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FRANK SCHILBACH: Welcome
to lecture three.

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Today and on
Wednesday, we're going

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to talk about time preferences
and particular theory.

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We're going to talk a lot
about a lot of applications,

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a lot of applications
that are sort of close

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to your real world, including
procrastination of problem

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sets, all sorts of other choices
such as credit card debt,

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and so on, and so forth.

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Can you be a little quiet?

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Thank you.

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Think of the lectures
today and on Wednesday

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building some framework
and some sort of structure

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and how to think
about these things.

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It's a little drier than
maybe other lectures, in part

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because it's about theory, and
about writing down a model,

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and trying to think
about the world.

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Partially we're doing
that to sort of try

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to explain behaviors
that we see in the world,

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partially we do that
because at the end,

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we try to think
about welfare and how

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to evaluate certain
outcomes-- is

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that good or bad-- certain
policies and things to do,

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which later in the course
we're going to talk about.

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But for that you,
need some structure

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how to think about
some of those things.

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At the heart of
it, a lot of this

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is about procrastination, about
choices between the present

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and the future.

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Your problem set, in part, is
also about procrastination.

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It will be posted later
today, probably late.

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Please do let us know if
you have any questions.

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As I said, please be on time.

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Do the readings.

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There will be
random pop quizzes.

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They will be at the
beginning of the class,

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so you should be on time.

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The laptop section
is still over there.

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If you want to use your laptop,
it should be there, ideally,

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in the front, in part
because you're not

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going to bother others.

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I saw quite a few people
using their phones

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in class in previous classes.

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Try to not do that.

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That's not good for you.

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You will not be able to take
away much from the class.

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Multitasking is very
hard for people to do.

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Again, I'll show you
some evidence on that.

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As I said, the problem set
will be posted shortly.

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If you have any questions,
please do let us know on Piazza

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and help others answer them
or answer them for others.

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I have office hours,
usually Tuesday afternoons.

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Please sign up for them.

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I'm very happy to meet you.

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It's very hard for me to meet
people or get to know you

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in the large class otherwise.

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So please come to office hours.

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I'm happy to talk to
you about anything

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you're interested
in, ideally related

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to behavioral economics.

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So let me give you an overview
of this and the next lecture.

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We're going to talk first
about exponential discounting.

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Why are we talking about
exponential discount?

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This is the workhorse model
of classical economics.

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This is how economists usually
think about choices over time.

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Second, we're going to identify
some problems with this model,

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and try to think about why
is this model perhaps not

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explaining things well,
at least in some settings?

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And how could we
improve on that?

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I'm going to propose an
alternative model, which

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is the quasi-hyperbolic
discounting model.

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And then we're going to
talk about sophistication

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and naivete, which is the
idea that if you think

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you have different preferences
in the present form

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in the future, then it becomes
very important to understand.

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Do you actually know
what's going on?

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Do you know that in the
future you might be impatient,

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or do you perhaps think
that in the future,

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I will be very patient,
and then perhaps make

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some mistakes accordingly?

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I'll get to this in more detail.

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So it's first
important to notice

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that any choice, essentially
almost any choice you

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make, almost always involves
some choice over time.

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Essentially, some trade-off
between the present,

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between some cost and
benefit that you might occur

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in the very short run, and
some costs and benefits

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that you might enjoy
or incur in the future.

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What examples do we have?

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What choices over
time do we face?

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Yes.

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STUDENT: Savings
versus consumption.

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FRANK SCHILBACH: Uh-huh.

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And how do you decide
how much to save?

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STUDENT: Depending on your
preferences and interests,

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right?

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FRANK SCHILBACH: Right.

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So you have the
choice, for example,

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if you think about should I
save some money, let's say,

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for next semester or next year.

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So your choice is either
to consume the money now

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in various ways--
eat food or whatever

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you would like to do with it,
spend it on various activities.

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So if you save, if you
make the decision to save,

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you have to give
up some money now,

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and you get some
benefits in the future.

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The benefits in the future
are determined by the interest

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rate, as you say.

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If you have a savings
account or the like,

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you can essentially get
some benefits in the future.

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And then you have some
costs in the present, which

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would be essentially
not consuming now,

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and some benefits in the
future, which is getting

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that money in the future.

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And then you need to somehow
decide is that worth doing.

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There's some cost and benefit.

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We need to aggregate somehow,
whether to make that choice.

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Any other choices
you make over time?

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Yes.

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STUDENT: Whether to
go to college or not

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or start working right
away and make some money

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or delay that income.

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FRANK SCHILBACH: Right.

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So I actually have this
example here-- going to school.

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It has some costs and benefits.

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And what are the costs and
benefits of doing that?

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STUDENT: You
sacrifice four years

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or whatever right
now versus supposedly

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a higher income later on.

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FRANK SCHILBACH: Exactly.

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So you have direct
costs of education,

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which is tuition in many cases.

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Sometimes that's sponsored,
but often there's tuition.

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It's quite a bit of money.

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It's also the opportunity cost,
which is often forgone wages.

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You could be working
otherwise and make more money.

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There's the joy of pain
of going to school.

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Some might think it's positive.

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Some might think it's negative.

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And then there's future
wages, which in many cases,

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at least for you
guys, tend to be

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higher from going to college.

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If you do a PhD, that
might not be the case.

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I'm not sure if the
TA's are here, but yes.

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I'm sorry for that.

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And then you have to decide
are you going to school or not.

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What do you need to do
is you need to determine

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the utility, the value of each
of these costs and benefits.

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And they occur in
different points in time.

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You need to make some estimates.

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And then, of course, there's
risk and other issues involved.

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You might not have full
information, and so on.

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But assuming that
all away, suppose

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you knew all the costs and
benefits of going to college.

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Then you have to decide,
is that worth doing?

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So somehow you need to aggregate
these costs and benefits

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over time by putting
appropriate weights

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on different periods
in time, and decide,

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should I do this or not.

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OK.

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Yes, any other similar
choices that people make?

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Yes.

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STUDENT: [INAUDIBLE]

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FRANK SCHILBACH: Right.

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For example, you
could think about

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should I do a problem set?

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Should I come to class?

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Should I study for
an exam, and so on.

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Often, there's costs
and benefits involved.

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Often, the costs are immediate.

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You have to work
on the problem set.

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That might not be pleasant.

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You have to study for the exam.

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That might not be pleasant.

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You could be doing other
things instead that you

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can't do because of that.

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And then there's going to
be rewards in the future,

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usually in the terms either
through increased knowledge

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that might be useful for
other things in the future,

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or through better grades, or
whatever you might be rewarded

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from having more knowledge.

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And then, again, there might
be uncertainty involved

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because it could be that you
might not fully know what

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the costs and benefits are.

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It could be that
it's sort of risky.

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You might come to class or
not come to class depending

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on whether there's a pop quiz or
not, so there's risk involved.

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But assuming that away,
there's essentially

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benefits and costs
in the present,

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and then benefits and costs,
potentially, in the future.

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And again, somehow you have to
aggregate these and weigh them

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in various ways.

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Any other choices?

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Yes.

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STUDENT: Exercise.

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FRANK SCHILBACH:
Exercise, yeah, exactly.

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Exercise is a good one.

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Again, in the present,
you might not enjoy it.

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Some people might
actually enjoy it a lot.

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Somebody would tell
me he was addicted

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to exercise-- that also happens.

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But usually, people, at
least in the short run,

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tend to not like
exercise that much.

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But I think it's useful for
them to do, in part because they

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feel better afterwards,
in part because they

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have long-run benefits.

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Maybe they're in better
shape eventually.

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Maybe the healthier eventually.

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Maybe they'll live longer
eventually, and so on, and so

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forth.

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And again, what
you need to do is

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you have some
costs and benefits.

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You have the costs of getting
ready, getting out of the door,

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and getting yourself to do it.

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That often is costly.

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There's the cost of exercising
itself, which often is costly,

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maybe not.

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But then the benefits
are often in the future,

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often really far
away in the future.

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So if you really were
eating healthier, often

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the same thing--

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essentially, you might not like
eating spinach and vegetables

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in the present.

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Some people, of
course, love that,

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but often, then,
the benefits come

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in the form of improved
health many, many years out.

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And again, what
you need to do is

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you need to quantify somehow
the costs and benefits

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of certain actions.

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And then you need to aggregate
the costs and benefits somehow,

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to be able to make a choice.

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Is that a good
idea or a bad idea?

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Do you want to do this or not?

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A number of different examples--
here's another example

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of something that's
very trivial--

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purchasing an
expensive software.

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You have to spend some
money of doing it.

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That usually entails
negative utility.

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People don't like
to give up money.

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Second, there's
pain and frustration

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of learning the software.

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Again, that's often
negative utility.

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And then there's
mastery, which is

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positive utility from knowing
or learning the software,

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until it becomes obsolete.

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So there's a stream of positive
utility sometime in the future.

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Now, how do you decide whether
to purchase the software?

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Well, you determine the
value of the utility

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of costs and benefits somehow.

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And we're going to talk about
in some degree how to do that.

253
00:10:09,248 --> 00:10:10,790
And then once you
have that, you need

254
00:10:10,790 --> 00:10:13,340
to weigh the costs and
benefits, and try to aggregate,

255
00:10:13,340 --> 00:10:16,310
and try to figure out, is
this a good idea or not.

256
00:10:16,310 --> 00:10:18,833
There's another choice,
which we're actually

257
00:10:18,833 --> 00:10:20,750
going to talk about when
we talk about welfare

258
00:10:20,750 --> 00:10:21,740
and about policies.

259
00:10:21,740 --> 00:10:24,350
Overall, it's deactivating a
social media account, in part

260
00:10:24,350 --> 00:10:26,308
because there's a very
nice study that actually

261
00:10:26,308 --> 00:10:27,510
studies precisely that.

262
00:10:27,510 --> 00:10:30,140
So if you think about
deactivating a social media

263
00:10:30,140 --> 00:10:31,670
account--

264
00:10:31,670 --> 00:10:35,450
Facebook, Twitter, Instagram,
whatever people are using--

265
00:10:35,450 --> 00:10:38,120
there's different costs
and benefits involved.

266
00:10:38,120 --> 00:10:40,940
And you can argue
about what those are.

267
00:10:40,940 --> 00:10:43,620
Part of that is the direct cost
of deactivating the account.

268
00:10:43,620 --> 00:10:45,120
Often, that's a
tedious thing to do.

269
00:10:45,120 --> 00:10:46,620
You have to figure
out how to do it.

270
00:10:46,620 --> 00:10:48,680
Often, companies try
to not make it too easy

271
00:10:48,680 --> 00:10:50,172
for you to actually do that.

272
00:10:50,172 --> 00:10:52,380
You might want to archive
some pictures, or whatever,

273
00:10:52,380 --> 00:10:52,880
and so on.

274
00:10:52,880 --> 00:10:54,530
Often, that's a
tedious thing to do.

275
00:10:54,530 --> 00:10:56,330
There's often a short-run
adjustment cost,

276
00:10:56,330 --> 00:10:58,160
where you want to be in
touch with your friends.

277
00:10:58,160 --> 00:11:00,327
Maybe it's harder to find
out where the parties are,

278
00:11:00,327 --> 00:11:02,390
or whatever,
whatever things are.

279
00:11:02,390 --> 00:11:04,520
So often, there's some
adjustment cost, likely also

280
00:11:04,520 --> 00:11:05,277
negative.

281
00:11:05,277 --> 00:11:06,860
And then there is
some long-run impact

282
00:11:06,860 --> 00:11:08,652
on your social life,
on your mental health,

283
00:11:08,652 --> 00:11:10,160
on your happiness,
and so on, that

284
00:11:10,160 --> 00:11:12,170
could be positive or negative.

285
00:11:12,170 --> 00:11:14,540
Assuming that perhaps
a positive, then again,

286
00:11:14,540 --> 00:11:17,660
you have to think about
short-run negative costs

287
00:11:17,660 --> 00:11:18,440
and benefits.

288
00:11:18,440 --> 00:11:20,607
You have to learn about,
think about what those are.

289
00:11:20,607 --> 00:11:22,003
Again, they might be uncertain.

290
00:11:22,003 --> 00:11:24,170
But to the extent that you
could tell what they are,

291
00:11:24,170 --> 00:11:26,923
then you have costs and benefits
at different points in time.

292
00:11:26,923 --> 00:11:28,340
And when you make
that choice, you

293
00:11:28,340 --> 00:11:31,160
have to figure
out whether that's

294
00:11:31,160 --> 00:11:35,720
worth doing by aggregating them
somehow to some point in time

295
00:11:35,720 --> 00:11:38,090
and, saying yes,
I'll do it, or not.

296
00:11:38,090 --> 00:11:40,760
And we'll get back
to this in, I think,

297
00:11:40,760 --> 00:11:42,990
something like lecture
20 or so, where

298
00:11:42,990 --> 00:11:46,230
there is a study that was
encouraging people to, in fact,

299
00:11:46,230 --> 00:11:50,390
precisely do that, and look at
happiness and other outcomes,

300
00:11:50,390 --> 00:11:53,810
mental health, and so
on, among students.

301
00:11:53,810 --> 00:11:55,995
OK, so what are other
important choices over time?

302
00:11:55,995 --> 00:11:58,370
If you think about almost
anything that you can think of,

303
00:11:58,370 --> 00:12:02,120
any choice that you make in
your life, almost any of these

304
00:12:02,120 --> 00:12:04,400
involve some aspects of time.

305
00:12:04,400 --> 00:12:07,160
So if you think about investing,
saving, borrowing, credit card

306
00:12:07,160 --> 00:12:10,220
spending, and so on, that
involves choices over time.

307
00:12:10,220 --> 00:12:12,170
If you think about
education, often, there's

308
00:12:12,170 --> 00:12:14,485
costs in the present,
benefits in the future.

309
00:12:14,485 --> 00:12:16,610
If you think about any sort
of health investments--

310
00:12:16,610 --> 00:12:19,490
eating healthy, taking
your medication,

311
00:12:19,490 --> 00:12:23,600
brushing your teeth, exercising,
and so on, if you think

312
00:12:23,600 --> 00:12:25,498
about sleeping,
often sleep involves

313
00:12:25,498 --> 00:12:27,290
choices between the
present and the future.

314
00:12:27,290 --> 00:12:29,730
You think about watching movies
at night-- that's fun to do.

315
00:12:29,730 --> 00:12:31,897
But often, that comes out
like pain on the following

316
00:12:31,897 --> 00:12:33,830
day in various forms.

317
00:12:33,830 --> 00:12:36,962
Eating patterns as
well, dating arguably

318
00:12:36,962 --> 00:12:38,420
involves sort of
costs and benefits

319
00:12:38,420 --> 00:12:39,810
in the present and the future.

320
00:12:39,810 --> 00:12:41,060
People make different choices.

321
00:12:41,060 --> 00:12:43,770
Again, there's all sorts of
other aspects involved as well,

322
00:12:43,770 --> 00:12:46,110
including risk,
information, and so on.

323
00:12:46,110 --> 00:12:48,312
But what I'm pointing
out is many choices

324
00:12:48,312 --> 00:12:50,270
that people make have
some aspects that involve

325
00:12:50,270 --> 00:12:51,530
different points in time.

326
00:12:51,530 --> 00:12:54,680
And you have to figure out
how to weigh these utility

327
00:12:54,680 --> 00:12:58,620
streams in some
ways accordingly.

328
00:12:58,620 --> 00:13:03,010
Now, here's a broad
history of how economists

329
00:13:03,010 --> 00:13:04,010
have thought about this.

330
00:13:04,010 --> 00:13:05,950
And it's interesting
to read, in fact.

331
00:13:05,950 --> 00:13:10,400
And this is what the Frederick
et al. article talks about.

332
00:13:10,400 --> 00:13:13,250
In fact, economists sort of
went full circle in some way.

333
00:13:13,250 --> 00:13:16,040
So it started with a
very complicated model

334
00:13:16,040 --> 00:13:19,910
of a production, the
amount of labor allocated

335
00:13:19,910 --> 00:13:21,710
to the production
of capital that

336
00:13:21,710 --> 00:13:23,990
depends on the effective
desire of accumulation,

337
00:13:23,990 --> 00:13:25,700
which is a bit of a mouthful.

338
00:13:25,700 --> 00:13:27,230
But essentially,
there was lots of

339
00:13:27,230 --> 00:13:30,200
rich psychological
considerations involved

340
00:13:30,200 --> 00:13:33,690
in trying to explain how
people make choices over time.

341
00:13:33,690 --> 00:13:36,215
People thought about
self-control, self-restraint,

342
00:13:36,215 --> 00:13:38,090
the bequest motive, how
much they think about

343
00:13:38,090 --> 00:13:40,460
their children,
anticipatory utility--

344
00:13:40,460 --> 00:13:43,610
people like to save because they
like to think they'll be happy

345
00:13:43,610 --> 00:13:44,370
in the future--

346
00:13:44,370 --> 00:13:45,480
and so on, and so forth.

347
00:13:45,480 --> 00:13:48,500
And it was a very complicated
model of intertemporal choice

348
00:13:48,500 --> 00:13:51,200
that people had
been thinking about.

