think some of what is going on
is a little bit hard to rule out all of those things,
but if you read the paper it's reasonable.
And since it's what I'm going to show you next
is like the implied gamma's like so large
that even if you sort of said, OK, half of this effect
is driven by other things, you would get still
like really absurdly large estimates of risk aversion.
But that's a great question.
Yes.
AUDIENCE: [INAUDIBLE]
PROFESSOR: Well, to some degree, in some sense,
I think the way they sort of--
The question was like, is the company deliberately
giving people choices that leads them to choose low deductibles?
And therefore, do we sort of overestimate people's gamma?
To some degree, yes, but it's not
like just we have low deductibles available.
There's a $1,000 option available.
I think maybe what you're alluding
to is like there's some sales pressure and so on going on.
That may well be true, and people
sort of might emphasize risk and make it particularly salient
and make customers nervous and say like, look, these floods
and so on are going on, and really, low deductibles
are good.
I think to some degree, that's true,
but you have to be pretty compelling in your reasoning.
One other comment is like, there's
lots of other examples of people choosing low deductibles
and sort of extended warranties and so on.
And in lots of cases, for example,
if you look at like iPhones or iPads and so on and so forth,
laptops, et cetera, Apple in particular,
but other companies try to sell extended warranties
that, if you actually did this exact same calculation,
are not worth engaging in or that
reveal essentially extreme risk aversion among customers.
I myself am looking at this kind of research.
There's lots of research that argues that people shouldn't
choose extended warranties.
Of course, then when I bought a laptop the last time,
I was like, of course I don't need extended warranties.
And then, of course, soon after, the laptop broke and so on,
and I didn't have a warranty and so on.
So of course, in specific examples that may happen,
but on average it's not a good idea to do.
OK.
So now what does Sydnor find?
So now here in this table, you can see the implied estimates
of gamma.
Remember, what we said is what we think
is a reasonable gamma is somewhere between 0 and 2
for large-scale choices.
He has different types of assumptions.
He has like lower bounds and upper bounds of gammas.
And what essentially you see is the gammas are like,
depending what the assumptions are, in the hundreds
or in the thousands.
It depends a little bit what people's wealth is.
So essentially depending on how much you assume people--
So the data that he does not have
is what is people's wealth actually like.
How much money do people actually have?
So he makes some reasonable assumptions by saying,
look, these are people whose houses are like $200,000,
$300,000, $400,000 worth.
So presumably, and we know from other data
sets roughly how much money people have available.
So then depending on essentially what utility function
you assume, he is mostly using like CRRA utility,
like then is wealth of like $1,000,000.
You can look at like $100,000, $50,000, $5,000, and so on.
You can also use CARA utility, which is constant absolute risk
aversion, and so on.
And essentially, what you have to assume
is like extremely low levels of wealth or something like $5,000
to get into like sort of single digits
or double digits of gamma.
It's extremely hard to sort of get
estimates that are reasonable in the sense
that we think are actually reasonable parameters of gamma.
Any questions on this?
OK.
So now, why do people choose those small deductibles?
And this is what you were saying before.
So one classical explanation would
be, well, they must be really, really risk-averse.
Their gamma must be really high.
There you might sort of say, well,
we know already that gamma shouldn't be that
high from some other choices.
So that's sort of hard to reconcile.
Was there a question?
No.
Second, you could say, well, there's really
high objective probability of claims.
We know that the objectives for probabilities
are only 4% or 5%.
You'd have to sort of have probabilities
of claims that are like 20%, 30%, 40%
to be able to match these data.
Now, it be that people have risk misperception.
It could be that people really think
the probability is actually 20% when it's, at the end, only 5
or 4.
Now, what's sort of inconsistent with that
is that like repeat customers, people that
have been at the company for 10, 15, 20 years,
are making very similar choices.
In some sense, it's hard to reconcile that everybody
is misperceiving this risk year after year after year
and spending lots of money.
There's some questions on is it borrowing constraint?
Is it like people just don't have enough money?
Are they worried about having to pay these deductibles?
That also seems quite unlikely because in fact,
the deductibles are particularly--
we're not talking about like $5,000.
People could sort of, if they really
faced these borrowing constraints,
they could save and so on.
So Sydnor also argues that that's not going on.
There's some questions about marketing social pressure
and so on, which is--
of course, the company has very much like incentives
to sell people these kinds of deductibles.
I think some of that is probably going on,
and it's hard to rule out entirely.