349
00:13:51,200 --> 00:13:53,580
At some point, then
Bohm-Bawerk, who

350
00:13:53,580 --> 00:13:55,640
was an Austrian
economist at some point

351
00:13:55,640 --> 00:13:58,430
realized or proposed that the
interest rate, in some sense,

352
00:13:58,430 --> 00:13:59,673
is just a price.

353
00:13:59,673 --> 00:14:02,090
So if you think about doing
something or saving some money

354
00:14:02,090 --> 00:14:04,730
from today until next
year, it's really

355
00:14:04,730 --> 00:14:08,208
just like choosing between
apples and bananas.

356
00:14:08,208 --> 00:14:10,000
When you choose between
apples and bananas,

357
00:14:10,000 --> 00:14:12,800
there's a relative price, which
is the price of apples divided

358
00:14:12,800 --> 00:14:14,480
by the price of bananas.

359
00:14:14,480 --> 00:14:17,810
If you think about
choices over time,

360
00:14:17,810 --> 00:14:21,920
if you think about consuming
$1 today versus $1 next year,

361
00:14:21,920 --> 00:14:24,080
the interest rate or 1
plus the interest rate

362
00:14:24,080 --> 00:14:26,530
is the relative price of that.

363
00:14:26,530 --> 00:14:29,990
So for any dollar
that I now consume,

364
00:14:29,990 --> 00:14:32,490
I could get 1 plus r
dollars in the future.

365
00:14:32,490 --> 00:14:34,920
That's just the relative
price of consumption

366
00:14:34,920 --> 00:14:36,330
now versus in the future.

367
00:14:36,330 --> 00:14:37,580
So you could think of--

368
00:14:37,580 --> 00:14:39,680
the same way we think
about apples and bananas

369
00:14:39,680 --> 00:14:42,110
and optimizing between
those, the same way we

370
00:14:42,110 --> 00:14:46,350
can think about consumption
in the present and the future,

371
00:14:46,350 --> 00:14:49,380
which are just sort of like
different goods over time.

372
00:14:49,380 --> 00:14:52,550
And so Irving Fisher,
then, came up and said,

373
00:14:52,550 --> 00:14:56,330
let's just write down a
two-good in difference diagram.

374
00:14:56,330 --> 00:14:59,420
This is exactly the
indifference diagram

375
00:14:59,420 --> 00:15:02,690
that you've seen in like 1401
or other introductory Micro

376
00:15:02,690 --> 00:15:04,310
classes.

377
00:15:04,310 --> 00:15:06,680
Still, there were actually
many psychological factors

378
00:15:06,680 --> 00:15:10,010
discussed, like personal
factors that determine

379
00:15:10,010 --> 00:15:12,140
how much you save, and so on.

380
00:15:12,140 --> 00:15:15,060
But it was progress
towards that.

381
00:15:15,060 --> 00:15:16,850
Now, what is the Fisher diagram?

382
00:15:16,850 --> 00:15:18,840
The Fisher diagram looks
something like this.

383
00:15:18,840 --> 00:15:21,500
This is what you should
be familiar with from,

384
00:15:21,500 --> 00:15:23,300
again, 1401.

385
00:15:23,300 --> 00:15:24,210
What do we see here?

386
00:15:24,210 --> 00:15:24,752
What is this?

387
00:15:28,630 --> 00:15:29,590
Yes.

388
00:15:29,590 --> 00:15:32,627
STUDENT: I guess it traces
between [INAUDIBLE]..

389
00:15:32,627 --> 00:15:33,960
FRANK SCHILBACH: Right, exactly.

390
00:15:33,960 --> 00:15:37,660
So we have here choices between
two goods, call them good

391
00:15:37,660 --> 00:15:38,940
a and good b.

392
00:15:38,940 --> 00:15:42,900
There's a consumption. c a
is consumption of good a,

393
00:15:42,900 --> 00:15:44,850
c b is a consumption of good b.

394
00:15:44,850 --> 00:15:47,370
We have a budget
set, essentially,

395
00:15:47,370 --> 00:15:51,330
which is determined here by how
much your budget's constrained,

396
00:15:51,330 --> 00:15:56,670
which is the triangle
line that you see there.

397
00:15:56,670 --> 00:15:58,650
The slope of that
budget set is determined

398
00:15:58,650 --> 00:15:59,700
by the relative price.

399
00:15:59,700 --> 00:16:03,818
That's essentially the
p a divided by p b.

400
00:16:03,818 --> 00:16:06,360
And then we have what's called
an "indifference curve," which

401
00:16:06,360 --> 00:16:08,443
essentially is the curve
that makes us indifferent

402
00:16:08,443 --> 00:16:11,670
between combinations
of two goods.

403
00:16:11,670 --> 00:16:13,488
And we choose the point
on the budget line

404
00:16:13,488 --> 00:16:15,030
that's the furthest
out, that gets us

405
00:16:15,030 --> 00:16:16,660
in the furthest
indifference curve.

406
00:16:16,660 --> 00:16:20,190
So that's 1401 that you
should be all familiar with.

407
00:16:20,190 --> 00:16:21,660
In part, that's
what was discussed

408
00:16:21,660 --> 00:16:24,185
in recitation on Friday.

409
00:16:24,185 --> 00:16:25,560
Now, Fisher then
pointed out when

410
00:16:25,560 --> 00:16:27,280
you think about
choices over time,

411
00:16:27,280 --> 00:16:29,710
in fact, that's
exactly the same thing.

412
00:16:29,710 --> 00:16:32,640
Think about it two periods,
period one and period two.

413
00:16:32,640 --> 00:16:34,470
We have, essentially,
a budget line, again,

414
00:16:34,470 --> 00:16:35,400
which is the budget set.

415
00:16:35,400 --> 00:16:37,317
Again, that's what was
discussed in recitation

416
00:16:37,317 --> 00:16:38,597
on Thursday and Friday.

417
00:16:38,597 --> 00:16:40,680
The difference here, of
course, is then the price.

418
00:16:40,680 --> 00:16:43,560
The relative price is determined
by the interest rates.

419
00:16:43,560 --> 00:16:47,850
So 1 plus r is now essentially
the relative price, or 1 over 1

420
00:16:47,850 --> 00:16:50,250
plus r, that determines
essentially how much we

421
00:16:50,250 --> 00:16:52,410
can maximally consume.

422
00:16:52,410 --> 00:16:54,230
Again, the triangle
that you see here

423
00:16:54,230 --> 00:16:56,265
is the potential set
that you consume.

424
00:16:56,265 --> 00:16:58,140
And then again, you have
a indifference curve

425
00:16:58,140 --> 00:17:00,960
that tells us the
sets of points that we

426
00:17:00,960 --> 00:17:03,960
are indifferent between,
good one and good two.

427
00:17:03,960 --> 00:17:06,839
And we choose what's furthest
out on the indifference curve.

428
00:17:06,839 --> 00:17:08,730
So essentially, we
can apply any tools

429
00:17:08,730 --> 00:17:11,910
that we have from 1401
or any Micro class,

430
00:17:11,910 --> 00:17:14,280
from choices between
apples and bananas

431
00:17:14,280 --> 00:17:18,983
to choices between period
one and period two.

432
00:17:18,983 --> 00:17:20,400
And so what we're
sort of ignoring

433
00:17:20,400 --> 00:17:22,200
here is then in period
one and period two,

434
00:17:22,200 --> 00:17:23,700
how are we going
to spend the money?

435
00:17:23,700 --> 00:17:27,119
So we think of c1 and c2
as consumption bundles.

436
00:17:27,119 --> 00:17:28,650
Think about this
like how much money

437
00:17:28,650 --> 00:17:31,020
is spent on certain
consumption goods in period one

438
00:17:31,020 --> 00:17:34,040
versus period two, ignoring
whether you buy apples

439
00:17:34,040 --> 00:17:37,530
or bananas, just how much money
do you want to spend in period

440
00:17:37,530 --> 00:17:40,440
one, how much money do you
want to spend in period two,

441
00:17:40,440 --> 00:17:42,750
ignoring how exactly are
you going to divide it,

442
00:17:42,750 --> 00:17:44,958
assuming that you're going
to get this right in terms

443
00:17:44,958 --> 00:17:48,700
of choosing within the
period what's best for you.

444
00:17:48,700 --> 00:17:49,710
Any questions on that?

445
00:17:56,590 --> 00:18:00,160
OK, so that gets us
to the workhorse model

446
00:18:00,160 --> 00:18:02,480
in economics, which is
Samuelson's discounted utility

447
00:18:02,480 --> 00:18:02,980
model.

448
00:18:02,980 --> 00:18:05,090
Paul Samuelson is a very
famous economist who

449
00:18:05,090 --> 00:18:07,720
was at MIT for many,
many years, one

450
00:18:07,720 --> 00:18:11,410
of the founders, if you
want, of modern economics,

451
00:18:11,410 --> 00:18:16,450
and the MIT Economics
Department as it is right now.

452
00:18:16,450 --> 00:18:19,405
And what Samuelson proposed
was a non-graphical version

453
00:18:19,405 --> 00:18:21,530
of that, where he said,
let's write down some math.

454
00:18:21,530 --> 00:18:23,320
Let's write down
the representation.

455
00:18:23,320 --> 00:18:27,490
How should we think about
utility maximization?

456
00:18:27,490 --> 00:18:30,580
And what essentially he was
proposing is to say at time t,

457
00:18:30,580 --> 00:18:34,130
people maximize their discounted
utility, which is just

458
00:18:34,130 --> 00:18:37,900
the sum of discounted utility
where there is a factor

459
00:18:37,900 --> 00:18:40,570
delta, which
determines how much we

460
00:18:40,570 --> 00:18:43,150
care about the present
versus the future.

461
00:18:43,150 --> 00:18:46,550
So we have, essentially, these
instantaneous utilities, u t,

462
00:18:46,550 --> 00:18:48,760
u t plus 1, u t
plus 2, and so on.

463
00:18:48,760 --> 00:18:51,220
This is your utility
at each point in time.

464
00:18:51,220 --> 00:18:52,750
Think of time as being discrete.

465
00:18:52,750 --> 00:18:55,150
In a sense, time
could be years, time

466
00:18:55,150 --> 00:18:56,500
could be days, and the like.

467
00:18:56,500 --> 00:18:58,300
Think of them perhaps
as years for now.

468
00:18:58,300 --> 00:19:01,450
There's your t, your t
plus 1, your t plus 2,

469
00:19:01,450 --> 00:19:03,610
your t plus three, and so on.

470
00:19:03,610 --> 00:19:07,750
u t summarizes, in some sense,
how you feel in that year

471
00:19:07,750 --> 00:19:09,460
overall in terms of utility.

472
00:19:09,460 --> 00:19:12,760
That's your utility in
that particular period.

473
00:19:12,760 --> 00:19:13,740
It could also be daily.

474
00:19:13,740 --> 00:19:15,490
It could be how you
feel on a certain day,

475
00:19:15,490 --> 00:19:18,340
could be hourly, and so on.

476
00:19:18,340 --> 00:19:21,460
That's just a matter
of definition.

477
00:19:24,010 --> 00:19:28,585
And again, u t is a function of
all activities that are going

478
00:19:28,585 --> 00:19:29,710
on in that particular year.

479
00:19:29,710 --> 00:19:32,043
That could be consumption,
leisure, all the other things

480
00:19:32,043 --> 00:19:32,830
that are going on.

481
00:19:32,830 --> 00:19:34,247
That's sort of
like in some sense,

482
00:19:34,247 --> 00:19:37,000
we abstract away what happens
within that particular time

483
00:19:37,000 --> 00:19:37,700
period.

484
00:19:37,700 --> 00:19:39,700
We're just summarizing
all the things

485
00:19:39,700 --> 00:19:42,610
you're doing in that year
yield to a certain utility.

486
00:19:42,610 --> 00:19:46,220
And now the question is, how do
we aggregate these utilities?

487
00:19:46,220 --> 00:19:48,130
How do we decide between
different options

488
00:19:48,130 --> 00:19:52,635
when the u t's differ
across different options?

489
00:19:52,635 --> 00:19:54,010
Now, what's coming
in here, then,

490
00:19:54,010 --> 00:19:57,940
is the discount factor
delta, which you see above,

491
00:19:57,940 --> 00:20:02,200
which essentially is
telling you how much is util

492
00:20:02,200 --> 00:20:06,400
or an amount of utility,
a unit of utility,

493
00:20:06,400 --> 00:20:09,430
worth in the future
compared to the present.

494
00:20:09,430 --> 00:20:13,720
And so what you see here is
a very simple functional form

495
00:20:13,720 --> 00:20:15,010
of doing that.

496
00:20:15,010 --> 00:20:17,410
Everything that's in the
future is discounted.

497
00:20:17,410 --> 00:20:20,560
Usually, we think of delta
being smaller than 1.

498
00:20:20,560 --> 00:20:23,930
So delta could be something
like 0.9, 0.8, or the like.

499
00:20:23,930 --> 00:20:32,182
So if you're in period t, period
t plus 1 is discounted by 0.9.

500
00:20:32,182 --> 00:20:33,640
Period two would
be then discounted

501
00:20:33,640 --> 00:20:37,360
by 0.9 to the power of 2,
and so on, and so forth.

502
00:20:37,360 --> 00:20:39,690
And so delta is essentially
a very simple way

503
00:20:39,690 --> 00:20:42,790
of replacing a very
complex psychology, how

504
00:20:42,790 --> 00:20:45,610
we think about
choices over time,

505
00:20:45,610 --> 00:20:49,750
by saying let's just assume
that people over time

506
00:20:49,750 --> 00:20:52,330
have a constant way of
discounting the future.

507
00:20:52,330 --> 00:20:56,680
And it's taken on a
simple mathematical form

508
00:20:56,680 --> 00:21:00,170
of exponentially doing so.

509
00:21:00,170 --> 00:21:03,640
Any questions on that?

510
00:21:03,640 --> 00:21:05,890
Yes.

511
00:21:05,890 --> 00:21:10,520
STUDENT: Why was Samuelson's
model adopted so widely?

512
00:21:13,160 --> 00:21:14,680
I mean, so it said
in the reading

513
00:21:14,680 --> 00:21:20,085
that it was very simple and very
pretty, but he's very much--

514
00:21:20,085 --> 00:21:24,540
it seemed like oversimplified
a lot of the research that

515
00:21:24,540 --> 00:21:26,520
had been done in the past.

516
00:21:26,520 --> 00:21:29,500
Why were people
so quick, I guess?

517
00:21:29,500 --> 00:21:30,401
FRANK SCHILBACH: Yes.

518
00:21:30,401 --> 00:21:31,818
STUDENT: Was it,
like, the fashion

519
00:21:31,818 --> 00:21:33,170
to have these [INAUDIBLE]?

520
00:21:33,170 --> 00:21:34,930
FRANK SCHILBACH:
Yeah, so I think

521
00:21:34,930 --> 00:21:37,480
one has to think a little bit
about where things are coming

522
00:21:37,480 --> 00:21:39,970
from, in the sense
that to start with,

523
00:21:39,970 --> 00:21:41,770
nobody had formalized
some of these choices

524
00:21:41,770 --> 00:21:42,670
that people were making.

525
00:21:42,670 --> 00:21:44,270
In some sense,
Samuelson was, like, OK,

526
00:21:44,270 --> 00:21:45,460
we have to assume something.

527
00:21:45,460 --> 00:21:47,650
So let's assume
exponential discounting.

528
00:21:47,650 --> 00:21:49,040
That's a simple thing to do.

529
00:21:49,040 --> 00:21:52,090
So let me just make that
assumption as a first pass.

530
00:21:52,090 --> 00:21:54,400
He actually never thought
this is the right model,

531
00:21:54,400 --> 00:21:57,100
or this is a normative model
how people should behave,

532
00:21:57,100 --> 00:21:57,910
or the like.

533
00:21:57,910 --> 00:21:59,048
That was all coming later.

534
00:21:59,048 --> 00:22:01,090
He was just proposing
something that's tractable.

535
00:22:01,090 --> 00:22:04,695
And for tractability,
he was proposing that.

536
00:22:04,695 --> 00:22:06,070
Now, it's important
to understand

537
00:22:06,070 --> 00:22:07,487
for a lot of
behavioral economics,

538
00:22:07,487 --> 00:22:11,050
a lot of neoclassical economics,
the traditional economics,

539
00:22:11,050 --> 00:22:12,220
simplicity is good.

540
00:22:12,220 --> 00:22:16,510
So usually, we like to
simplify a lot of choices.

541
00:22:16,510 --> 00:22:20,500
And when things are simple,
you can, in a tractable way,

542
00:22:20,500 --> 00:22:21,790
analyze things in the world.

543
00:22:21,790 --> 00:22:23,500
And for many problems
in the world,

544
00:22:23,500 --> 00:22:25,090
like for example,
economic growth,

545
00:22:25,090 --> 00:22:27,590
or like how the economy
evolves as a whole,

546
00:22:27,590 --> 00:22:30,722
and so on, some of these, the
exponential discounting model

547
00:22:30,722 --> 00:22:32,680
might actually be the
right model in some ways.

548
00:22:32,680 --> 00:22:35,920
Or if you think about
how managers of firms,

549
00:22:35,920 --> 00:22:37,973
or whatever, et cetera,
behave, in some ways

550
00:22:37,973 --> 00:22:39,640
that might be the
right-- or the economy

551
00:22:39,640 --> 00:22:42,920
as a whole-- that might be
the right model overall.