Again, like, it's hard to actually sell people stuff they
don't really want to.
So there must be lots of social pressure to, in fact, do that.
Menu effects.
Already talked about it a little bit.
There we think that maybe menu effects
can explain why people choose to 500
or, like the interior choices, why they don't choose 1,000.
It's hard to explain with menu effects
why people choose 50 over 500.
So then Sydnor's preferred explanation
is then reference-dependent preferences and loss aversion,
which we're going to talk about next.
Yes.
AUDIENCE: Is there any data on whether the probability
of the claim is correlated with which menu option the people
chose?
PROFESSOR: Yes, there is.
So you have it here.
So it's sort of weakly correlated in a sense.
Like, if you choose--
or weekly negatively correlated.
So people who choose $1,000 have 2.5% claim rates, and the $100
are 4.7.
So that's kind of not quite explaining things either.
Yeah.
AUDIENCE: I think the use of [INAUDIBLE] regression
to control for fact that those with lower deductibles
may claim multiple times.
PROFESSOR: I see.
Yes.
Great, yes.
OK.
So what do we learn from this?
I think this is very much sort of confirming
some of the lab evidence data on relatively small-scale gambles.
These are not like small-scale gambles of like a dollar
or 2 or 5 or 10.
These are about several hundreds of dollars,
but they're not about hundreds of thousands of dollars.
So these are relatively small relative to like people's
lifetime wealth.
And what we see for those kinds of choices is
it really looks like people appear
to be very, very risk-averse.
This is what I was saying already previously.
When looking at sort of reasonably small-scale
choices--
and I count the Sydnor evidence as reasonably small-scale
choices because it's not about like hundreds of thousands
of dollars--
you essentially see that such choices imply
people seem very risk-averse.
These choices imply enormous risk aversion
for large-scale risks.
But people are not avoiding all sorts of large-scale risks.
People take on lots of large-scale risk.
So in some sense, that can't be true in some ways.
We also find that individuals are moderately
risk-averse a large-scale risk.
People are taking on some risk, as I said.
Now, if you sort of take that seriously
and say, well, people might not be risk-averse, that in turn
implies that people are nearly risk-neutral.
They should be nearly risk-neutral
for small-scale risk.
So it can't be that both of these things
are true at the same time.
Now, in fact, there's a much older paper
that's a very famous and seminal paper by Kahneman and Tversky.
Kahneman got the Nobel Prize, in fact,
for this work and similar work.
Kahneman is a psychologist and they
were doing psychology experiments,
and it just turned out that these psychology experiments
they're extremely influential in affecting how economists think
about risk and risk preferences, and in particular,
sort of preference-dependent preferences.
And so what Kahneman and Tversky were doing at the time way
before a lot of this other literature
that I just showed you--
A, they showed even more sort of evidence
against the expected utility model.
But perhaps more importantly, they also
proposed an alternative model in saying,
look, here's some choices that we
think are hard to explain and hard to rationalize
using expected utility.
Now here's a different model that can explain things perhaps
better in some situations.
So what did Kahneman and Tversky actually do?
The experiments are actually extremely
simple in various ways.
They're very clever and very clean,
but actually very simple.
And so what do these experiments look like?
These are survey responses.
Like, essentially they just asked
people about what would you do in different situations.
This is not what economists were doing at the time.
Economists at the time were saying
like, revealed preferences are important.
I need to make you do actual choices.
Whatever you say in surveys doesn't
matter because who knows whether you actually mean what you say.
It turns out that the survey responses are actually--
these are hypothetical stakes, but it turns out
that if you do this with actual stakes,
you find very similar results.
And the experiments were as follows.
There were things like questions like, which of the following
would you prefer, kind of like I showed you in the first class
at the end of the survey that you did.
Would you prefer option A, which is
a 50% of winning $1,000 or 50% chance of winning nothing,
versus option B is like $450 for sure?
And so they did a series of these types of questions.
Now, one of the things that then they
showed is one key prediction of expected utility
is that, as I said before, people only
care about final outcomes and their associated probabilities.
Kahneman and Tversky show a bunch
of different striking contradictions of that.
I want you to focus on the first row-- problem three and problem
three prime.
And look at that and tell me what of that
example is contradicting expected utility.
I don't know if you can see this.
So let me just read this for you if it's hard to see,
but think of them for a second.
Problem three says, "Would you prefer
an 80% chance of $4,000 over $3,000 for sure?"
What do you see below then?
These are always 100 people.
You see the number of people who preferred
one option over the other.
So 80 people preferred the 3,000 option.
20 people said I'd rather have the 80% chance of $4,000.
That's problem three.
Problem three prime is about what
they call negative prospects.
Would you prefer an 80% chance of losing $4,000,
or for sure losing $3,000?
And there you see 92% choose the first option and 80%
choose the $3,000 loss for sure.
Let's start with the left example.
What did we learn from the left example?
Are people risk-averse, risk-neutral, risk-loving,
or what have we learned from that?
AUDIENCE: Risk-averse.
PROFESSOR: Risk-averse, and why is that?
AUDIENCE: If you calculate the expected monetary value,
I guess you would expect to [INAUDIBLE]..
PROFESSOR: Right.
So we said before somebody is risk neutral
if the person is indifferent between two options
when they have the same expected monetary value.
And so in this case, an 80% chance of $4,000
is $3,200 in expectation, right?
But there's a bunch of people who say,
I'd rather get the $3,000, which is less than 3,200, for sure.
Which means essentially they take a surer--
like an option that's for sure they get.
They prefer that over the uncertainty
of getting 0 versus 4,000, which on average gets them more,
3,200.
Expected utility would say if you choose that option,
it must be that you are risk-averse.
Now, not everybody seems risk-averse.
There's 80 people out of 100 choose that,
or I think it's 80% choose that and the remaining ones
choose the other option.
These other people we don't know much about.
They're not very risk-averse, but they
could be also risk-averse just like it was
revealed in their choice there.
OK.
So from the left side, we say we know
at least 80 people, or 80% of the sample, is risk-averse.
Now let's look at the right side.
What do you see on the right side?
Yes.
AUDIENCE: Well, they seem to be risk [INAUDIBLE],,
because unexpected risk minus 3,200 versus minus 3,000,
but they prefer the minus 3,200 on expectation.
PROFESSOR: Right.
So if you look at the left option, it's minus 3,200.
So the left option has more risk,
and it also has a lower expected monetary value.
As you said in the expected monetary value,
it's just a flip of the problem three.
It's minus 3,200, and the other one is minus 3,000.
So if you're in a risk-neutral, surely you
would choose the minus 3,000.
If instead you choose the minus 3,200, well,
it must be that you really appreciate that there
is additional risk there.
So it looks like you're risk-loving.
OK.
And now we find here that 92% of the sample
choose the first option, but at the same time,
with the same people, when they're offered or given
the choice between problem three, 80% of people
choose the other option.
So there are a bunch of people essentially
that choose the $3,000 for sure in problem three.
At the same time, they choose the minus 4,000
with an 80% chance when given problem three prime.
So that means essentially we have two choices here.
One choice says people are risk-averse.
The other choice says people are risk-loving.
In expected utility terms in our world, this cannot happen.
The reason being that we have one parameter, which is gamma.
Gamma tells us how risk-averse or how risk-loving
or the risk-neutral alike.
That parameter tells us everything
about your risk preferences for all choices
that I'm giving you.
It cannot be that you're simultaneously risk-loving
and risk-averse.
So this evidence essentially sort of rejecting the expected
utility model or cannot explain this behavior.
Does this make sense?
I sort of wrote this down here, but I
think I said everything that's to be said.
Any questions on this?
So where we're going to go is essentially A,
these people seem to be behaving differently
for gains versus losses and, in addition
to that, so not only do people seem to dislike losses--
I'll show you some evidence of that--
but in addition, people seem to be risk-loving for losses
and risk-averse for gains.
And that's kind of what Kahneman and Tversky are claiming.
And once you make that claim, you'll
be able to explain these patterns in the data.
Now, a second thing that they show is the following.
They show in problem 11 and problem 12.
I'll let you read it for yourself.
And essentially, you see that 84%--
so the choice here is in addition to whatever you have,
for sure you're going to be given
$1,000, or shekels I guess.
You are now asked to choose between 1,000 with a 50% chance
and 500 for sure.
OK?
84% say option B.
Problem two is, in addition to whatever your own,
you have been given 2,000.
You're now asked to choose between option
C, which is minus 1,000 with 50% chance,
and option D, which is minus 500.
69% of people here say they choose option C. OK?
So what's the problem with this?
Yes.
AUDIENCE: I mean, at the end of it,
you would say that problem 11 option
B, you end up with 1,500.
Whereas problem 12 option B, you still end up with 1,500.
People were inconsistent with these decisions
based on how the question's framed.