552
00:22:42,920 --> 00:22:44,920
So in some sense, the
answer is kind of like, A,

553
00:22:44,920 --> 00:22:47,770
some choices are actually
explained reasonably well

554
00:22:47,770 --> 00:22:49,360
with exponential discounting.

555
00:22:49,360 --> 00:22:53,860
B, it was simple and easy to do,
and you had to start somewhere.

556
00:22:53,860 --> 00:22:58,203
And then C, I guess people tend
to stick to traditional things.

557
00:22:58,203 --> 00:23:00,370
So in some ways, once you
have written down a model,

558
00:23:00,370 --> 00:23:03,460
and people have written papers
and invested their career

559
00:23:03,460 --> 00:23:06,460
in it, they tend to defend that,
where in fact, maybe that's not

560
00:23:06,460 --> 00:23:09,970
the right thing to do, and
become dogmatic about it.

561
00:23:09,970 --> 00:23:12,250
But that's now changing.

562
00:23:12,250 --> 00:23:14,770
And exactly as you say, there's
problems with this model,

563
00:23:14,770 --> 00:23:19,240
and we're going to talk
about those right now.

564
00:23:19,240 --> 00:23:24,280
Now let me tell you a little
bit about some definitions,

565
00:23:24,280 --> 00:23:26,423
just to be clear what
we're talking about.

566
00:23:26,423 --> 00:23:28,090
So one is, what's a
"discount function,"

567
00:23:28,090 --> 00:23:31,430
what's a "discount rate," and
what's a "discount factor?"

568
00:23:31,430 --> 00:23:32,680
So these are just definitions.

569
00:23:32,680 --> 00:23:35,350
A discount function
essentially is

570
00:23:35,350 --> 00:23:38,530
when you have a stream of future
utilities, u t, u t plus 1,

571
00:23:38,530 --> 00:23:40,720
u t plus 2, and so
on, and so forth, you

572
00:23:40,720 --> 00:23:42,340
have to write down
a function how

573
00:23:42,340 --> 00:23:43,970
to weigh these in the future.

574
00:23:43,970 --> 00:23:46,600
So d of tau, as I'm
calling it, is essentially

575
00:23:46,600 --> 00:23:48,100
giving you this
discount function

576
00:23:48,100 --> 00:23:50,170
that specifies essentially
all the weights

577
00:23:50,170 --> 00:23:56,080
that you're putting on future
utilities and future periods.

578
00:23:56,080 --> 00:23:57,580
That could be that
functional form.

579
00:23:57,580 --> 00:23:58,330
Could be anything.

580
00:23:58,330 --> 00:24:01,150
That's just a very
general definition.

581
00:24:01,150 --> 00:24:03,400
Now, what's the discount rate?

582
00:24:03,400 --> 00:24:04,900
It's essentially
the rate of decline

583
00:24:04,900 --> 00:24:05,980
of the discount function.

584
00:24:05,980 --> 00:24:08,470
We call that rho and rho
of tau, which essentially

585
00:24:08,470 --> 00:24:10,660
is just the derivative
with respect to time

586
00:24:10,660 --> 00:24:16,070
divided by the discount
function at that point in time.

587
00:24:16,070 --> 00:24:19,810
And the negative of that,
because we think usually as

588
00:24:19,810 --> 00:24:24,640
positive as in the discount
function tends to decline,

589
00:24:24,640 --> 00:24:27,100
as in stuff that's
further away in the future

590
00:24:27,100 --> 00:24:30,940
you put less weight on than
stuff that's closer to you

591
00:24:30,940 --> 00:24:32,990
or closer to the present.

592
00:24:32,990 --> 00:24:35,170
And so again, rho
of tau specifies

593
00:24:35,170 --> 00:24:39,880
the rate at which value a
util declines with delay.

594
00:24:39,880 --> 00:24:42,640
And then finally, what does
exponential discounting do?

595
00:24:42,640 --> 00:24:47,080
Exponential discounting
specifies a specific functional

596
00:24:47,080 --> 00:24:49,750
form of the discount function.

597
00:24:49,750 --> 00:24:50,600
What does that mean?

598
00:24:50,600 --> 00:24:53,017
Essentially, we just take the
discount function, d of tau,

599
00:24:53,017 --> 00:24:55,150
and what Samuelson was
doing then was essentially

600
00:24:55,150 --> 00:24:57,710
just proposing a specific
functional form, saying,

601
00:24:57,710 --> 00:24:58,870
OK, let's try that one.

602
00:24:58,870 --> 00:25:00,985
That's a simple thing to do.

603
00:25:00,985 --> 00:25:02,110
Why do you choose that one?

604
00:25:02,110 --> 00:25:06,310
Well, it's delta to
the power of tau.

605
00:25:06,310 --> 00:25:07,990
The discount factor
now is delta.

606
00:25:07,990 --> 00:25:10,563
This is essentially when
you think about two periods,

607
00:25:10,563 --> 00:25:12,730
how much weight do you put
on each of those periods.

608
00:25:12,730 --> 00:25:14,350
Let me just go
back for a second.

609
00:25:14,350 --> 00:25:17,800
Here, when you think about
going from u t to u t plus 1,

610
00:25:17,800 --> 00:25:19,180
you just add an
additional delta.

611
00:25:19,180 --> 00:25:22,750
And going from u t plus 1 to u
t plus 2, you add another delta,

612
00:25:22,750 --> 00:25:23,342
and so on.

613
00:25:23,342 --> 00:25:25,300
That gives you essentially
the relative weights

614
00:25:25,300 --> 00:25:27,820
between two adjacent periods.

615
00:25:27,820 --> 00:25:30,670
Now crucially, as you see
here in that functional form,

616
00:25:30,670 --> 00:25:31,692
this is constant.

617
00:25:31,692 --> 00:25:34,150
So every time you have a time
period, you go to the future,

618
00:25:34,150 --> 00:25:35,470
you add another delta.

619
00:25:35,470 --> 00:25:36,860
And that's an assumption.

620
00:25:36,860 --> 00:25:38,530
So that's a very
convenient thing to do.

621
00:25:38,530 --> 00:25:40,300
In part what it tells
you, then, is also

622
00:25:40,300 --> 00:25:42,820
that the discount rate
is constant over time.

623
00:25:42,820 --> 00:25:44,500
Again, so that you
could do some math,

624
00:25:44,500 --> 00:25:47,870
and calculate the discount
rate, if you do that,

625
00:25:47,870 --> 00:25:49,690
you'll find out
that the discount

626
00:25:49,690 --> 00:25:56,800
rate is minus log delta, which
is approximately 1 minus delta.

627
00:25:56,800 --> 00:25:59,740
That is to say, not only is
the discount factor constant,

628
00:25:59,740 --> 00:26:02,050
but also the discount
rate is constant.

629
00:26:02,050 --> 00:26:05,470
And that's an assumption,
again, that's made by Samuelson.

630
00:26:05,470 --> 00:26:06,530
So you can do that math.

631
00:26:06,530 --> 00:26:08,980
We can also do some of
that in recitation in case

632
00:26:08,980 --> 00:26:10,210
you have questions.

633
00:26:10,210 --> 00:26:12,165
Now let me give you
an example on how

634
00:26:12,165 --> 00:26:13,540
does that help us
think about how

635
00:26:13,540 --> 00:26:16,630
people make choices over time.

636
00:26:16,630 --> 00:26:19,700
Student Amy considers
writing a term paper today

637
00:26:19,700 --> 00:26:24,440
so as to give herself a
free evening in the future.

638
00:26:24,440 --> 00:26:28,660
So this is essentially the idea
that the student now, tonight,

639
00:26:28,660 --> 00:26:30,160
has some stuff to do.

640
00:26:30,160 --> 00:26:32,500
There's some opportunity
costs right now.

641
00:26:32,500 --> 00:26:34,360
An outside option--
she could watch TV,

642
00:26:34,360 --> 00:26:36,190
she could meet her
friends, or whatever,

643
00:26:36,190 --> 00:26:39,550
or she could write
her a paper right now.

644
00:26:39,550 --> 00:26:41,530
The paper, if you write
the paper right now,

645
00:26:41,530 --> 00:26:44,020
it comes at a utility
cost of minus 1,

646
00:26:44,020 --> 00:26:46,345
costs 1 util because
the other activities

647
00:26:46,345 --> 00:26:47,470
would be more fun to do it.

648
00:26:47,470 --> 00:26:49,300
She'd rather watch movies.

649
00:26:49,300 --> 00:26:52,780
However, if, instead, she
also has some other stuff

650
00:26:52,780 --> 00:26:54,820
to do tonight, so
she doesn't really

651
00:26:54,820 --> 00:26:57,310
have a free evening if she
doesn't write the paper,

652
00:26:57,310 --> 00:27:00,070
but she just prefers not
to write it right now.

653
00:27:00,070 --> 00:27:02,530
Now, if she writes
the paper right now,

654
00:27:02,530 --> 00:27:04,210
she will get a free
evening sometime

655
00:27:04,210 --> 00:27:06,490
in the future in a
few days from now.

656
00:27:06,490 --> 00:27:07,972
And that would be
a lot more fun.

657
00:27:07,972 --> 00:27:08,680
She could go out.

658
00:27:08,680 --> 00:27:10,360
She could do whatever other
things she likes to do.

659
00:27:10,360 --> 00:27:13,180
She could go to the symphony
or whatever she likes doing.

660
00:27:13,180 --> 00:27:16,410
The instantaneous benefit, the
utility of getting a free unit,

661
00:27:16,410 --> 00:27:19,810
is 4/3 utils, so it's higher
than the cost right now.

662
00:27:19,810 --> 00:27:22,810
But it's in the future,
in some future evening.

663
00:27:22,810 --> 00:27:28,060
Suppose Amy's daily
discount factor is 0.9.

664
00:27:28,060 --> 00:27:29,498
Now, what does she do?

665
00:27:29,498 --> 00:27:30,790
How do we think about this now?

666
00:27:34,900 --> 00:27:37,135
So the daily discount
factor is 0.9.

667
00:27:37,135 --> 00:27:39,385
Is she going to do it if the
free evening is tomorrow?

668
00:27:43,250 --> 00:27:46,005
Yes.

669
00:27:46,005 --> 00:27:46,963
STUDENT: [INAUDIBLE].

670
00:27:55,220 --> 00:27:57,281
FRANK SCHILBACH: And that's
positive or negative?

671
00:28:00,890 --> 00:28:02,090
It's positive.

672
00:28:02,090 --> 00:28:02,590
Exactly.

673
00:28:02,590 --> 00:28:03,350
But it's exactly right.

674
00:28:03,350 --> 00:28:05,980
So you have to think about she
gets the immediate costs right

675
00:28:05,980 --> 00:28:09,550
now, which is minus 1, the
benefits of 4/3 on the future.

676
00:28:09,550 --> 00:28:11,830
Since her daily
discount factor is 0.9,

677
00:28:11,830 --> 00:28:14,170
she's going to
discount that by 0.9.

678
00:28:14,170 --> 00:28:15,550
That's still larger than 1.

679
00:28:15,550 --> 00:28:17,350
So she decides to do that.

680
00:28:17,350 --> 00:28:19,540
That's how she
weighs, essentially,

681
00:28:19,540 --> 00:28:21,160
the present and the future.

682
00:28:21,160 --> 00:28:23,650
Now, in two periods, she
does the exact same thing.

683
00:28:23,650 --> 00:28:26,480
But two periods are now
further away in the future.

684
00:28:26,480 --> 00:28:30,010
So she discounts it by
delta to the power of 2.

685
00:28:30,010 --> 00:28:32,320
And that gives her,
again, something

686
00:28:32,320 --> 00:28:35,020
that's larger than 0,
if I got the math right.

687
00:28:35,020 --> 00:28:39,640
So still she's willing to
do it, if the free night

688
00:28:39,640 --> 00:28:41,800
comes two nights from now.

689
00:28:41,800 --> 00:28:44,180
If it's in three periods,
however, turns out

690
00:28:44,180 --> 00:28:48,310
then minus 1 plus delta to
the power of 3 times 4/3

691
00:28:48,310 --> 00:28:51,700
is, in fact, smaller than 0.

692
00:28:51,700 --> 00:28:53,240
So she will not do it.

693
00:28:53,240 --> 00:28:55,870
So essentially, when she thinks
about costs and benefits,

694
00:28:55,870 --> 00:28:58,955
it depends a lot on how far away
are the benefits in the future.

695
00:28:58,955 --> 00:29:01,330
The further they're away in
the future, the more they get

696
00:29:01,330 --> 00:29:02,872
discounted, and the
less likely she's

697
00:29:02,872 --> 00:29:05,890
doing something that will
cost her utility now and yield

698
00:29:05,890 --> 00:29:08,210
benefits in the future.

699
00:29:08,210 --> 00:29:10,570
Now, of course that's
highly stylized.

700
00:29:10,570 --> 00:29:12,301
Yeah.

701
00:29:12,301 --> 00:29:16,028
STUDENT: [INAUDIBLE]

702
00:29:16,028 --> 00:29:17,070
FRANK SCHILBACH: Correct.

703
00:29:17,070 --> 00:29:17,500
Correct.

704
00:29:17,500 --> 00:29:18,880
So what I'm assuming
here, I was not

705
00:29:18,880 --> 00:29:20,713
saying, when is the
best time of doing that.

706
00:29:20,713 --> 00:29:23,170
What I was assuming is
choice between today

707
00:29:23,170 --> 00:29:24,550
versus in a few days from now.

708
00:29:24,550 --> 00:29:26,290
There was no option of
saying today, actually,

709
00:29:26,290 --> 00:29:27,400
I'd rather do it tomorrow.

710
00:29:27,400 --> 00:29:29,230
We'll get to that.

711
00:29:29,230 --> 00:29:32,920
I was just giving you an
example of a very simple choice

712
00:29:32,920 --> 00:29:36,160
between today versus sometime
in the future, and then

713
00:29:36,160 --> 00:29:38,943
another choice between
today versus tomorrow, today

714
00:29:38,943 --> 00:29:40,360
versus in two days
from now, today

715
00:29:40,360 --> 00:29:43,210
versus three days from now,
assuming that other days are

716
00:29:43,210 --> 00:29:45,160
not an option for now.

717
00:29:45,160 --> 00:29:46,990
We'll get to-- so
procrastination,

718
00:29:46,990 --> 00:29:48,680
you need several days.

719
00:29:48,680 --> 00:29:51,607
We'll get to that later.

720
00:29:51,607 --> 00:29:53,940
So again, the bottom line--
one second-- the bottom line

721
00:29:53,940 --> 00:29:56,398
is she will do it if the nice
evening comes the next period

722
00:29:56,398 --> 00:29:58,930
or in two periods, but
not if it comes later.

723
00:29:58,930 --> 00:29:59,715
Yeah.

724
00:29:59,715 --> 00:30:01,990
STUDENT: Doesn't
in all the periods

725
00:30:01,990 --> 00:30:06,144
she gets more utility if she
rather gets a free day today

726
00:30:06,144 --> 00:30:12,010
and she switches the options,
so she can [INAUDIBLE]??

727
00:30:12,010 --> 00:30:13,100
FRANK SCHILBACH: Yes.

728
00:30:13,100 --> 00:30:15,550
Yeah, so what I'm assuming
here-- and this is, again,

729
00:30:15,550 --> 00:30:17,730
an assumption-- is that
the free night cannot--

730
00:30:17,730 --> 00:30:21,220
so I was saying a little bit,
but perhaps not clearly--

731
00:30:21,220 --> 00:30:22,937
she has something to
do tonight anyway,

732
00:30:22,937 --> 00:30:24,520
so she can't really
have a free night.

733
00:30:24,520 --> 00:30:27,540
Maybe she needs to call
her friends and so on.

734
00:30:27,540 --> 00:30:29,290
So that option is not
available right now.

735
00:30:29,290 --> 00:30:30,200
You're exactly right.

736
00:30:30,200 --> 00:30:32,658
If the free night came tonight,
she would do that, and then

737
00:30:32,658 --> 00:30:35,650
do the stuff later,
because she prefers

738
00:30:35,650 --> 00:30:37,480
the present over the future.

739
00:30:37,480 --> 00:30:40,070
But I was assuming that
away for simplicity.

740
00:30:40,070 --> 00:30:43,360
But in general, as it
happens, many choices

741
00:30:43,360 --> 00:30:47,260
are often in the form
of either current costs

742
00:30:47,260 --> 00:30:49,870
and future benefits,
and then you'd

743
00:30:49,870 --> 00:30:53,860
rather defer those things.

744
00:30:53,860 --> 00:30:56,110
You only do that,
essentially, if the benefits

745
00:30:56,110 --> 00:30:57,790
are sufficiently high.

746
00:30:57,790 --> 00:31:01,120
Other options are current
benefits and future costs,

747
00:31:01,120 --> 00:31:04,900
and then the entire thing
is essentially flipped.

748
00:31:04,900 --> 00:31:07,150
So now, the next
question, then, you

749
00:31:07,150 --> 00:31:11,140
might have is to say, well, how
do we actually estimate delta?

750
00:31:11,140 --> 00:31:15,730
So we see people doing
choices, but in some sense

751
00:31:15,730 --> 00:31:17,230
in the real world,
we actually don't

752
00:31:17,230 --> 00:31:18,880
know what somebody's delta is.