PROFESSOR: Exactly.
So framing matters, or reference to points matter.
And so what assumption of the expected utility model
is that rejecting?
AUDIENCE: [INAUDIBLE]
PROFESSOR: Exactly.
So we postulated that only final outcomes matter.
Here, if you write this down, it turns out
option A and option C are exactly the same in terms
of final outcomes.
Turns out option B and D are also exactly the same.
I'll let you look at this for a second.
So A and C are the same in terms of the final outcomes.
B and D are also exactly the same
in terms of final outcomes.
So that means essentially when you compare A versus B and C
versus D, If you only cared about final outcomes,
you cannot choose different things here in this lottery.
It cannot be that your utility is defined over just final
outcomes, because you just told me you like two different
things for the exact same thing.
And there's 84% who choose option B while 69% choose
option C. So there's a bunch of people who essentially switch.
Is that clear?
OK.
So now, what is that?
What's going on here?
Well, where we're going to go is like well,
it seems like, exactly as you say, framing matters.
How you frame the problem matters,
but why does it matter?
Well, it's because we setting like a reference point.
In the first place, in the first example,
the reference point is like 1,000 and there is like a gain
relative to 1,000.
We look at like people evaluate this gamble as like gains.
In the second example, the reference point
is set to like 2,000, and now people essentially
evaluate this gamble as losses relative to the 2,000.
And of depending on how people think
about gains versus losses, it turns out
that people make different choices.
I'll be more formal about this, but that's essentially
the idea of, like in Kahneman and Tversky,
their prospect theory they proposed,
why can explain these behaviors as opposed to expected utility?
OK.
So now what are sort of the most important points?
There's three of them.
I'm going to show you two and then get
to the third one at the end.
So one is like what matters a lot for people's behaviors
is changes rather than levels.
So what they argue is utility is not defined by people's final
status-- how much they end up with--
but as opposed to like how much changes
relative to some reference point.
That could be changes relative to like a status quo.
How much do I have right now and how much
does it change positively or negatively?
Or, it could be relative to some expectation
or some other reference point.
What I showed you here in this example
is like this is not the status quo that people evaluate
their utility against because the outcome is always the same.
The reference point here is kind of like the expectation
I sent you and say, OK, here's 1,000.
And now what seems to be happening
is that people's expectations, in fact, become 1,000.
And then relative to that expectation,
people are going to evaluate gains and losses.
And similarly, if I give you-- like, say you get 2,000,
again, people will evaluate the utility
or the outcomes as gains and losses relative to that.
Second, there seems to be loss aversion.
Losses loom larger than gains.
That is to say people dislike a loss that's
as large as a gain by a lot more than they like the gain.
OK?
So it's like if you say you lose 100 versus you gain 100,
people really dislike losing 100 a lot more
than they like gaining 100.
And once you sort of postulate that,
well then, that can explain why you reject a bunch of gambles.
Because if say if the gamble is like minus 10 with 50% chance
and plus 11 with 50% chance, well,
if you dislike the losses a lot more, if you dislike
losing $10 a lot more than gaining $10 or $11, well then,
you're going to reject this gamble
even if the expected value is positive.
OK?
We'll write down sort of like a utility function next time.
That's sort of does this more formally,
but essentially those are the two key areas.
There's a third one, which I'm going to get to in a second.
Now, the key part here is like there is essentially
reference dependence.
People evaluate their outcomes relative to some reference
point.
What kinds of examples do we actually
have a reference point?
When you look in the world-- and again,
that's kind of very much what I'd like you to do--
when you think about things that you see in the world,
what kinds of examples do we have that people care
about reference points as opposed to final outcomes?
Yeah.
AUDIENCE: My first thought was, you know how we have to pay
$0.10 for shopping bags?
Where I was from a couple years ago,
we did it so that if you used a reusable bag,
you got $0.05 back.
That was like not effective.
[INAUDIBLE]
PROFESSOR: Right.
Yeah.
So exactly.
When you think about pricing of different options,
it matters a lot to people.
It seems that when you add $0.05,
were to subtract $0.05 or $0.10 or whatever,
the same changes about like it's just $0.05 at the end
of the day that you have to pay more or less,
depending on whether you use a bag,
your choice of using a bag versus not should not be
affected by whether it's framed or put as like a loss versus
a gain or like a whatever rebate or whatever that you might get.
And I think that's true for many different-- that's
true for shopping plastic bags or any other shopping bags,
but it's also true for many other options.
It depends a lot whether you sort of add on that option
or whether you get sort of essentially
subtracted the option as some discount.
Yes.
AUDIENCE: [INAUDIBLE]
PROFESSOR: Right.
I think some of it is not exactly--
I think there's some legal constraints
to that specific behavior because you're not
supposed to sort of trick people, but surely some of that
is going on.
People love discounts.
Like, they love making good deals.
They love sort of getting things cheaper
in various ways compared to some reference point.
And the reference point, since it's
hard to tell what actually should the price be,
is often like the previous price.
It's something that seems really expensive
and now they're getting it for less money.
And so if you get it for half the price,
even if it's still quite expensive,
you think like you saved half of the price somehow.
AUDIENCE: So how you feel about what
you have may depend on what you see your neighbor having.
PROFESSOR: Right.
So reference points could not just
be prices or sort of things that affect yourself
in certain ways, and price is the key example overall.
The reference point could just be your environment,
your social environment.
We kind of talk about this to some degree
also when we talk about social preferences.
People care a lot about what others do,
and their reference point might very much
be formed by what their neighbors do.
Like, how big is their house?
How big is their car?
Do they have a swimming pool or not?
It could be also like your neighbor's-- like,
how good are they at school?
Are they smart, how good looking?
And so on and so forth.
So when people evaluate certain outcomes,
they often don't evaluate the levels, but rather
kind of how much another person makes
or whatever other people's outcomes are.
And part of the reason might be that
like evaluating absolute outcomes is really hard.
It's very hard to actually understand.
Is $10,000, $50,000, $100,000, a million--
how much money do you actually need to be happy
or that you like, or what kinds of outcomes
are you excited about and so on?
But it's much easier to say you have something
and another person does not or the other way around.
It's much easier to compare with others.
It's very hard to actually evaluate absolute outcomes,
because who knows how you should feel about that.
Much easier to say I have this, they
don't, or the other way around.
Yeah.
AUDIENCE: People sometimes don't want
to let go of fallen stock they own
because they don't want to see that they sold at a good price.
PROFESSOR: Right.
Exactly.
That's called what people call the disposition effect.
There's actually pretty large literature
studying this and lots of debates
on whether it's really going on or not,
how important it is, and so on and so forth.
But sort of one very basic stylized
fact is that when people are looking at stocks that they
might want to sell, they are much more likely to sell
winners compared to losers.
Now, why is that bad, or should you not do that?
AUDIENCE: Is that because the winners [INAUDIBLE]
PROFESSOR: There's a bit of a question
of is there like momentum or reversal or the like.
But if you believe in efficient markets, which
many economists do, or at least some
of them who are in Chicago--
if you believe in efficient markets,
then the current stock price should essentially
not be-- or like the previous losses
and so on should not be informative of what's
going on in the future.
So in expectations, your losers and your winners,
if there's any information about the future,
about the future valuation, that should already
be incorporated in the price.
So if you look at two stocks, one
lost some money and one gained some money,
they're equally likely to make you money.
And so if anything, what they show in these papers
is like there's momentum.
This is what you're saying is that the winners actually
are, in fact, going to be more likely to try to increase value
compared to the losers.
But people tend to essentially want to sort of realize gains.
People seem to be happy about making gains.
They seem to be very reluctant to sell the losers,
and there's some questions on how costly is that actually,
but that's a very robust pattern in the data.
The same is also true--
I'm going to show you on Monday, the same
is also true for houses.
People are much less likely to sell their house
when it has lost value compared to when it gained value.
I'm controlling for a bunch of things.
Yeah.
AUDIENCE: [INAUDIBLE]
PROFESSOR: Yeah, so that's a little tricky.
There might be other things going on, but exactly.
It could just be that like if you don't go to a movie
when you have bought a ticket yourself,
it's sort of perceived as a loss and you really don't like that.
It's a little complicated to think
about this in simple terms, because in some sense,
the loss is still there.
But anyway, yeah, exactly.
It's like you lost money.
It's almost like as if you lost the movie ticket
and didn't get some value from it.
There's a bit of a question whether you sort of integrate
these two things or not because people think
about monetary terms versus other things often
in separation, but I think some of that is exactly.
People feel like they have a loss if they don't take
advantage of the movie tickets.
So I'm going to show you some examples that are actually
much more basic in some ways.
When you think about like visual illusions,
this is what's called like the size contrast illusion.
So one of those things is like when
you look at circles or things that's
supposed to look the same, and in fact are the same size,
they look quite different.