753
00:31:18,880 --> 00:31:22,030
So how can we actually estimate
people's delta over all?

754
00:31:22,030 --> 00:31:24,220
Let's stick with the
stylized example.

755
00:31:24,220 --> 00:31:27,640
What do we need to estimate
delta in this specific example?

756
00:31:27,640 --> 00:31:30,130
Well, you would need
several choices over time,

757
00:31:30,130 --> 00:31:32,230
and then essentially,
you need to know

758
00:31:32,230 --> 00:31:34,780
what the costs and benefits
of those choices are.

759
00:31:34,780 --> 00:31:37,300
And if you knew
that, then you could

760
00:31:37,300 --> 00:31:40,180
learn about what delta is.

761
00:31:40,180 --> 00:31:42,200
Let me just write
this down for you.

762
00:31:42,200 --> 00:31:43,810
Suppose we didn't
know Amy's delta,

763
00:31:43,810 --> 00:31:47,380
but we knew that u
tau's for all periods

764
00:31:47,380 --> 00:31:49,230
for the different
options that she has.

765
00:31:49,230 --> 00:31:51,760
So how could we estimate
this from the above data?

766
00:31:51,760 --> 00:31:54,590
So we learned,
essentially, over here,

767
00:31:54,590 --> 00:31:56,230
suppose we see this
behavior overall.

768
00:31:56,230 --> 00:31:59,890
What we get is several
inequalities involving delta

769
00:31:59,890 --> 00:32:04,210
and involving u t's or u
tau's that people choose

770
00:32:04,210 --> 00:32:05,980
in different points in time.

771
00:32:05,980 --> 00:32:08,170
So once we have
these inequalities,

772
00:32:08,170 --> 00:32:11,650
then we can essentially
just estimate what is delta.

773
00:32:11,650 --> 00:32:14,812
We just back out what delta
is from these choices.

774
00:32:14,812 --> 00:32:15,520
So what do we do?

775
00:32:15,520 --> 00:32:17,770
Well, we can just
essentially do the math.

776
00:32:17,770 --> 00:32:18,790
It's very simple.

777
00:32:18,790 --> 00:32:21,460
And what we'll find
is, for example, if you

778
00:32:21,460 --> 00:32:24,650
see that the behavior
that we just saw,

779
00:32:24,650 --> 00:32:27,760
which was essentially
that she does it

780
00:32:27,760 --> 00:32:29,920
when the free night
comes one day from now

781
00:32:29,920 --> 00:32:33,610
or two days from now, that
gives us two inequalities,

782
00:32:33,610 --> 00:32:36,640
the first two inequalities
that are written down,

783
00:32:36,640 --> 00:32:40,180
which is essentially delta
must be larger than 3/4,

784
00:32:40,180 --> 00:32:43,630
delta must be larger than
3/4 to the power of 1/2,

785
00:32:43,630 --> 00:32:45,730
which is about 0.87.

786
00:32:45,730 --> 00:32:48,888
And then we have a third
choice, where she doesn't do it

787
00:32:48,888 --> 00:32:51,430
if the free night comes three
nights from now, which gives us

788
00:32:51,430 --> 00:32:53,140
another inequality,
which tells us

789
00:32:53,140 --> 00:32:57,100
delta must be lower than 0.91.

790
00:32:57,100 --> 00:32:59,140
So if you saw those
choices, but if you

791
00:32:59,140 --> 00:33:02,110
knew the utility of a
person, you could then

792
00:33:02,110 --> 00:33:03,250
back out what delta is.

793
00:33:03,250 --> 00:33:08,780
And delta in this case would
be between 0.87 and 0.91.

794
00:33:08,780 --> 00:33:12,780
Does this make sense or
any questions about that?

795
00:33:12,780 --> 00:33:14,722
So all I was doing
here is to say,

796
00:33:14,722 --> 00:33:16,430
suppose we didn't know
delta, but we just

797
00:33:16,430 --> 00:33:18,440
saw the Amy's choices.

798
00:33:18,440 --> 00:33:20,000
What can we learn
about her delta

799
00:33:20,000 --> 00:33:24,420
if we knew what the utilities
are at each point in time?

800
00:33:24,420 --> 00:33:26,597
And if you do that,
from this behavior

801
00:33:26,597 --> 00:33:27,680
we get these inequalities.

802
00:33:27,680 --> 00:33:30,830
And we can then back
out what the delta is.

803
00:33:30,830 --> 00:33:32,330
Now in reality,
we actually don't

804
00:33:32,330 --> 00:33:34,030
know what the u tau's are.

805
00:33:34,030 --> 00:33:36,440
We don't know what utility
is for different options

806
00:33:36,440 --> 00:33:37,020
from people.

807
00:33:37,020 --> 00:33:39,103
So if you see people's
behavior, we can't actually

808
00:33:39,103 --> 00:33:42,020
estimate the delta from that.

809
00:33:42,020 --> 00:33:44,330
So what could we do instead,
or what kinds of choices

810
00:33:44,330 --> 00:33:46,830
can we make or can we elicit?

811
00:33:54,180 --> 00:33:54,680
Yes.

812
00:33:54,680 --> 00:33:56,222
STUDENT: If you can
do it with money,

813
00:33:56,222 --> 00:33:57,741
there are different options.

814
00:33:57,741 --> 00:33:59,582
You have a chance
to win [INAUDIBLE]..

815
00:33:59,582 --> 00:34:00,540
FRANK SCHILBACH: Right.

816
00:34:00,540 --> 00:34:03,230
And what additional assumptions
do we need for that?

817
00:34:03,230 --> 00:34:04,230
So that's exactly right.

818
00:34:04,230 --> 00:34:07,770
That's exactly what
people have done a lot.

819
00:34:07,770 --> 00:34:10,980
So this is Rick Thaler
again, a Nobel Prize winner

820
00:34:10,980 --> 00:34:15,330
who has done exactly
that in 1981,

821
00:34:15,330 --> 00:34:18,449
getting people to start with
hypothetical monetary choices.

822
00:34:18,449 --> 00:34:21,162
So say suppose--
this is kind of what

823
00:34:21,162 --> 00:34:23,370
I was asking you at the
beginning in the first class.

824
00:34:23,370 --> 00:34:25,530
I was asking you
different numbers,

825
00:34:25,530 --> 00:34:29,250
but what x makes you
indifferent between $15 today

826
00:34:29,250 --> 00:34:34,679
and x dollars in a month, a
year, and 10 years from now?

827
00:34:34,679 --> 00:34:36,510
What do we need to
assume for that now?

828
00:34:36,510 --> 00:34:40,239
Or what other
assumptions do we need?

829
00:34:40,239 --> 00:34:43,917
How do we go from
money to your utility?

830
00:34:43,917 --> 00:34:47,718
STUDENT: There's an
old study [INAUDIBLE]..

831
00:34:47,718 --> 00:34:48,760
FRANK SCHILBACH: Exactly.

832
00:34:48,760 --> 00:34:51,179
I need to assume something
that's quite important.

833
00:34:51,179 --> 00:34:54,820
I need to assume utility
is linear in money,

834
00:34:54,820 --> 00:34:58,060
either to say I'm just looking
at that specific problem,

835
00:34:58,060 --> 00:35:02,403
u of X equals X. Or
slightly more complicated,

836
00:35:02,403 --> 00:35:04,195
but in principle the
same, marginal utility

837
00:35:04,195 --> 00:35:06,520
is constant over time.

838
00:35:06,520 --> 00:35:08,923
And that's sort of related.

839
00:35:08,923 --> 00:35:10,340
For our purposes,
what we're going

840
00:35:10,340 --> 00:35:13,550
to assume for now is
just to say your utility

841
00:35:13,550 --> 00:35:14,590
is linear in money.

842
00:35:14,590 --> 00:35:16,720
You have X equals X.

843
00:35:16,720 --> 00:35:22,420
And then what you can do is
if I give you an amount Y--

844
00:35:22,420 --> 00:35:25,300
Y is $15-- and
then I ask you what

845
00:35:25,300 --> 00:35:27,310
makes you indifferent
between X dollars in, say,

846
00:35:27,310 --> 00:35:29,710
a month or a year from now?

847
00:35:29,710 --> 00:35:32,200
I'm just going to write down
an equation, which essentially

848
00:35:32,200 --> 00:35:35,770
is to say u of Y, which
is the utility of getting

849
00:35:35,770 --> 00:35:37,390
the $15 right now--

850
00:35:37,390 --> 00:35:40,390
is you're indifferent between
that because you just told me

851
00:35:40,390 --> 00:35:44,350
so, and u of X, which X is the
amount that you just told me.

852
00:35:44,350 --> 00:35:46,270
And now I need to
discount that by delta

853
00:35:46,270 --> 00:35:50,020
to the power of t, which is
because it's in the future,

854
00:35:50,020 --> 00:35:52,120
you need to discount that.

855
00:35:52,120 --> 00:35:54,100
Once I know that, I know
essentially everything

856
00:35:54,100 --> 00:35:56,642
on the left-hand side and the
right-hand side of the equation

857
00:35:56,642 --> 00:35:57,620
except for the delta.

858
00:35:57,620 --> 00:36:00,882
I can just back out
delta from that.

859
00:36:00,882 --> 00:36:03,340
So what we're going to do is
we're going to just use, then,

860
00:36:03,340 --> 00:36:07,270
the linearity assumption
of the utility

861
00:36:07,270 --> 00:36:10,690
is linear in money, which
is like u of Y equals Y,

862
00:36:10,690 --> 00:36:12,670
and u of X equals X.

863
00:36:12,670 --> 00:36:14,710
We take logs on both
sides and rearrange,

864
00:36:14,710 --> 00:36:19,600
and then get rho, which is,
again, the discount rate,

865
00:36:19,600 --> 00:36:21,370
equals minus log delta.

866
00:36:21,370 --> 00:36:24,730
And that's log of X
divided by Y and divided

867
00:36:24,730 --> 00:36:28,960
by t, which is the time period
that I'm asking you about.

868
00:36:28,960 --> 00:36:32,830
That's a simple algebra
and rearranging things.

869
00:36:32,830 --> 00:36:35,020
We talked about a
little bit in recitation

870
00:36:35,020 --> 00:36:37,017
and in the problem set as well.

871
00:36:37,017 --> 00:36:38,600
But is it clear what
we're doing here?

872
00:36:38,600 --> 00:36:40,058
Are there any
questions about that?

873
00:36:46,312 --> 00:36:48,020
So just to summarize
what I'm doing here,

874
00:36:48,020 --> 00:36:51,520
I'm just asking you between
different choices over time.

875
00:36:51,520 --> 00:36:53,710
I'm assuming a utility
function of money.

876
00:36:53,710 --> 00:36:55,550
So I'm imposing on
you in some way--

877
00:36:55,550 --> 00:36:57,383
and it might be a good
or a bad assumption--

878
00:36:57,383 --> 00:36:59,410
but I'm essentially
assuming how you value money

879
00:36:59,410 --> 00:37:00,880
at different points in time.

880
00:37:00,880 --> 00:37:02,470
And with that
assumption, then, I

881
00:37:02,470 --> 00:37:04,900
can back out from
your choices over time

882
00:37:04,900 --> 00:37:08,830
how much you discounting
utility in the future.

883
00:37:08,830 --> 00:37:12,770
And then the rest is just
rearranging and doing

884
00:37:12,770 --> 00:37:13,270
some math.

885
00:37:17,850 --> 00:37:20,380
So now, how do you do that?

886
00:37:20,380 --> 00:37:22,830
Here's an example of how to
do that, then, for Y equals 15

887
00:37:22,830 --> 00:37:24,190
and X equals 20.

888
00:37:24,190 --> 00:37:25,920
So if you told me
that what makes

889
00:37:25,920 --> 00:37:29,670
you indifferent between
$15 now and X in a month,

890
00:37:29,670 --> 00:37:33,150
if you told me $20, I can
just write down the equation,

891
00:37:33,150 --> 00:37:36,690
and I get essentially
a delta of 0.003.

892
00:37:36,690 --> 00:37:39,240
The reason being that
if you are indifferent

893
00:37:39,240 --> 00:37:44,903
between $15 and $20
right now, you're

894
00:37:44,903 --> 00:37:46,320
discounting,
essentially, anything

895
00:37:46,320 --> 00:37:48,600
that's in the future by 3/4.

896
00:37:48,600 --> 00:37:54,390
Essentially $20 in a month
from now or 3/4 as much--

897
00:37:54,390 --> 00:37:56,868
or the money in the future
is 3/4 as much worth for you

898
00:37:56,868 --> 00:37:57,910
than the money right now.

899
00:37:57,910 --> 00:38:00,325
That's the 20 versus
15 in a month from now.

900
00:38:00,325 --> 00:38:01,950
And then I have to
do this every month.

901
00:38:01,950 --> 00:38:04,500
So every month, it's
3/4 to the power of 12

902
00:38:04,500 --> 00:38:10,350
will give you something
like 0.03 as delta.

903
00:38:10,350 --> 00:38:16,080
So I'm just calculating
the yearly discount factor

904
00:38:16,080 --> 00:38:17,680
using your monthly choice.

905
00:38:17,680 --> 00:38:18,471
Yeah.

906
00:38:18,471 --> 00:38:21,202
STUDENT: [INAUDIBLE].

907
00:38:21,202 --> 00:38:22,160
FRANK SCHILBACH: Right.

908
00:38:22,160 --> 00:38:25,680
So usually, what people do
is yearly discount factors.

909
00:38:25,680 --> 00:38:27,380
So usually the delta is yearly.

910
00:38:27,380 --> 00:38:28,640
That's just a convention.

911
00:38:28,640 --> 00:38:31,530
You could also do it monthly,
or daily, or whatever.

912
00:38:31,530 --> 00:38:33,710
So what I'm doing is
yearly discount factors,

913
00:38:33,710 --> 00:38:40,350
partially because I want to make
them comparable across choices.

914
00:38:40,350 --> 00:38:41,870
But you could
similarly also just do

915
00:38:41,870 --> 00:38:43,220
the monthly one, or whatever.

916
00:38:43,220 --> 00:38:48,110
And a lot of economic analyses,
yearly is the frequency.

917
00:38:48,110 --> 00:38:50,060
When it comes to your
problem set questions,

918
00:38:50,060 --> 00:38:53,030
it's going to be
daily, because students

919
00:38:53,030 --> 00:38:56,778
tend to think in days,
not necessarily in years.

920
00:38:56,778 --> 00:38:58,215
STUDENT: [INAUDIBLE].

921
00:39:03,490 --> 00:39:04,780
FRANK SCHILBACH: Right.

922
00:39:04,780 --> 00:39:07,690
So in some sense, this is
what we're getting here

923
00:39:07,690 --> 00:39:09,160
in some ways in saying--

924
00:39:09,160 --> 00:39:11,140
here I'm asking you about--

925
00:39:11,140 --> 00:39:14,030
so you see the choice here, and
these are actually real choices

926
00:39:14,030 --> 00:39:15,160
that people have made.

927
00:39:15,160 --> 00:39:20,980
When I ask you now between
Y dollars, $15, right now

928
00:39:20,980 --> 00:39:22,870
and X dollars in
10 years from now,

929
00:39:22,870 --> 00:39:24,890
people tend to give
different answers.

930
00:39:24,890 --> 00:39:27,010
And one constant
finding there is

931
00:39:27,010 --> 00:39:28,810
that people tend to
be more patient when

932
00:39:28,810 --> 00:39:31,780
it comes to longer run choices
compared to shorter run

933
00:39:31,780 --> 00:39:33,040
choices.

934
00:39:33,040 --> 00:39:35,240
I'm calculating the
same discount factor.

935
00:39:35,240 --> 00:39:37,870
And what I just told you
earlier is in the exponential

936
00:39:37,870 --> 00:39:40,540
discounting model, the
discount factor delta

937
00:39:40,540 --> 00:39:42,700
should be constant over time.

938
00:39:42,700 --> 00:39:45,340
Should be the same
whether you decide

939
00:39:45,340 --> 00:39:49,090
between today and tomorrow,
between a year from now

940
00:39:49,090 --> 00:39:51,580
and a year and a day from
now, or between any time

941
00:39:51,580 --> 00:39:52,540
in the future.

942
00:39:52,540 --> 00:39:55,250
But what we find or tend to
find in these kinds of choices

943
00:39:55,250 --> 00:39:57,400
is that people's
discount factor is

944
00:39:57,400 --> 00:40:00,820
a lot higher in the future
compared to in the present.

945
00:40:00,820 --> 00:40:01,900
I'll get back to that.

946
00:40:01,900 --> 00:40:04,840
So actually, your question
is exactly on point.

947
00:40:04,840 --> 00:40:08,320
When eliciting choices between
different days versus months

948
00:40:08,320 --> 00:40:12,130
versus years, you get
a lot different answers

949
00:40:12,130 --> 00:40:13,300
depending on what you ask.

950
00:40:15,810 --> 00:40:16,410
OK.

951
00:40:16,410 --> 00:40:19,940
So now, we can say-- and this
is exactly what you're asking--

952
00:40:19,940 --> 00:40:20,900
let's see.

953
00:40:20,900 --> 00:40:23,750
When you do this in different
settings, what kinds of answers

954
00:40:23,750 --> 00:40:24,950
do you actually get.