Depending on what you contrast things with,
things look quite different.
For example, if you look at these circles in the middle,
they're in fact exactly the same size,
but in fact, they don't really look like that.
Similarly, if you look at these two circles,
it's perhaps more stark.
These circles are, in fact, exactly the same size
that are in the middle.
Every time I'm teaching this class,
I sort of have to convince myself that they are actually
the same size.
So I print it out and sort of measure
to make sure that it's actually the same size, and they are.
I checked.
But when you see this, even if you know it's an illusion,
it's very hard to convince yourself that it's not.
But they are the same size.
When you look at these bars, when
you look at the upper black bar and the lower black bar,
again, it seems like somehow the upper one is like wider,
but in fact, it's not, and again, it's
all about the contrast to the other side.
There's this one which throws me off the most.
When you look at fields A and B, they are the same color.
That's hard to believe once you see it.
They are actually the same color,
and again, I would print it out and actually
put them next to each other.
They are the exact same color.
I checked.
There's also a video that you can
watch that sort of shows this.
And exactly what's happening is the way
we perceive colors is coming from contrast, right?
So like black does not or gray doesn't look as gray when white
or darker gray is next to it.
Similarly here, if you look at the gray of this bar,
this is the exact same gray.
Again, you can print it out and sort of look at it.
It's the exact same.
When you look at it, it just does
look like on the right side it's darker than on the left.
Now, there's plenty of examples of reference dependence
for vision.
There's tons of them.
They're kind of quite interesting.
At some level, it tells us something about the brain.
Like, in some ways, we can learn about essentially the way we
evaluate certain outcomes overall is essentially--
it's much easier for us, or we think about in contrast,
it's very hard for us often to think about levels.
But of course, that's vision.
So in some sense, what did we learn really about utility?
One thing you can look at is bronze and silver medal winners
at the Olympics.
Presumably or arguably, winning a silver medal
is better than a bronze medal winner.
If you look at these two women, one of them
won the silver medal, one of them won bronze.
So what people have done and psychologists have done
is like took actually a bunch of pictures
from like ceremonies of bronze and silver winners
and just looked at who looks happier.
And when you do that, essentially
the bronze medalists look on average happier than the silver
medalists.
Presumably it's because they just missed gold
while the other person sort of won bronze
because it's great to be third as opposed to fourth.
And there's more.
You can read more about this, but that's sort of like one
finding.
Now, it's true for lots of different feelings,
perceptions, judgment, and so on.
People compare stimuli in various ways
when it comes to temperature, when
it comes to all sorts of things relative to reference levels.
It's very hard for them to evaluate it in absolute terms.
So it's easy to say-- when you look at water,
it's very hard to say what's the temperature
even if you sort of practice it a lot.
It's very easy to say one bucket of water
is warmer than another.
It's very hard to sort of say it's like 70 degrees or 60
or whatever.
It's very hard to sort of understand
what absolute temperatures are, and I
think that's the same in some ways for a lot of consumption
or other decisions.
It's very hard to say how much would you pay for this
or how happy should I be with certain outcomes,
because people need some reference,
and often then the reference are either
some expectations, or their neighbors,
or just comparing between different options.
So that's the example I mentioned previously,
which is it's much easier to compare
your income or any outcomes-- your grades,
et cetera-- compared to what your friend has.
It's much harder to say how much an extra $1,000 or having
$50,000 per year, is that good or bad?
It depends a lot on what you compare it against.
So what people tend to do, and this
is exactly what Kahneman and Tversky were postulating,
is that people compare the outcomes
relative to reference points.
And again, we're going to write this down
in more detail at the beginning of next class,
but what Kahneman and Tversky were postulating
were essentially two things.
They're postulating A, there's a reference level
of consumption or any outcomes.
We can talk a little bit about what actually is this reference
level, where it's coming from.
For now, we just assume there's a reference level that people
compare the outcomes against.
And then against that, outcomes are compared.
And in particular, the function is
like steeper on the left compared to the right, right?
Essentially losses loom larger than gains.
So like going down by 10 units on the left or 1 unit
on the left is more painful than going up
on the right relative to those reference points.
OK?
And so that's all said.
So then what experimental evidence do we in fact
have for that?
So one example-- so we have some experimental evidence of this.
And I'm going to show you next time
a bunch of different examples of real choices,
starting from golfing, to selling houses,
to lots of other outcomes.