955
00:40:24,950 --> 00:40:28,070
And what you see here is here's
people's choices of delta

956
00:40:28,070 --> 00:40:31,340
and different types of
experiments people have done.

957
00:40:31,340 --> 00:40:33,047
This is different
years of publication.

958
00:40:33,047 --> 00:40:34,880
But overall, what do
you see is essentially,

959
00:40:34,880 --> 00:40:37,040
these estimates are
all over the place.

960
00:40:37,040 --> 00:40:38,720
So you think we
know what delta is.

961
00:40:38,720 --> 00:40:42,150
We think it's 0.9, or
0.8, or 0.95, or whatever.

962
00:40:42,150 --> 00:40:44,330
But in fact, when you
look at people's choices

963
00:40:44,330 --> 00:40:46,010
in different types
of experiments,

964
00:40:46,010 --> 00:40:48,480
these choices tend to
be all over the place.

965
00:40:48,480 --> 00:40:50,090
So that's not a good
sign for a model,

966
00:40:50,090 --> 00:40:54,650
because you're trying to
identify a parameter that

967
00:40:54,650 --> 00:40:55,890
fits many settings.

968
00:40:55,890 --> 00:40:59,300
Well, here, it seems to be that
these choices are essentially

969
00:40:59,300 --> 00:41:02,270
all over the place, which tells
you already maybe something is

970
00:41:02,270 --> 00:41:05,780
wrong in this model that
we should try to fix.

971
00:41:05,780 --> 00:41:09,320
Now, one thing I
already said here

972
00:41:09,320 --> 00:41:11,690
is to say, when you
look at short-run

973
00:41:11,690 --> 00:41:14,720
versus long-run choices, we tend
to find that people are really

974
00:41:14,720 --> 00:41:16,280
impatient in the short run.

975
00:41:16,280 --> 00:41:18,440
However, people are
patient in the long run.

976
00:41:21,480 --> 00:41:24,760
There's lots to learn from this
experiment in various ways,

977
00:41:24,760 --> 00:41:29,388
in part about strategies to
overcome self-control problems.

978
00:41:29,388 --> 00:41:30,930
For example, a lot
of kids are trying

979
00:41:30,930 --> 00:41:32,700
to manage their
attention, are looking at,

980
00:41:32,700 --> 00:41:34,470
and looking away, and so on.

981
00:41:34,470 --> 00:41:36,060
But mostly, I think
the key part you

982
00:41:36,060 --> 00:41:38,940
learn is how painful
it can be to resist.

983
00:41:38,940 --> 00:41:42,690
In the short run, there's
lots of essentially

984
00:41:42,690 --> 00:41:44,520
short-run discounting
or essentially

985
00:41:44,520 --> 00:41:46,560
short-run impatience
that we see in the world.

986
00:41:46,560 --> 00:41:49,230
And if you think about it, often
it's very hard in the short run

987
00:41:49,230 --> 00:41:49,982
to resist.

988
00:41:49,982 --> 00:41:51,690
Often when you think
about in the future,

989
00:41:51,690 --> 00:41:53,628
it's much easier to do so.

990
00:41:53,628 --> 00:41:55,170
When you think about
choices that you

991
00:41:55,170 --> 00:41:57,360
might face in your life--

992
00:41:57,360 --> 00:41:59,190
be it marshmallows
or something else--

993
00:41:59,190 --> 00:42:01,620
would you rather have one
marshmallow right now versus

994
00:42:01,620 --> 00:42:03,708
two marshmallows in an
hour, you might say,

995
00:42:03,708 --> 00:42:06,000
well, maybe one marshmallow
looks actually pretty good.

996
00:42:06,000 --> 00:42:08,220
Let's just take that one
marshmallow right now.

997
00:42:08,220 --> 00:42:12,710
And a lot of these kids, I
guess, opted for doing so.

998
00:42:12,710 --> 00:42:14,550
When I ask you
instead, would you

999
00:42:14,550 --> 00:42:16,680
like to have a marshmallow
in a week from now

1000
00:42:16,680 --> 00:42:19,260
versus two marshmallows in
a week from now and an hour,

1001
00:42:19,260 --> 00:42:20,520
it almost becomes ridiculous.

1002
00:42:20,520 --> 00:42:22,478
Of course you're going
to take two marshmallows

1003
00:42:22,478 --> 00:42:24,870
in a week and an hour from now.

1004
00:42:24,870 --> 00:42:27,000
What does it matter in
terms of when exactly you

1005
00:42:27,000 --> 00:42:28,140
get the marshmallow?

1006
00:42:28,140 --> 00:42:31,290
When I ask you the same
questions about one marshmallow

1007
00:42:31,290 --> 00:42:34,290
in a year from now versus
two marshmallows in a year

1008
00:42:34,290 --> 00:42:37,357
and an hour from now, it becomes
very obvious that of course, I

1009
00:42:37,357 --> 00:42:38,940
want the two
marshmallows-- unless you

1010
00:42:38,940 --> 00:42:43,480
think in a year from now,
you might be on a diet.

1011
00:42:43,480 --> 00:42:45,720
But the exponential
discounting model

1012
00:42:45,720 --> 00:42:47,190
has precisely that assumption.

1013
00:42:47,190 --> 00:42:49,890
The assumption is that
how much you discount

1014
00:42:49,890 --> 00:42:52,765
an hour in this case
does not vary depending

1015
00:42:52,765 --> 00:42:54,390
on whether it's right
now, whether it's

1016
00:42:54,390 --> 00:42:56,015
in a week from now,
versus whether it's

1017
00:42:56,015 --> 00:42:57,310
in a year from now.

1018
00:42:57,310 --> 00:43:00,090
And the short-run
discounting essentially

1019
00:43:00,090 --> 00:43:01,920
tends to violate
that assumption,

1020
00:43:01,920 --> 00:43:04,560
in part because it leads to
pretty absurd implications,

1021
00:43:04,560 --> 00:43:06,942
as I'm going to
show you in a bit.

1022
00:43:06,942 --> 00:43:08,400
So what other
evidence in the world

1023
00:43:08,400 --> 00:43:11,960
do we have about
short-run impatience,

1024
00:43:11,960 --> 00:43:13,523
other than the marshmallows?

1025
00:43:17,600 --> 00:43:18,450
Yes.

1026
00:43:18,450 --> 00:43:23,182
STUDENT: [INAUDIBLE]
get concentrated.

1027
00:43:23,182 --> 00:43:24,140
FRANK SCHILBACH: Right.

1028
00:43:24,140 --> 00:43:26,150
There's lots of-- I
think among you guys,

1029
00:43:26,150 --> 00:43:30,470
not that many people smoke,
but lots of smokers would say,

1030
00:43:30,470 --> 00:43:33,440
oh, I'd love to stop
smoking in the future.

1031
00:43:33,440 --> 00:43:35,570
I really want to quit.

1032
00:43:35,570 --> 00:43:39,433
But then they find it
very hard to do right now.

1033
00:43:39,433 --> 00:43:40,850
And maybe next
time in the future,

1034
00:43:40,850 --> 00:43:42,440
I will quit, and so
on, and so forth.

1035
00:43:42,440 --> 00:43:44,630
Lots of people try, and
then fail, and so on.

1036
00:43:44,630 --> 00:43:48,320
And in part, it's like
the short-run impatience

1037
00:43:48,320 --> 00:43:50,812
or short-run
difficulty to do that

1038
00:43:50,812 --> 00:43:53,270
compared to maybe the long-run
desires of wanting to do so.

1039
00:43:53,270 --> 00:43:54,770
We'll get back to
smoking, actually,

1040
00:43:54,770 --> 00:43:56,480
at some point in the future.

1041
00:43:56,480 --> 00:43:58,820
But that's exactly a
great example of that.

1042
00:43:58,820 --> 00:44:01,400
That's also true for other
drugs, other addictions,

1043
00:44:01,400 --> 00:44:02,850
and so on.

1044
00:44:02,850 --> 00:44:04,910
Actually, some of
the social media,

1045
00:44:04,910 --> 00:44:06,860
or computers, or
phones, or whatever,

1046
00:44:06,860 --> 00:44:08,650
you can also think of
like that being sort

1047
00:44:08,650 --> 00:44:09,650
of addictive in a sense.

1048
00:44:09,650 --> 00:44:12,120
In the short run, it's very
hard to get away from that.

1049
00:44:12,120 --> 00:44:14,550
But in the very long run, it
would be nice thing to do.

1050
00:44:14,550 --> 00:44:18,410
Often, then, there's
short-run impatience involved.

1051
00:44:18,410 --> 00:44:20,192
Yeah.

1052
00:44:20,192 --> 00:44:23,507
STUDENT: Taking a break
now versus [INAUDIBLE]..

1053
00:44:23,507 --> 00:44:25,340
FRANK SCHILBACH: Yeah,
so a break now always

1054
00:44:25,340 --> 00:44:26,690
seems like a great idea.

1055
00:44:26,690 --> 00:44:28,310
And then in the
future, you're going

1056
00:44:28,310 --> 00:44:30,020
to work really hard and so on.

1057
00:44:30,020 --> 00:44:32,300
And then the future
comes, and again,

1058
00:44:32,300 --> 00:44:36,390
taking a break right now
seems really appealing.

1059
00:44:36,390 --> 00:44:37,100
Yeah.

1060
00:44:37,100 --> 00:44:38,267
STUDENT: Aggressive driving.

1061
00:44:38,267 --> 00:44:39,933
FRANK SCHILBACH: Oh,
that's interesting.

1062
00:44:39,933 --> 00:44:41,187
Can you say more?

1063
00:44:41,187 --> 00:44:43,020
STUDENT: In the short
run, you're impatient.

1064
00:44:43,020 --> 00:44:45,320
You're concerned
about your [INAUDIBLE]

1065
00:44:45,320 --> 00:44:47,828
so you might try to get
to the destination faster.

1066
00:44:47,828 --> 00:44:50,286
Or just in general, people try
to get to the destination as

1067
00:44:50,286 --> 00:44:52,732
fast as possible [INAUDIBLE].

1068
00:44:52,732 --> 00:44:53,690
FRANK SCHILBACH: Right.

1069
00:44:53,690 --> 00:44:56,070
So of course, there's also
other factors involved,

1070
00:44:56,070 --> 00:44:57,350
including risk and the like.

1071
00:44:57,350 --> 00:45:00,110
You might think-- you
underestimate how risky it is,

1072
00:45:00,110 --> 00:45:02,480
and you might think, oh,
I might be overconfident,

1073
00:45:02,480 --> 00:45:04,770
that you're never going
to have an accident.

1074
00:45:04,770 --> 00:45:06,982
But exactly as you say, in
the short run, essentially

1075
00:45:06,982 --> 00:45:08,690
there's some short-run
benefits, which is

1076
00:45:08,690 --> 00:45:10,280
like I could be there faster.

1077
00:45:10,280 --> 00:45:13,670
It's kind of annoying to
drive, and so on, and so forth.

1078
00:45:13,670 --> 00:45:16,550
The costs are in the future
in some sense, so uncertain.

1079
00:45:16,550 --> 00:45:20,090
You might crash
and so on, and you

1080
00:45:20,090 --> 00:45:21,920
might be impatient in
the very short run.

1081
00:45:21,920 --> 00:45:22,462
That's right.

1082
00:45:22,462 --> 00:45:24,673
But I think that's a
little tricky as an example

1083
00:45:24,673 --> 00:45:26,340
because there's all
these other factors.

1084
00:45:26,340 --> 00:45:28,910
I do think, however, that
short-run impatience is

1085
00:45:28,910 --> 00:45:31,610
involved in that as well.

1086
00:45:31,610 --> 00:45:32,300
Yes.

1087
00:45:32,300 --> 00:45:34,550
STUDENT: I think credit cards
are also a good example.

1088
00:45:34,550 --> 00:45:37,370
Like, you can buy this now
with a credit card instead

1089
00:45:37,370 --> 00:45:39,515
of saving to buy the thing.

1090
00:45:39,515 --> 00:45:40,390
FRANK SCHILBACH: Yes.

1091
00:45:40,390 --> 00:45:43,640
So a lot of essentially
choices of money over time,

1092
00:45:43,640 --> 00:45:47,020
you can see the choices that I
was asking you guys in class.

1093
00:45:47,020 --> 00:45:51,430
That essentially shows some
short-run impatience as well.

1094
00:45:51,430 --> 00:45:56,050
There's perhaps even
more salient payday loans

1095
00:45:56,050 --> 00:45:57,680
that you might be familiar with.

1096
00:45:57,680 --> 00:46:01,570
So payday loans are essentially
a very interesting phenomenon,

1097
00:46:01,570 --> 00:46:03,070
where essentially,
there are workers

1098
00:46:03,070 --> 00:46:06,070
who get their paycheck
by the end of the month

1099
00:46:06,070 --> 00:46:07,720
or the beginning of
the month, but then

1100
00:46:07,720 --> 00:46:10,390
on the 20th of the month
or sometime earlier, they

1101
00:46:10,390 --> 00:46:12,803
would like to have some
money earlier than that.

1102
00:46:12,803 --> 00:46:14,470
So you can essentially
just say, give me

1103
00:46:14,470 --> 00:46:16,600
some money at a very
high interest rate,

1104
00:46:16,600 --> 00:46:20,470
and once my payday comes,
I'm going to pay you back.

1105
00:46:20,470 --> 00:46:22,570
The interest rates
are usually enormous.

1106
00:46:22,570 --> 00:46:25,750
Usually it's something like up
to 5,000 annualized compound

1107
00:46:25,750 --> 00:46:27,880
interest, which is insane.

1108
00:46:27,880 --> 00:46:29,260
These are huge interest rates.

1109
00:46:29,260 --> 00:46:31,600
It's also an enormous
industry in the US.

1110
00:46:31,600 --> 00:46:34,405
It's more stores than McDonalds
and Starbucks combined,

1111
00:46:34,405 --> 00:46:36,280
which I'm not sure how
many stores there are,

1112
00:46:36,280 --> 00:46:38,740
but I think there's
lots of them.

1113
00:46:38,740 --> 00:46:41,410
And people pay huge
interest rates,

1114
00:46:41,410 --> 00:46:43,360
and it's a huge
industry of doing that.

1115
00:46:43,360 --> 00:46:46,060
What's kind of funny about
payday loans, in some ways,

1116
00:46:46,060 --> 00:46:49,810
is actually in some ways, it's
an odd thing of the world--

1117
00:46:49,810 --> 00:46:50,860
that's sort of an aside--

1118
00:46:50,860 --> 00:46:53,230
as in workers have worked
already for 20 days.

1119
00:46:53,230 --> 00:46:55,540
In some sense, the
employer owes them money.

1120
00:46:55,540 --> 00:46:58,090
But instead, they're
essentially taking loans

1121
00:46:58,090 --> 00:47:00,040
from a salary that's
actually, in some sense,

1122
00:47:00,040 --> 00:47:02,290
theirs already anyway
in various ways.

1123
00:47:02,290 --> 00:47:03,670
But that's just an aside.

1124
00:47:03,670 --> 00:47:05,480
So that's a huge industry.

1125
00:47:05,480 --> 00:47:06,950
You were saying
something similar,

1126
00:47:06,950 --> 00:47:08,140
which is credit card debt.

1127
00:47:08,140 --> 00:47:10,420
Usually there, the
annual interest rate

1128
00:47:10,420 --> 00:47:11,560
is lower than that.

1129
00:47:11,560 --> 00:47:15,648
It's something like 20% in many
cases, sometimes also higher.

1130
00:47:15,648 --> 00:47:17,440
There's lots of credit
card debt in the US.

1131
00:47:17,440 --> 00:47:19,315
And you can think of
this as like essentially

1132
00:47:19,315 --> 00:47:20,980
signs of short-run impatience.

1133
00:47:20,980 --> 00:47:26,500
What you see is people
wanting to spend money now

1134
00:47:26,500 --> 00:47:27,460
on various things.

1135
00:47:27,460 --> 00:47:29,020
And they get the
gains of doing that.

1136
00:47:29,020 --> 00:47:31,480
The cost of that comes sometime
in the future when you actually

1137
00:47:31,480 --> 00:47:32,350
have to pay it back.

1138
00:47:34,990 --> 00:47:37,790
Finally, there's also some
evidence of payday effects.

1139
00:47:37,790 --> 00:47:41,210
These are often involved
in things like people,

1140
00:47:41,210 --> 00:47:44,410
for example, who get food
stamps or any other monthly

1141
00:47:44,410 --> 00:47:47,110
or other cash
transfers-- that people

1142
00:47:47,110 --> 00:47:50,380
get either food stamps
or money at some point

1143
00:47:50,380 --> 00:47:53,050
conditional/unconditional
cash transfers

1144
00:47:53,050 --> 00:47:54,490
at the beginning of the month.

1145
00:47:54,490 --> 00:47:56,933
And then usually, there's
these cycles in consumption

1146
00:47:56,933 --> 00:47:59,350
or also expenditures, where
at the beginning of the month,

1147
00:47:59,350 --> 00:48:01,930
people live large and
have lots of money.

1148
00:48:01,930 --> 00:48:07,030
Same is also true for graduate
students on their stipends.

1149
00:48:07,030 --> 00:48:12,010
The first weeks or months
after getting your paychecks

1150
00:48:12,010 --> 00:48:13,280
often is really great.

1151
00:48:13,280 --> 00:48:16,353
And then it sort of declines
over the course of that cycle.

1152
00:48:16,353 --> 00:48:17,770
The same is also
true, by the way,

1153
00:48:17,770 --> 00:48:21,160
for farmers and harvest cycles
in India and other places.

1154
00:48:21,160 --> 00:48:23,230
And then usually towards
the end of the cycle,

1155
00:48:23,230 --> 00:48:25,750
people either are hungry,
or have low caloric intake,

1156
00:48:25,750 --> 00:48:27,880
or are just not very happy.

1157
00:48:27,880 --> 00:48:30,130
That's a very common phenomenon.

1158
00:48:30,130 --> 00:48:33,683
And at the heart of that, there
is some short-run impatience,

1159
00:48:33,683 --> 00:48:35,600
in the sense of at the
beginning of the month,

1160
00:48:35,600 --> 00:48:37,267
you're really impatient,
want to consume

1161
00:48:37,267 --> 00:48:40,720
some stuff, and discount what's
in the end of the cycle, what's

1162
00:48:40,720 --> 00:48:43,420
further away, where the
costs are coming, then,

1163
00:48:43,420 --> 00:48:46,480
in terms of not having
enough resources or money

1164
00:48:46,480 --> 00:48:48,730
available anymore.

1165
00:48:48,730 --> 00:48:52,300
Here's some examples
of payday loans.

1166
00:48:52,300 --> 00:48:54,580
I was wondering
what this woman--

1167
00:48:54,580 --> 00:48:56,230
this is from wonga.com.

1168
00:48:56,230 --> 00:48:59,187
Apparently, they are
advertising with grandmothers,

1169
00:48:59,187 --> 00:49:01,270
because you wonder what
this woman is doing there.

1170
00:49:01,270 --> 00:49:04,540
But what you see here on the
right-hand side is essentially,

1171
00:49:04,540 --> 00:49:08,041
the interest rates are
something in the 1,000%.

1172
00:49:08,041 --> 00:49:10,790
These are the annualized
interest rates.

1173
00:49:10,790 --> 00:49:12,280
These are enormous
interest rates.

1174
00:49:12,280 --> 00:49:16,180
Usually people take
many loans of that.

1175
00:49:16,180 --> 00:49:17,560
They also take repeated loans.

1176
00:49:17,560 --> 00:49:20,380
So it's not just as an emergency
where people take a loan,

1177
00:49:20,380 --> 00:49:23,020
but people tend to roll over
these loans over and over

1178
00:49:23,020 --> 00:49:25,540
again, and actually pay
lots and lots of money

1179
00:49:25,540 --> 00:49:26,950
to these companies.

1180
00:49:26,950 --> 00:49:30,370
There's often very
high credit card APRs,

1181
00:49:30,370 --> 00:49:33,790
which 20%, 25%, and
so on are very common.

1182
00:49:33,790 --> 00:49:36,160
Again, lots of people have
lots of credit card debt.

1183
00:49:36,160 --> 00:49:38,590
And often, it's again, not
just to deal with shocks.

1184
00:49:38,590 --> 00:49:39,760
You might say, well,
if you have a health

1185
00:49:39,760 --> 00:49:41,530
shock or some other
shock in the family,

1186
00:49:41,530 --> 00:49:44,960
if people get perhaps unemployed
for a short period of time,

1187
00:49:44,960 --> 00:49:48,130
maybe that makes sense
to deal with that shock.

1188
00:49:48,130 --> 00:49:51,160
But often, people
tend to roll over

1189
00:49:51,160 --> 00:49:53,380
this interest for
many, many cycles,

1190
00:49:53,380 --> 00:49:56,920
and keep paying these
really high interest rates.

1191
00:49:56,920 --> 00:49:59,770
Now, in some sense, that's
just empirical evidence.

1192
00:49:59,770 --> 00:50:02,030
That's just a fact that
these things exist.

1193
00:50:02,030 --> 00:50:04,360
However, when you
think that through,

1194
00:50:04,360 --> 00:50:08,210
you get very absurd implications
of this short-run impatience.

1195
00:50:08,210 --> 00:50:10,630
So what I showed you now is
several pieces of evidence

1196
00:50:10,630 --> 00:50:12,640
of short-run impatience.

1197
00:50:12,640 --> 00:50:14,980
Now taking the exponential
discounting model

1198
00:50:14,980 --> 00:50:16,960
very seriously, we're
going to think about some

1199
00:50:16,960 --> 00:50:18,730
of these implications
of what does

1200
00:50:18,730 --> 00:50:22,720
the exponential discounting
model say and imply from that.

1201
00:50:22,720 --> 00:50:25,450
And one way to think
about this is the money

1202
00:50:25,450 --> 00:50:26,770
now versus later choices.

1203
00:50:26,770 --> 00:50:31,060
As I told you before, when
you look at number one here,

1204
00:50:31,060 --> 00:50:32,560
I was asking you
about what makes

1205
00:50:32,560 --> 00:50:35,890
you indifferent between $100
now and $X in two weeks.

1206
00:50:35,890 --> 00:50:41,047
And the median student was
saying something $120, $115.

1207
00:50:41,047 --> 00:50:42,880
And you can think about
what does that imply

1208
00:50:42,880 --> 00:50:44,470
for the yearly delta.

1209
00:50:44,470 --> 00:50:48,520
Well, it implies for the yearly
delta that it's about 5/6.

1210
00:50:48,520 --> 00:50:50,260
So you're indifferent
between $100

1211
00:50:50,260 --> 00:50:52,700
now versus $120 in the future.

1212
00:50:52,700 --> 00:50:56,590
So that must mean the
future is 5/6 as much worth

1213
00:50:56,590 --> 00:50:59,710
as the present is
for you right now.

1214
00:50:59,710 --> 00:51:02,830
Now, that's fine.

1215
00:51:02,830 --> 00:51:05,270
Excuse me, that
was the two weeks

1216
00:51:05,270 --> 00:51:09,760
that was I was asking you
about, $100 now versus X

1217
00:51:09,760 --> 00:51:11,190
dollars in 2 weeks from now.

1218
00:51:11,190 --> 00:51:13,487
So the two-week delta is 5/6.

1219
00:51:13,487 --> 00:51:15,070
Now you can think
about what does that

1220
00:51:15,070 --> 00:51:18,310
mean for your four-week delta.

1221
00:51:18,310 --> 00:51:20,050
Well, it's 5/6 to
the power of 2.

1222
00:51:23,080 --> 00:51:25,930
So that's essentially you're
indifferent between $100 now

1223
00:51:25,930 --> 00:51:28,600
and $144 in four weeks from now.

1224
00:51:28,600 --> 00:51:31,000
You're also indifferent
between $100 now

1225
00:51:31,000 --> 00:51:34,000
and $11,400 in a year from now.

1226
00:51:34,000 --> 00:51:36,130
And you're also indifferent
between $100 now

1227
00:51:36,130 --> 00:51:38,020
and I don't even know
what that number is,

1228
00:51:38,020 --> 00:51:40,310
but a very, very large number.

1229
00:51:40,310 --> 00:51:42,490
So if you think the
discount factor is delta,

1230
00:51:42,490 --> 00:51:44,740
and you just roll
that forward, you

1231
00:51:44,740 --> 00:51:46,510
get essentially
absurd implications,

1232
00:51:46,510 --> 00:51:50,080
the reason being that we
assume the discount factor

1233
00:51:50,080 --> 00:51:50,807
is constant.

1234
00:51:50,807 --> 00:51:52,390
And so that, then,
essentially, if you

1235
00:51:52,390 --> 00:51:56,440
are reasonably impatient
between the present and any time

1236
00:51:56,440 --> 00:51:58,715
in the near future, like
two or four weeks from now,

1237
00:51:58,715 --> 00:52:00,340
that must imply that
you really, really

1238
00:52:00,340 --> 00:52:02,048
don't care about what's
happening in five

1239
00:52:02,048 --> 00:52:04,820
years from now, and so on.

1240
00:52:04,820 --> 00:52:07,210
Now, that's completely
unrealistic.

1241
00:52:07,210 --> 00:52:09,512
The discount factor for
two-week delays in the future

1242
00:52:09,512 --> 00:52:11,470
must be, in some ways,
higher than the discount

1243
00:52:11,470 --> 00:52:13,220
factor for two-week
delays in the present.

1244
00:52:13,220 --> 00:52:15,803
And that's essentially what the
quasi-hyperbolic, or the model

1245
00:52:15,803 --> 00:52:17,830
I'm going to propose to
you in the next class,

1246
00:52:17,830 --> 00:52:20,540
is going to try and explain.

1247
00:52:20,540 --> 00:52:21,850
So why is that unrealistic?

1248
00:52:21,850 --> 00:52:23,830
Well, we know for many
situations in the world,

1249
00:52:23,830 --> 00:52:25,810
people care a lot
about the future.

1250
00:52:25,810 --> 00:52:27,130
People save for retirement.

1251
00:52:27,130 --> 00:52:28,540
People invest in education.

1252
00:52:28,540 --> 00:52:29,830
People exercise, often.

1253
00:52:29,830 --> 00:52:31,000
People do problem sets.

1254
00:52:31,000 --> 00:52:32,260
People brush their teeth.

1255
00:52:32,260 --> 00:52:33,760
People eat healthy, and so on.

1256
00:52:33,760 --> 00:52:35,420
People invest a
lot in the future,

1257
00:52:35,420 --> 00:52:38,620
in stuff that happens four
or five, six, seven, 10

1258
00:52:38,620 --> 00:52:39,740
years from now.

1259
00:52:39,740 --> 00:52:42,460
So they care a lot about
the future in some ways.

1260
00:52:42,460 --> 00:52:44,750
Yet we find the
short-run impatience.

1261
00:52:44,750 --> 00:52:49,930
So now we need to find some
model that can bridge this gap.

1262
00:52:49,930 --> 00:52:52,780
And so another
way to put this is

1263
00:52:52,780 --> 00:52:55,960
when you look at the evidence
that we have in terms

1264
00:52:55,960 --> 00:52:58,780
of my time horizon, when
you look at discount

1265
00:52:58,780 --> 00:53:02,350
factors conducted in
studies such as the one

1266
00:53:02,350 --> 00:53:07,330
that I just showed you, or using
real-world decisions, what you

1267
00:53:07,330 --> 00:53:10,060
see usually is that the discount
factor in the very short run

1268
00:53:10,060 --> 00:53:12,880
tends to be very small.

1269
00:53:12,880 --> 00:53:15,755
This is what you see on the
left-hand side of the graph.

1270
00:53:15,755 --> 00:53:17,380
When you look at
further in the future,

1271
00:53:17,380 --> 00:53:19,540
the discount factor
tends to be higher.

1272
00:53:19,540 --> 00:53:22,330
Or another way to put this is
the estimated delta increases

1273
00:53:22,330 --> 00:53:23,980
by time horizon.

1274
00:53:23,980 --> 00:53:27,430
Again, that's a violation of the
exponential discounting model.

1275
00:53:30,250 --> 00:53:32,000
So that's the first
piece of evidence.

1276
00:53:32,000 --> 00:53:33,730
The second one is
preference reversal,

1277
00:53:33,730 --> 00:53:35,370
dynamic inconsistency.

1278
00:53:35,370 --> 00:53:37,120
What I mean by that
is dynamic consistency

1279
00:53:37,120 --> 00:53:39,370
is essentially the
property that when

1280
00:53:39,370 --> 00:53:42,850
you make a choice for the future
between two future periods,

1281
00:53:42,850 --> 00:53:45,790
and when the future then
comes absent new information

1282
00:53:45,790 --> 00:53:47,800
or any other things
that have happened,

1283
00:53:47,800 --> 00:53:49,785
you will stick to that choice.

1284
00:53:49,785 --> 00:53:51,160
A formal decision
or a definition

1285
00:53:51,160 --> 00:53:52,750
here is, the action
a person thinks

1286
00:53:52,750 --> 00:53:55,150
she should take in
the future always

1287
00:53:55,150 --> 00:53:57,310
coincides with the action
that she actually prefers

1288
00:53:57,310 --> 00:53:59,620
to take once the time comes.

1289
00:53:59,620 --> 00:54:02,320
So if I make a plan
to exercise tomorrow,

1290
00:54:02,320 --> 00:54:04,590
or if I make a plan
to eat salad tomorrow,

1291
00:54:04,590 --> 00:54:05,840
I'm going to actually do that.

1292
00:54:05,840 --> 00:54:08,080
I'm not going to be,
actually watching movies

1293
00:54:08,080 --> 00:54:11,170
seems like a good idea, or
the potato chips instead

1294
00:54:11,170 --> 00:54:12,550
look better.

1295
00:54:12,550 --> 00:54:14,080
I have perfect
foresight in what I'm

1296
00:54:14,080 --> 00:54:15,560
going to plan for the future.

1297
00:54:15,560 --> 00:54:16,960
I know my future preferences.

1298
00:54:16,960 --> 00:54:19,510
And my future preferences for
what I want for the future

1299
00:54:19,510 --> 00:54:24,650
coincide with what I actually
want in the future, as well.

1300
00:54:24,650 --> 00:54:28,390
And so put differently, there's
no intrapersonal conflicts.

1301
00:54:28,390 --> 00:54:31,180
That is to say what I want
for the future is also

1302
00:54:31,180 --> 00:54:35,810
what my future self
wants for itself.

1303
00:54:35,810 --> 00:54:39,970
And so that's closely
connected to the assumption

1304
00:54:39,970 --> 00:54:43,180
of exponential discounting--
that is to say exponential

1305
00:54:43,180 --> 00:54:46,660
discounting has the assumption
that how much I care between

1306
00:54:46,660 --> 00:54:49,270
the present and the
future is always--

1307
00:54:49,270 --> 00:54:51,280
the weight is always
determined by delta,

1308
00:54:51,280 --> 00:54:53,510
and that delta doesn't
change over time.

1309
00:54:53,510 --> 00:54:55,240
So when I think now
about what I want

1310
00:54:55,240 --> 00:54:57,400
in the future, between
a year from now

1311
00:54:57,400 --> 00:54:59,110
and two years from
now, the difference

1312
00:54:59,110 --> 00:55:01,900
between those or the discounting
will always be delta.

1313
00:55:01,900 --> 00:55:04,390
Once the future
comes, the difference

1314
00:55:04,390 --> 00:55:06,973
between a year from then and--

1315
00:55:06,973 --> 00:55:08,890
at the time, then, it
will be like the present

1316
00:55:08,890 --> 00:55:10,598
and a year from now--
will also be delta.

1317
00:55:10,598 --> 00:55:12,800
So there's no difference there.

1318
00:55:12,800 --> 00:55:15,370
So what's the formal argument
of the exponential discounting

1319
00:55:15,370 --> 00:55:16,120
model?

1320
00:55:16,120 --> 00:55:18,010
Well, it is essentially
if at time 0,

1321
00:55:18,010 --> 00:55:19,983
I prefer an action
A over an action B,

1322
00:55:19,983 --> 00:55:21,400
suppose there's
different actions.

1323
00:55:21,400 --> 00:55:23,410
There's action A
and action B that I

1324
00:55:23,410 --> 00:55:26,680
can do starting in period one.

1325
00:55:26,680 --> 00:55:30,040
Well, if I prefer action A over
action B, on the left-hand side

1326
00:55:30,040 --> 00:55:32,290
there's the utilities
associated with that.

1327
00:55:32,290 --> 00:55:36,670
There's u0 plus delta
times u1 A of action

1328
00:55:36,670 --> 00:55:41,050
A plus delta squared of
u2 of action A, and so on.

1329
00:55:41,050 --> 00:55:43,150
If I prefer that over
action B, well, it

1330
00:55:43,150 --> 00:55:45,100
must be that I prefer
the stream of utility

1331
00:55:45,100 --> 00:55:47,590
on the left-hand side
to the stream of utility

1332
00:55:47,590 --> 00:55:49,780
on the right-hand side.

1333
00:55:49,780 --> 00:55:53,140
But now that implies if I take
away the u0, because they're

1334
00:55:53,140 --> 00:55:55,030
the same on both
sides, because I'm

1335
00:55:55,030 --> 00:55:59,210
making choices for the future,
and then divide by delta, what

1336
00:55:59,210 --> 00:56:05,740
I get is essentially, again, an
equality that at time 1, again,

1337
00:56:05,740 --> 00:56:11,600
I still prefer option A over
option B. That is to say,

1338
00:56:11,600 --> 00:56:13,720
if I prefer option
A over option B

1339
00:56:13,720 --> 00:56:15,910
at time 0, that
implies essentially

1340
00:56:15,910 --> 00:56:20,395
that I also prefer option
A over option B at time 1.

1341
00:56:20,395 --> 00:56:22,270
So that essentially is
another way to say it,

1342
00:56:22,270 --> 00:56:25,030
is that the exponential
discounting factor

1343
00:56:25,030 --> 00:56:28,610
implies time and consistency.

1344
00:56:28,610 --> 00:56:29,750
Any questions about that?

1345
00:56:41,630 --> 00:56:43,962
So what examples do we have
that violate this property?

1346
00:56:43,962 --> 00:56:46,420
We already talked about this
a bit in the previous classes,

1347
00:56:46,420 --> 00:56:49,162
but just remind ourselves.