But sort of the experimental evidence, the earlier
experimental evidence that people showed
were preferences over risky gambles.
I showed you some of those already, and then in particular
unwillingness to trade different options compared
to like an alternative option that I showed.
That's what people refer to as the endowment effect.
So let me show you first the gambles.
We already had that in some sense.
These are like essentially gambles.
People seem really risk averse when
they are offered these gambles.
Kahneman and Tversky would say people are essentially
loss averse.
People really dislike the loss of $10
relative to the gain of $11.
We can explain that behavior.
And that's a very robust finding that people decline these kinds
of types of gambles.
Kahneman and Tversky would say that's evidence
of loss aversion.
Now, you might say these are really small gambles.
Do we really care about them?
Well, once you do this with $500, $550
or whatever, large amounts, people also do the same.
It's hard to do this with like real-world money
because it's quite a bit of money.
It turns out there's actually some studies who
do that as well.
They did this for real with MBA students, financial analysts,
and rich investors.
And even those people like tend to then turn down
those kinds of gambles.
So there seems to be quite evidence
of lots of loss aversion.
Given the choices between gains and losses,
people seem to really dislike losses.
Now, what's the endowment effect?
That's sort of the perhaps most famous evidence in this domain.
It essentially is people, when endowed with a certain item,
they really do not like to trade.
And so the way you would do an experiment--
you would give people an item, and then
you ask them essentially-- and a randomly selected fraction
of people are given an item.
And then either people are offered the choice--
you would you either keep your item,
or would you get another item that's sort of the same value
overall?
Or, what people do is like they have some experiments--
there's many of these experiments--
you give some people one item and some other people
another item, and then see would you
like to trade with each other.
And what you see is essentially people
are extremely reluctant to trade.
There's many of these kinds of examples.
Like, for example, so one example-- sorry,
I skipped that.
One example is like if you just give people an item--
usually it's like a mug-- if you give people a mug
and asked like, how much do I have to pay you
to give me to sell me this mug?
People say large amounts.
They would say like $5.
If, instead, you asked them, here's a mug.
Would you like to purchase this mug?
And sort of controlling for how much money they have and so on.
If you ask them like, would you like to buy this mug,
people would say like $2 or something.
It's the same mug, and essentially their choice
depends on whether you give them the mug versus whether you
endow them with the mug, which is where the endowment effect
name comes from, or whether you just sort of like
ask their willingness to pay when they don't have it.
There's tons of different experiments
that do exactly that.
Now, a different version of that is like
so this one is about like buying a mug, selling a mug,
buying and selling prices.
Different versions of that is to say
you have a population of students or different people,
and what you do is essentially you
find two items that on average have the same valuation.
Knetsch was doing that.
And so he had like mugs and pens,
and he sort of calibrated such that on average, when you just
asked, people's willingness to pay for these mugs and pens
are like on average roughly the same.
Of course, there's variation, but on average it's the same.
And then you offered half the students mugs
and half the students pens and then offered in exchange.
He also offered in exchange for an addition of $0.05
and saying like, OK, maybe you're
just exactly indifferent.
So I'm giving you $0.05 in case you exchange.
And it turns out that the mug people like to keep their mugs,
and the pen people like to keep the pens, and 90% of people
do that.
That's one of the most robust findings
in experimental economics.
There are some questions on expectations.
Do people expect to keep the mugs and so on and so forth?
There's some complications for that,
but the basic result is very robust
and has been shown in many different settings.
Any questions on this?
OK.
So what's going on here?
Well, essentially, the reference point
seems to be essentially affected by ownership.
So if you own a mug, your reference point
is owning a mug.
So now if I asked you, would you like to sell me this mug?
Well, now you have a loss of a mug.
So essentially, you're in the lost domain of mugs.
So I have to pay you more money to compensate you for that.
If, in contrast, you do not own the mug, so like you have zero
mugs, your reference point is zero mugs, and I'm asking you,
would you like to receive a mug or like buy a mug from me,
then you're essentially on the gain domain.
And sort of what I showed you here previously--
one second.
So when I'm asking you to purchase your mug,
essentially you're on the left side of this figure.
You're in the loss domain.
Your marginal utility of mugs is very high.
I have to pay you a lot of money to receive the mug from you.
In contrast, if you have zero mugs, I'm asking you,
would you like to purchase a mug,
you're on the right side of the suffering point.
So essentially now you're in the gain domain.
Now you're not willing to pay a lot of money
because you're gaining a mug.
On top of that, you also on the gain loss domain of money,
but like I'm setting that sort of aside.
Does that make any sense?
OK.
And so people hate losses more than they like the gain.
So they stick with the mug.
And similarly, that's the same thing for the pen owners.
There's lots of different examples
of those kinds of behaviors.
For example, law school students were
asked to assess compensation for pain and suffering damages
in one study.
This is expected to last--
or in this example-- is expected to last three years
and be quite unpleasant.
There's no impact on earnings capacity.
For example, it would be extreme stiffness in the upper back
and neck.
I think that would probably affect your earning capacity,
but anyway let's assume that's not the case.
So then some students are led to imagine
they were being injured.
How much would you be willing to pay to get better?
OK.
So your reference point is like you're injured.
How much are you willing to pay to get better?
And people said 151,448 on average.
Now, another group of students was--
this is randomized-- was led to imagine being uninjured.
Like, how much would I need to pay you to accept the injury?
You're not injured.
Now I'm asking you, how much are you willing to pay,
or how much do I have to pay you,
how much do I have to compensate you to accept this injury?
Now, you would think this is like the same thing,
but what's your price of not being injured?
The price of health should be independent on which way I'm
asking you.
Turns out, when people have their good health,
they're willing to pay a lot more to keep it
or to not lose it compared to like when they have lost it
and they want to regain it.
There's another quite nice example.
I'm showing you here.
One second.
So in case you didn't see, that was Dan Ariely,
who has several nice books.
One of them is predictably irrational,
which is a quite nice read.
So there's lots of these kinds of examples of loss aversion
or what's called the endowment effect.
When people have stuff essentially,
they're not willing to part it.
When they don't have it, they're willing to pay less.
One nice thing that Ariely was also talking about-- a little
bit about how people then explain
these kinds of behaviors.
We're going to get back to that in I
think lecture 20 or something, which
is about kind of like I think what's going on here
is very obvious.
Potentially, people are loss-averse
and they're randomized into like gains or losses,
and that's kind of what's explaining their behavior.
But people don't necessarily understand
that they're being randomized in one of the other conditions,
and they then sort of try to explain their behavior
in various ways and saying, I want to tell my grandchildren
about this.
But in some sense, they're sort of
like rationalizing their preferences
and they don't necessarily sort of understand these stories,
and they don't necessarily understand
where these preferences are coming from even though we kind
of know, because the person has been manipulated
into those kinds of choices.
We'll get back to that.
Now, the third part of Kahneman and Tversky's prospect theory
of their paper is essentially what's
called diminishing sensitivity.
I'm going to get back to this and sort of write this down
in more detail on Monday, but essentially it's
like people are risk-averse in the gain domain,
but risk-loving and the loss region.
What does it look like?
Essentially the utility function is
a little bit different from what I showed you before.
It's not only like more steep on the left
relative to the reference point compared to the right,
but it's also concave on the right and convex on the left.
And what that gets you and what that buys you essentially
is that people are risk averse in the gain domain,
but people are risk-loving in the loss domain,
and that sort of is needed to be able to explain some
of the behaviors that I showed you
early on in the Kahneman and Tversky evidence.
So again, I'll tell you about this in more detail
and sort of write this down more precisely.
And then we're going to talk about
like many different applications.
And particularly, there's the endowment effect
which is kind of what I talked to you already about before.
There's labor supply, employment,
and effort depending on what people expect,
how much they earn.
They make different choices about how many hours
they actually work depending on the expectation,
whether it's above or below a reference point.
People are reluctant to sell their houses
if they're at a loss compared to again
even for very similar houses.
And marathon-running people are trying
to reach essentially certain targets.
People like to be below four hours or three
hours and the like.
There's the disposition effect that we mentioned,
which essentially is people like to sell winners
compared to losers.
And the insurance choice that I already showed you before--
there's some evidence on violence in the household.
The particular example is about football or games essentially--
I think football games where essentially depending
on whether people expected a loss or win of their team
and when then a loss or a win of the team actually happens,
there's more violence when there are unexpected losses compared
to expected losses which is, again,
consistent with loss aversion.
What's next?
So next we're going to talk about many applications
of reference dependence on Monday.
I'd like you to sort of read the Kahneman and Tversky
paper, at least the first pages to get
some sense of their work.
And then on Wednesday, we're going
to start talking about social preferences.
In particular, we can have some experiments in class.
There's going to be no readings for that.
There's the opportunity to make money
in class, at least some of it.