1348
00:56:54,090 --> 00:56:55,930
Yes.

1349
00:56:55,930 --> 00:56:57,640
STUDENT: The betting
on how much weight

1350
00:56:57,640 --> 00:56:59,280
you lose when you're on a diet.

1351
00:56:59,280 --> 00:57:04,988
You make sure that you'll
want to change your behavior.

1352
00:57:04,988 --> 00:57:06,030
FRANK SCHILBACH: Exactly.

1353
00:57:06,030 --> 00:57:08,880
So dieting in general seems
a great example of saying,

1354
00:57:08,880 --> 00:57:11,010
I really would like
to lose some weight,

1355
00:57:11,010 --> 00:57:12,870
or have some target
weight, or some target

1356
00:57:12,870 --> 00:57:14,910
exercising, or a certain
behavior of eating

1357
00:57:14,910 --> 00:57:16,900
and exercising or combined.

1358
00:57:16,900 --> 00:57:18,900
And I really would
like to do that.

1359
00:57:18,900 --> 00:57:20,940
For now-- I mean, I
think about the future.

1360
00:57:20,940 --> 00:57:23,118
Often at New Year's
or certain points

1361
00:57:23,118 --> 00:57:24,660
of the year, our
birthdays and so on,

1362
00:57:24,660 --> 00:57:26,460
people think, OK,
I'm going to do this.

1363
00:57:26,460 --> 00:57:27,870
I have great plans and so on.

1364
00:57:27,870 --> 00:57:29,880
They have certain
preferences for the future.

1365
00:57:29,880 --> 00:57:32,340
But then the future comes a
week or a month from then.

1366
00:57:32,340 --> 00:57:35,310
People don't follow through.

1367
00:57:35,310 --> 00:57:35,850
Exactly.

1368
00:57:35,850 --> 00:57:37,590
That's essentially
a clear example

1369
00:57:37,590 --> 00:57:40,050
of a preference reversal,
which is essentially

1370
00:57:40,050 --> 00:57:42,540
another way of
saying preferences

1371
00:57:42,540 --> 00:57:44,220
are dynamically inconsistent.

1372
00:57:49,310 --> 00:57:50,585
Any other example?

1373
00:58:13,970 --> 00:58:15,316
Yes.

1374
00:58:15,316 --> 00:58:17,534
STUDENT: [INAUDIBLE]
say we should

1375
00:58:17,534 --> 00:58:19,753
do something, kind of
like this is, like,

1376
00:58:19,753 --> 00:58:22,218
what we want our future to be.

1377
00:58:22,218 --> 00:58:24,808
[INAUDIBLE]

1378
00:58:24,808 --> 00:58:25,850
FRANK SCHILBACH: Exactly.

1379
00:58:25,850 --> 00:58:28,627
So that's true for,
did you say exercising?

1380
00:58:28,627 --> 00:58:29,210
STUDENT: Yeah.

1381
00:58:29,210 --> 00:58:32,480
FRANK SCHILBACH: Yeah,
for exercising, exactly.

1382
00:58:32,480 --> 00:58:35,660
I'll show you some examples of
people, for example, signing up

1383
00:58:35,660 --> 00:58:37,770
for gyms that pay
yearly membership fees,

1384
00:58:37,770 --> 00:58:40,250
and so on, that tend
to be very expensive.

1385
00:58:40,250 --> 00:58:41,750
The idea often is
then they think

1386
00:58:41,750 --> 00:58:46,910
about they will go to the gym
weekly, or daily, or whatever.

1387
00:58:46,910 --> 00:58:49,850
And then under that assumption
for your preferences

1388
00:58:49,850 --> 00:58:52,650
for the future, then it
makes a lot of sense.

1389
00:58:52,650 --> 00:58:55,298
But then if you then
not actually go,

1390
00:58:55,298 --> 00:58:56,840
or if your preferences
are different,

1391
00:58:56,840 --> 00:58:59,240
then it turns out to be
different in the future, that's

1392
00:58:59,240 --> 00:59:01,070
a pretty bad idea.

1393
00:59:01,070 --> 00:59:03,130
Yes, you were saying.

1394
00:59:03,130 --> 00:59:06,093
STUDENT: So consider
apples or bananas.

1395
00:59:06,093 --> 00:59:08,873
If I'm choosing [INAUDIBLE].

1396
00:59:17,420 --> 00:59:19,430
FRANK SCHILBACH:
Yeah, to be clear,

1397
00:59:19,430 --> 00:59:22,610
if you just start eating
apples because you

1398
00:59:22,610 --> 00:59:24,658
had too many bananas
in the past, that's

1399
00:59:24,658 --> 00:59:25,950
not what we were talking about.

1400
00:59:25,950 --> 00:59:29,900
So it's not about
people's past choices

1401
00:59:29,900 --> 00:59:32,900
affecting future choices through
some form of habit formation,

1402
00:59:32,900 --> 00:59:35,450
or people getting bored,
or tired, or the like.

1403
00:59:35,450 --> 00:59:38,150
But it's about if I today
choose today I want bananas,

1404
00:59:38,150 --> 00:59:42,380
tomorrow I want apples, and then
tomorrow I'm actually saying,

1405
00:59:42,380 --> 00:59:45,950
actually, I don't like
apples, I really like bananas,

1406
00:59:45,950 --> 00:59:47,262
then that would be a violation.

1407
00:59:47,262 --> 00:59:49,220
But it needs to be
something that's essentially

1408
00:59:49,220 --> 00:59:54,440
either new information or
some new options or so on that

1409
00:59:54,440 --> 00:59:56,637
become available.

1410
00:59:56,637 --> 00:59:58,220
In the example that
you're mentioning,

1411
00:59:58,220 --> 00:59:59,360
there was none of that.

1412
00:59:59,360 --> 01:00:02,600
So that's not quite what
we're talking about.

1413
01:00:02,600 --> 01:00:05,700
More common is-- and there's a
paper that does this, in fact,

1414
01:00:05,700 --> 01:00:08,720
with Dutch employees by Read
and van Leeuwen that essentially

1415
01:00:08,720 --> 01:00:10,630
asked people about
next week first.

1416
01:00:10,630 --> 01:00:12,350
So it asked them
about-- this is actually

1417
01:00:12,350 --> 01:00:15,618
an actual company, where
workers were asked, after lunch,

1418
01:00:15,618 --> 01:00:16,910
would you like to have a snack?

1419
01:00:16,910 --> 01:00:18,950
And what snack would
you like to have?

1420
01:00:18,950 --> 01:00:21,690
Would you like to have
apples or chocolate?

1421
01:00:21,690 --> 01:00:24,930
When you're asked to do
that today for next week,

1422
01:00:24,930 --> 01:00:27,940
74% chose fruit or
apples, essentially.

1423
01:00:27,940 --> 01:00:31,020
So lots of people tend to want
to be virtuous in the future,

1424
01:00:31,020 --> 01:00:32,580
eat healthily, and so on.

1425
01:00:32,580 --> 01:00:34,330
When you ask them then
the same question--

1426
01:00:34,330 --> 01:00:36,930
so then in the actual
experiment, what

1427
01:00:36,930 --> 01:00:39,840
they did is then they went
back to the workers, and said,

1428
01:00:39,840 --> 01:00:41,080
oh, I forgot your choice.

1429
01:00:41,080 --> 01:00:43,420
Why don't you choose again.

1430
01:00:43,420 --> 01:00:44,190
Let us know.

1431
01:00:44,190 --> 01:00:46,530
That was a little bit
cheating, but then essentially,

1432
01:00:46,530 --> 01:00:52,620
70% of people, when it comes for
the same day, choose chocolate.

1433
01:00:52,620 --> 01:00:54,870
And here's none of
that, in the sense

1434
01:00:54,870 --> 01:00:56,970
of there's no habit
formation, there's

1435
01:00:56,970 --> 01:00:59,233
no people ate too many
apples and now they

1436
01:00:59,233 --> 01:01:00,150
really want chocolate.

1437
01:01:00,150 --> 01:01:01,680
That was only one choice.

1438
01:01:01,680 --> 01:01:03,510
And so now, when I
make some choices

1439
01:01:03,510 --> 01:01:05,340
for the future and
the future comes,

1440
01:01:05,340 --> 01:01:09,310
I should stick to that choice.

1441
01:01:09,310 --> 01:01:11,450
Similarly, there's
movie choices.

1442
01:01:11,450 --> 01:01:13,210
It used to be--

1443
01:01:13,210 --> 01:01:15,490
you guys are probably
too young for this--

1444
01:01:15,490 --> 01:01:19,647
Netflix used to send
you movies to your home.

1445
01:01:19,647 --> 01:01:21,730
But often what lots of
people had was this issue--

1446
01:01:21,730 --> 01:01:25,180
they had great plans of watching
highbrow, or high culture,

1447
01:01:25,180 --> 01:01:31,005
and often sad or deep
movies in the future.

1448
01:01:31,005 --> 01:01:32,380
There's really
things they wanted

1449
01:01:32,380 --> 01:01:34,480
to watch, be it The
Piano or Schindler's List

1450
01:01:34,480 --> 01:01:37,280
and so on, which
by some category

1451
01:01:37,280 --> 01:01:38,560
we might call highbrow.

1452
01:01:38,560 --> 01:01:40,690
But instead, when
the present comes,

1453
01:01:40,690 --> 01:01:44,230
people often like to watch
essentially lowbrow movies

1454
01:01:44,230 --> 01:01:46,870
like comedies, and
so on and so forth,

1455
01:01:46,870 --> 01:01:50,080
for example, Four Weddings and
a Funeral, Speed, and so on,

1456
01:01:50,080 --> 01:01:51,538
so action movies or the like.

1457
01:01:51,538 --> 01:01:53,080
And then what would
happen in Netflix

1458
01:01:53,080 --> 01:01:55,930
often is you would get all
these movies that you'd really

1459
01:01:55,930 --> 01:01:59,710
love to watch in the future,
but never in the present,

1460
01:01:59,710 --> 01:02:01,720
then get stuck with them.

1461
01:02:01,720 --> 01:02:03,970
And there's, in fact,
an example or a paper

1462
01:02:03,970 --> 01:02:06,530
who does this, which essentially
elicits people's preferences

1463
01:02:06,530 --> 01:02:08,530
for what they would like
to watch in the present

1464
01:02:08,530 --> 01:02:09,880
versus in the future.

1465
01:02:09,880 --> 01:02:11,350
And what you see,
essentially, is

1466
01:02:11,350 --> 01:02:14,140
people tend to
systematically pick

1467
01:02:14,140 --> 01:02:16,270
for the present,
for tonight, people

1468
01:02:16,270 --> 01:02:19,360
tend to watch or want
to watch lowbrow movies.

1469
01:02:19,360 --> 01:02:22,990
Action, rom com, or whatever
sounds really good for tonight.

1470
01:02:22,990 --> 01:02:25,610
When you think about what would
you like to watch next week,

1471
01:02:25,610 --> 01:02:28,660
people tend to pick
highbrow movies instead.

1472
01:02:32,690 --> 01:02:37,040
And there's lots of
examples of that kind.

1473
01:02:37,040 --> 01:02:39,350
And so just to summarize,
these preference reversals,

1474
01:02:39,350 --> 01:02:41,870
again, these are not really
possible in the exponential

1475
01:02:41,870 --> 01:02:43,070
discounting model.

1476
01:02:43,070 --> 01:02:44,070
That should not occur.

1477
01:02:44,070 --> 01:02:46,643
That's by assumption not
possible in that model,

1478
01:02:46,643 --> 01:02:48,560
as I just showed you
before, yet we see plenty

1479
01:02:48,560 --> 01:02:51,120
of examples in the real world.

1480
01:02:51,120 --> 01:02:54,110
Now, the third piece of evidence
is demand for commitment.

1481
01:02:54,110 --> 01:02:56,670
That's really closely
related to that.

1482
01:02:56,670 --> 01:02:59,000
So one example here is
demand for commitment

1483
01:02:59,000 --> 01:03:02,960
is essentially when you know
that your future preferences

1484
01:03:02,960 --> 01:03:05,360
will be different from
your present preferences,

1485
01:03:05,360 --> 01:03:07,740
you might engage in
commitment devices.

1486
01:03:07,740 --> 01:03:08,900
What does that mean?

1487
01:03:08,900 --> 01:03:11,957
You might want to change
the prices of your options

1488
01:03:11,957 --> 01:03:12,540
in the future.

1489
01:03:12,540 --> 01:03:14,415
And particularly, you
might want to take away

1490
01:03:14,415 --> 01:03:16,760
some options in the future.

1491
01:03:16,760 --> 01:03:20,420
One example is Ulysses
and the Sirens.

1492
01:03:20,420 --> 01:03:23,300
Who knows that story or
can tell me what it is?

1493
01:03:23,300 --> 01:03:24,149
Yes.

1494
01:03:24,149 --> 01:03:28,061
STUDENT: So basically,
there are these Sirens,

1495
01:03:28,061 --> 01:03:35,396
and they're singing
and [INAUDIBLE]..

1496
01:03:35,396 --> 01:03:45,070
But [INAUDIBLE] but it's hard to
tear yourself from [INAUDIBLE]..

1497
01:03:45,070 --> 01:03:49,552
So he had [INAUDIBLE]
tied to the ship

1498
01:03:49,552 --> 01:03:51,490
so that he wouldn't be able to.

1499
01:03:51,490 --> 01:03:52,760
FRANK SCHILBACH: Yes, exactly.

1500
01:03:52,760 --> 01:03:53,510
So here's Ulysses.

1501
01:03:53,510 --> 01:03:57,070
I think he was on his way
back from his long journey.

1502
01:03:59,950 --> 01:04:03,070
He knew that the Sirens
were going to come.

1503
01:04:03,070 --> 01:04:05,500
He knew that his preferences
would change in the future--

1504
01:04:05,500 --> 01:04:07,190
that he would not
be able to resist

1505
01:04:07,190 --> 01:04:10,120
their power or their songs.

1506
01:04:10,120 --> 01:04:12,880
And so what he did
is he asked his crew

1507
01:04:12,880 --> 01:04:15,070
to bind him to the
mast so he would not

1508
01:04:15,070 --> 01:04:18,672
be able to leave the ship, even
if he wanted to in the future.

1509
01:04:18,672 --> 01:04:21,130
And that's demand for commitment
because he was taking away

1510
01:04:21,130 --> 01:04:24,100
some options in the
future, with a goal

1511
01:04:24,100 --> 01:04:27,040
to change his future behavior,
knowing that his preferences

1512
01:04:27,040 --> 01:04:29,800
would change in the future.

1513
01:04:29,800 --> 01:04:32,290
If you wonder why the
guys who are rowing

1514
01:04:32,290 --> 01:04:33,430
are not leaving the ship.

1515
01:04:33,430 --> 01:04:35,320
They had wax in their ears.

1516
01:04:35,320 --> 01:04:38,090
I don't know why Ulysses
couldn't use the wax either,

1517
01:04:38,090 --> 01:04:41,080
but anyway--

1518
01:04:41,080 --> 01:04:43,060
So that's one example
of a commitment device.

1519
01:04:43,060 --> 01:04:45,310
There's another one, which
is sort of financial advice

1520
01:04:45,310 --> 01:04:47,890
that people often get,
which is the following--

1521
01:04:47,890 --> 01:04:51,100
cut up your credit card
and store the cards.

1522
01:04:51,100 --> 01:04:55,360
If possible, get rid of
all your credit cards

1523
01:04:55,360 --> 01:04:57,040
or put temptation out of reach.

1524
01:04:57,040 --> 01:04:59,230
If you really can't do
without a credit card,

1525
01:04:59,230 --> 01:05:00,340
limit yourself to one.

1526
01:05:00,340 --> 01:05:03,080
Put it in a tub of water,
and stick it in the freezer.

1527
01:05:03,080 --> 01:05:05,380
And so the idea here
is if you really

1528
01:05:05,380 --> 01:05:09,640
have self-control
problems, well,

1529
01:05:09,640 --> 01:05:11,920
when you want to buy
something really quickly,

1530
01:05:11,920 --> 01:05:13,660
when temptation
sort of takes over,

1531
01:05:13,660 --> 01:05:16,418
you have to limit your
options in some ways.

1532
01:05:16,418 --> 01:05:18,460
So in some sense, have
you some cool down period.

1533
01:05:18,460 --> 01:05:21,498
It takes a while to get your
credit card out of the freezer.

1534
01:05:21,498 --> 01:05:22,040
I don't know.

1535
01:05:22,040 --> 01:05:23,635
I asked my wife about
is this a thing?

1536
01:05:23,635 --> 01:05:25,510
And she was saying,
well, haven't you watched

1537
01:05:25,510 --> 01:05:27,070
"Confessions of a Shopaholic?"

1538
01:05:27,070 --> 01:05:28,150
I have not.

1539
01:05:28,150 --> 01:05:30,130
If you want to watch
that video, you

1540
01:05:30,130 --> 01:05:33,490
see, in fact, apparently
that is, in fact, a thing.

1541
01:05:33,490 --> 01:05:36,920
But the idea of having
some cool down period,

1542
01:05:36,920 --> 01:05:39,770
which essentially is to
deal with essentially

1543
01:05:39,770 --> 01:05:42,430
short-run impatience,
comes in many settings

1544
01:05:42,430 --> 01:05:43,390
and many variations.

1545
01:05:43,390 --> 01:05:45,940
In fact, for example, if
you'd like to get married,

1546
01:05:45,940 --> 01:05:48,610
often you have to
go to some office

1547
01:05:48,610 --> 01:05:51,023
and declare that you would
like to get married, and then

1548
01:05:51,023 --> 01:05:52,690
wait for another three
days or something

1549
01:05:52,690 --> 01:05:54,370
until you actually get married.

1550
01:05:54,370 --> 01:05:58,450
Often, the idea is people
sometimes come to their senses

1551
01:05:58,450 --> 01:06:00,640
and it takes a few days.

1552
01:06:06,250 --> 01:06:08,410
So what do these examples show?

1553
01:06:08,410 --> 01:06:10,450
Well, they show that
people have a tendency

1554
01:06:10,450 --> 01:06:12,010
for immediate gratification.

1555
01:06:12,010 --> 01:06:17,530
And they tend to
discount quite heavily

1556
01:06:17,530 --> 01:06:19,665
in short-term decisions.

1557
01:06:19,665 --> 01:06:21,790
Now, what does the demand
for commitment then show?

1558
01:06:21,790 --> 01:06:26,230
It's we, in fact, tend to
disapprove of this tendency

1559
01:06:26,230 --> 01:06:27,460
beforehand.

1560
01:06:27,460 --> 01:06:29,210
That is to say we know
that in the future,

1561
01:06:29,210 --> 01:06:30,400
we might be impatient.

1562
01:06:30,400 --> 01:06:31,730
We don't like that.

1563
01:06:31,730 --> 01:06:34,030
And because of that, we
bind ourselves to the mast,

1564
01:06:34,030 --> 01:06:38,950
or we freeze our credit cards,
or some people, at least, do.

1565
01:06:41,630 --> 01:06:43,090
And so all of these
decision makers

1566
01:06:43,090 --> 01:06:44,507
are time inconsistent
in the sense

1567
01:06:44,507 --> 01:06:48,945
that when they make certain
choices for the future, what

1568
01:06:48,945 --> 01:06:51,320
they will want to choose in
the future will be different.

1569
01:06:51,320 --> 01:06:54,040
And knowing that, they will
restrict their options.

1570
01:06:54,040 --> 01:06:59,830
That is to say, different
selves want different things.

1571
01:06:59,830 --> 01:07:03,030
So then what's the
heart of the issue?

1572
01:07:03,030 --> 01:07:04,780
Well, the heart of the
issue is that there

1573
01:07:04,780 --> 01:07:07,533
are conflicts rooted between
short and long-run patience.

1574
01:07:07,533 --> 01:07:09,700
What we want in the short
run is different from what

1575
01:07:09,700 --> 01:07:10,868
we want in the long run.

1576
01:07:10,868 --> 01:07:12,910
That is to say when we
think ahead of the future,

1577
01:07:12,910 --> 01:07:14,050
we tend to be very patient.

1578
01:07:14,050 --> 01:07:17,810
There's all sorts of good things
we want to do in the future.

1579
01:07:17,810 --> 01:07:19,420
When the time
actually comes, when

1580
01:07:19,420 --> 01:07:22,728
we think about the present,
we tend to be impatient.

1581
01:07:22,728 --> 01:07:24,520
Now the issue with
exponential discounting,

1582
01:07:24,520 --> 01:07:27,400
then, is the exponential
discounting model

1583
01:07:27,400 --> 01:07:29,980
has only one parameter
which captures

1584
01:07:29,980 --> 01:07:32,260
essentially discounting.

1585
01:07:32,260 --> 01:07:33,700
But it can sort of--

1586
01:07:33,700 --> 01:07:35,710
by assumption, the
discounting needs

1587
01:07:35,710 --> 01:07:38,080
to be the same across
all time horizons.

1588
01:07:38,080 --> 01:07:41,350
That is to say, it can only
match one of those two things,

1589
01:07:41,350 --> 01:07:42,520
but not both.

1590
01:07:42,520 --> 01:07:45,820
It can only match either your
short-run discounting, but then

1591
01:07:45,820 --> 01:07:47,610
the long-run discounting
is off, or you

1592
01:07:47,610 --> 01:07:49,360
can try to match the
long-run discounting,

1593
01:07:49,360 --> 01:07:51,220
but then the short-run
discounting is off.

1594
01:07:51,220 --> 01:07:54,670
So what that tells us,
we need two parameters

1595
01:07:54,670 --> 01:07:57,640
to deal with that.

1596
01:07:57,640 --> 01:07:59,440
So what we want, and
I'll talk about this

1597
01:07:59,440 --> 01:08:02,570
a lot more in the next class
or in the next few minutes.

1598
01:08:02,570 --> 01:08:04,510
And then in the next
class, we want a model

1599
01:08:04,510 --> 01:08:07,480
that has greater patience
for trade-offs in the future

1600
01:08:07,480 --> 01:08:09,700
than for trade-offs
in the present.

1601
01:08:09,700 --> 01:08:12,130
And then we want another model.

1602
01:08:12,130 --> 01:08:14,860
So one is we want different
levels of patience

1603
01:08:14,860 --> 01:08:17,020
over different time
horizons, and we

1604
01:08:17,020 --> 01:08:19,240
want a model that
explains or helps us

1605
01:08:19,240 --> 01:08:21,819
explain dynamic inconsistency.

1606
01:08:21,819 --> 01:08:23,430
So what is that model?

1607
01:08:23,430 --> 01:08:26,937
So I just showed you before the
exponential discounting model.

1608
01:08:26,937 --> 01:08:28,479
That's just what I
showed you before,

1609
01:08:28,479 --> 01:08:30,970
but that's exactly the
same, where essentially,

1610
01:08:30,970 --> 01:08:35,470
your discounted or lifetime
utility is essentially

1611
01:08:35,470 --> 01:08:37,779
what's given here,
where we have delta.

1612
01:08:37,779 --> 01:08:39,100
It's between 0 and 1.

1613
01:08:39,100 --> 01:08:41,229
And delta is a short-term
discount factor

1614
01:08:41,229 --> 01:08:43,479
and it's a long-run
discount factor.

1615
01:08:43,479 --> 01:08:47,109
If I'm trying to decide
between t and t plus 1,

1616
01:08:47,109 --> 01:08:49,300
the difference between
that is essentially delta.

1617
01:08:49,300 --> 01:08:51,939
And if I decide between
t plus 3 and t plus 4,

1618
01:08:51,939 --> 01:08:55,569
it's also delta that
regulates this factor.

1619
01:08:55,569 --> 01:08:57,880
Now, what does the
quasi-hyperbolic discounting

1620
01:08:57,880 --> 01:08:58,510
model do?

1621
01:08:58,510 --> 01:09:00,399
It has another parameter.

1622
01:09:00,399 --> 01:09:02,800
And this parameter
is called beta.

1623
01:09:02,800 --> 01:09:06,970
And beta governs, essentially,
short-run discounting,

1624
01:09:06,970 --> 01:09:09,640
while delta is the
long-run discount factor.

1625
01:09:09,640 --> 01:09:11,290
What is that telling us?

1626
01:09:11,290 --> 01:09:15,170
Essentially, beta discounts
anything that's in the future.

1627
01:09:15,170 --> 01:09:17,380
So essentially, if you
look at the equation now,

1628
01:09:17,380 --> 01:09:20,050
anything that's in the
future, that's not period t,

1629
01:09:20,050 --> 01:09:22,520
is discounted by beta.

1630
01:09:22,520 --> 01:09:24,350
And then within
any future periods,

1631
01:09:24,350 --> 01:09:26,562
we have another discount
factor that's essentially

1632
01:09:26,562 --> 01:09:27,770
the long-run discount factor.

1633
01:09:27,770 --> 01:09:29,149
That's delta.

1634
01:09:29,149 --> 01:09:30,680
Now, why does that help us?

1635
01:09:30,680 --> 01:09:32,600
It helps us because
now we can essentially

1636
01:09:32,600 --> 01:09:34,870
separate short-run and
long-run discounting.

1637
01:09:34,870 --> 01:09:37,850
You can say short-run
discounting is governed by beta

1638
01:09:37,850 --> 01:09:41,120
and long-run discounting
is governed by delta.

1639
01:09:41,120 --> 01:09:42,770
And now we can
match a lot of facts

1640
01:09:42,770 --> 01:09:47,510
that we couldn't match earlier.

1641
01:09:47,510 --> 01:09:48,950
Any questions on that?

1642
01:09:53,140 --> 01:09:53,760
Yeah.

1643
01:09:53,760 --> 01:09:57,890
STUDENT: Yeah, I was wondering
if the evidence [INAUDIBLE]

1644
01:09:57,890 --> 01:09:59,384
was comparable to this.

1645
01:09:59,384 --> 01:10:01,874
Because if you have a
beta that really discounts

1646
01:10:01,874 --> 01:10:06,854
any future consumption,
would the commitment device

1647
01:10:06,854 --> 01:10:08,348
[INAUDIBLE].

1648
01:10:08,348 --> 01:10:10,340
Because many [INAUDIBLE].

1649
01:10:14,867 --> 01:10:17,200
FRANK SCHILBACH: So you're
asking two separate questions

1650
01:10:17,200 --> 01:10:17,700
here.

1651
01:10:17,700 --> 01:10:20,140
So one question
is, can we explain,

1652
01:10:20,140 --> 01:10:21,763
in theory, commitment devices?

1653
01:10:21,763 --> 01:10:23,680
Can we explain essentially--
can we write down

1654
01:10:23,680 --> 01:10:25,870
a theory that says
you should be at least

1655
01:10:25,870 --> 01:10:28,570
under some assumptions,
under some parameters,

1656
01:10:28,570 --> 01:10:30,620
willing to engage in
commitment devices

1657
01:10:30,620 --> 01:10:31,990
to demand for commitment?

1658
01:10:31,990 --> 01:10:35,380
The answer is yes, depending
a little bit on your naivete

1659
01:10:35,380 --> 01:10:37,430
and sophistication, which
we're going to get to.

1660
01:10:37,430 --> 01:10:38,860
But so you in
principle, at least,

1661
01:10:38,860 --> 01:10:42,940
can in theory write down a
version of this model that

1662
01:10:42,940 --> 01:10:45,283
predicts demand for commitment.

1663
01:10:45,283 --> 01:10:46,700
You're asking a
separate question,

1664
01:10:46,700 --> 01:10:50,305
which is are these commitment
devices actually going to help?

1665
01:10:50,305 --> 01:10:52,930
So A, are some people are going
to make use of these commitment

1666
01:10:52,930 --> 01:10:54,730
devices, and B, are
they going to help?

1667
01:10:54,730 --> 01:10:56,200
The answer is maybe.

1668
01:10:56,200 --> 01:10:58,660
In many situations, in fact, no.

1669
01:10:58,660 --> 01:11:01,330
The reason being
often people then--

1670
01:11:01,330 --> 01:11:03,940
they might demand commitment
but then not follow through

1671
01:11:03,940 --> 01:11:06,340
in various ways, which
can be then explained

1672
01:11:06,340 --> 01:11:08,260
by people are sort
of overconfident

1673
01:11:08,260 --> 01:11:10,560
when it comes to their
self-control problems.

1674
01:11:10,560 --> 01:11:12,410
We're going to talk
about this next time.

1675
01:11:12,410 --> 01:11:15,830
So the idea here is that people
might understand that they

1676
01:11:15,830 --> 01:11:16,955
have self-control problems.

1677
01:11:16,955 --> 01:11:18,497
They might demand
commitment devices.

1678
01:11:18,497 --> 01:11:21,190
They might say, I'd like to have
a commitment device to help me,

1679
01:11:21,190 --> 01:11:23,857
but they might underestimate how
bad their self-control problems

1680
01:11:23,857 --> 01:11:24,880
actually are.

1681
01:11:24,880 --> 01:11:26,800
So then they demand
a commitment device

1682
01:11:26,800 --> 01:11:29,470
that's actually kind of
helpful but not quite enough,

1683
01:11:29,470 --> 01:11:30,982
that's not powerful enough.

1684
01:11:30,982 --> 01:11:32,440
They demand that
commitment device,

1685
01:11:32,440 --> 01:11:34,868
but then they
actually fail and do

1686
01:11:34,868 --> 01:11:36,910
the thing they want to do
anyway, and essentially

1687
01:11:36,910 --> 01:11:39,743
have to pay money, or
other things like that.

1688
01:11:39,743 --> 01:11:40,660
We'll talk about that.

1689
01:11:40,660 --> 01:11:42,910
But that's not a
theoretical problem.

1690
01:11:42,910 --> 01:11:46,570
That's an empirical problem,
in the sense of in principle,

1691
01:11:46,570 --> 01:11:48,340
commitment devices should help.

1692
01:11:48,340 --> 01:11:52,120
They might not be able
to do so in practice.

1693
01:11:52,120 --> 01:11:53,800
Let me tell you
a little bit more

1694
01:11:53,800 --> 01:11:55,540
about specifics of the model.

1695
01:11:55,540 --> 01:11:57,790
And then we're going to talk
about this in more detail

1696
01:11:57,790 --> 01:11:59,630
next time.

1697
01:11:59,630 --> 01:12:02,260
So usually, we tend to
assume that beta is lower

1698
01:12:02,260 --> 01:12:05,470
than 1 and delta is close to 1.

1699
01:12:05,470 --> 01:12:10,330
So for example, we think beta
is 2/3, or 3/4, or the like,

1700
01:12:10,330 --> 01:12:12,070
and delta equals 1.

1701
01:12:12,070 --> 01:12:15,860
So then your discounted utility
becomes something like this.

1702
01:12:15,860 --> 01:12:17,590
So relative to the
current period,

1703
01:12:17,590 --> 01:12:19,855
all future periods
are worth much less.

1704
01:12:19,855 --> 01:12:21,730
So everything in the
future, essentially, you

1705
01:12:21,730 --> 01:12:23,410
discount by 2/3.

1706
01:12:23,410 --> 01:12:25,210
And then within
any future periods,

1707
01:12:25,210 --> 01:12:27,350
you don't discount
very much anymore.

1708
01:12:27,350 --> 01:12:31,740
Usually, we think delta is
0.99, 0.95, or the like.

1709
01:12:31,740 --> 01:12:34,210
So there's some
discounting in the future.

1710
01:12:34,210 --> 01:12:37,390
You care more about stuff that's
one year from now compared

1711
01:12:37,390 --> 01:12:39,800
to 10 years from now
or 30 years from now,

1712
01:12:39,800 --> 01:12:41,350
but not that much differently.

1713
01:12:41,350 --> 01:12:43,690
You care a lot about whether
stuff is in the present

1714
01:12:43,690 --> 01:12:46,960
versus in two weeks from
now or in a year from now.

1715
01:12:52,570 --> 01:12:57,370
And so then similarly, if beta
equals 1/2 and delta equals 1,

1716
01:12:57,370 --> 01:12:59,630
then again, your
discount function--

1717
01:12:59,630 --> 01:13:02,140
this is the d of tau that I
was writing down earlier--

1718
01:13:02,140 --> 01:13:04,420
is essentially you care
about the present 1,

1719
01:13:04,420 --> 01:13:07,540
and then everything
in the future is 1/2.

1720
01:13:07,540 --> 01:13:09,880
So again, relative
to the present,

1721
01:13:09,880 --> 01:13:13,750
all future periods are
worth less, weighed 1/2.

1722
01:13:13,750 --> 01:13:17,620
And then all discounting takes
place between the present

1723
01:13:17,620 --> 01:13:20,740
and the immediate future.

1724
01:13:20,740 --> 01:13:22,570
So then again, what
we can explain now

1725
01:13:22,570 --> 01:13:25,090
is essentially short
run impatience.

1726
01:13:25,090 --> 01:13:27,225
I'm essentially impatient
between the present

1727
01:13:27,225 --> 01:13:27,850
and the future.

1728
01:13:27,850 --> 01:13:30,100
Anything that's in the future
is essentially far away

1729
01:13:30,100 --> 01:13:34,120
or gets the weight of, in this
case, 1/2 or 2/3 or the like.

1730
01:13:34,120 --> 01:13:36,580
I can also explain
long-run patience,

1731
01:13:36,580 --> 01:13:39,852
because essentially across
the years in the future,

1732
01:13:39,852 --> 01:13:41,560
there's no discounting
happening anymore.

1733
01:13:41,560 --> 01:13:45,010
People tend to be
relatively patient.

1734
01:13:45,010 --> 01:13:47,200
And so then,
decisions, of course,

1735
01:13:47,200 --> 01:13:51,880
are very sensitive to the
timing of costs and benefits.

1736
01:13:51,880 --> 01:13:54,500
We're going to talk
about that next time.

1737
01:13:54,500 --> 01:13:58,840
So as I said in the email I sent
you, readings until Wednesday

1738
01:13:58,840 --> 01:14:01,270
are the [INAUDIBLE] paper.

1739
01:14:01,270 --> 01:14:03,820
We're going to discuss or
finish the same set of slides

1740
01:14:03,820 --> 01:14:05,157
that I've given you now.

1741
01:14:05,157 --> 01:14:06,740
Let me know if you
have any questions.

1742
01:14:06,740 --> 01:14:08,400
Thank you.