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  • FRANK SCHILBACH: Welcome to lecture three.

  • Today and on Wednesday, we're going

  • to talk about time preferences and particular theory.

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

  • a lot of applications that are sort of close

  • to your real world, including procrastination of problem

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

  • and so on, and so forth.

  • Can you be a little quiet?

  • Thank you.

  • Think of the lectures today and on Wednesday

  • building some framework and some sort of structure

  • and how to think about these things.

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

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

  • and trying to think about the world.

  • Partially we're doing that to sort of try

  • to explain behaviors that we see in the world,

  • partially we do that because at the end,

  • we try to think about welfare and how

  • to evaluate certain outcomes-- is

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

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

  • But for that you, need some structure

  • how to think about some of those things.

  • At the heart of it, a lot of this

  • is about procrastination, about choices between the present

  • and the future.

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

  • It will be posted later today, probably late.

  • Please do let us know if you have any questions.

  • As I said, please be on time.

  • Do the readings.

  • There will be random pop quizzes.

  • They will be at the beginning of the class,

  • so you should be on time.

  • The laptop section is still over there.

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

  • in the front, in part because you're not

  • going to bother others.

  • I saw quite a few people using their phones

  • in class in previous classes.

  • Try to not do that.

  • That's not good for you.

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

  • Multitasking is very hard for people to do.

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

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

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

  • and help others answer them or answer them for others.

  • I have office hours, usually Tuesday afternoons.

  • Please sign up for them.

  • I'm very happy to meet you.

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

  • in the large class otherwise.

  • So please come to office hours.

  • I'm happy to talk to you about anything

  • you're interested in, ideally related

  • to behavioral economics.

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

  • We're going to talk first about exponential discounting.

  • Why are we talking about exponential discount?

  • This is the workhorse model of classical economics.

  • This is how economists usually think about choices over time.

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

  • and try to think about why is this model perhaps not

  • explaining things well, at least in some settings?

  • And how could we improve on that?

  • I'm going to propose an alternative model, which

  • is the quasi-hyperbolic discounting model.

  • And then we're going to talk about sophistication

  • and naivete, which is the idea that if you think

  • you have different preferences in the present form

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

  • Do you actually know what's going on?

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

  • or do you perhaps think that in the future,

  • I will be very patient, and then perhaps make

  • some mistakes accordingly?

  • I'll get to this in more detail.

  • So it's first important to notice

  • that any choice, essentially almost any choice you

  • make, almost always involves some choice over time.

  • Essentially, some trade-off between the present,

  • between some cost and benefit that you might occur

  • in the very short run, and some costs and benefits

  • that you might enjoy or incur in the future.

  • What examples do we have?

  • What choices over time do we face?

  • Yes.

  • STUDENT: Savings versus consumption.

  • FRANK SCHILBACH: Uh-huh.

  • And how do you decide how much to save?

  • STUDENT: Depending on your preferences and interests,

  • right?

  • FRANK SCHILBACH: Right.

  • So you have the choice, for example,

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

  • for next semester or next year.

  • So your choice is either to consume the money now

  • in various ways-- eat food or whatever

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

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

  • you have to give up some money now,

  • and you get some benefits in the future.

  • The benefits in the future are determined by the interest

  • rate, as you say.

  • If you have a savings account or the like,

  • you can essentially get some benefits in the future.

  • And then you have some costs in the present, which

  • would be essentially not consuming now,

  • and some benefits in the future, which is getting

  • that money in the future.

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

  • There's some cost and benefit.

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

  • Any other choices you make over time?

  • Yes.

  • STUDENT: Whether to go to college or not

  • or start working right away and make some money

  • or delay that income.

  • FRANK SCHILBACH: Right.

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

  • It has some costs and benefits.

  • And what are the costs and benefits of doing that?

  • STUDENT: You sacrifice four years

  • or whatever right now versus supposedly

  • a higher income later on.

  • FRANK SCHILBACH: Exactly.

  • So you have direct costs of education,

  • which is tuition in many cases.

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

  • It's quite a bit of money.

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

  • You could be working otherwise and make more money.

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

  • Some might think it's positive.

  • Some might think it's negative.

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

  • at least for you guys, tend to be

  • higher from going to college.

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

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

  • I'm sorry for that.

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

  • What do you need to do is you need to determine

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

  • And they occur in different points in time.

  • You need to make some estimates.

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

  • You might not have full information, and so on.

  • But assuming that all away, suppose

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

  • Then you have to decide, is that worth doing?

  • So somehow you need to aggregate these costs and benefits

  • over time by putting appropriate weights

  • on different periods in time, and decide,

  • should I do this or not.

  • OK.

  • Yes, any other similar choices that people make?

  • Yes.

  • STUDENT: [INAUDIBLE]

  • FRANK SCHILBACH: Right.

  • For example, you could think about

  • should I do a problem set?

  • Should I come to class?

  • Should I study for an exam, and so on.

  • Often, there's costs and benefits involved.

  • Often, the costs are immediate.

  • You have to work on the problem set.

  • That might not be pleasant.

  • You have to study for the exam.

  • That might not be pleasant.

  • You could be doing other things instead that you

  • can't do because of that.

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

  • usually in the terms either through increased knowledge

  • that might be useful for other things in the future,

  • or through better grades, or whatever you might be rewarded

  • from having more knowledge.

  • And then, again, there might be uncertainty involved

  • because it could be that you might not fully know what

  • the costs and benefits are.

  • It could be that it's sort of risky.

  • You might come to class or not come to class depending

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

  • But assuming that away, there's essentially

  • benefits and costs in the present,

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

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

  • in various ways.

  • Any other choices?

  • Yes.

  • STUDENT: Exercise.

  • FRANK SCHILBACH: Exercise, yeah, exactly.

  • Exercise is a good one.

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

  • Some people might actually enjoy it a lot.

  • Somebody would tell me he was addicted

  • to exercise-- that also happens.

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

  • tend to not like exercise that much.

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

  • feel better afterwards, in part because they

  • have long-run benefits.

  • Maybe they're in better shape eventually.

  • Maybe the healthier eventually.

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

  • forth.

  • And again, what you need to do is

  • you have some costs and benefits.

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

  • and getting yourself to do it.

  • That often is costly.

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

  • maybe not.

  • But then the benefits are often in the future,

  • often really far away in the future.

  • So if you really were eating healthier, often

  • the same thing--

  • essentially, you might not like eating spinach and vegetables

  • in the present.

  • Some people, of course, love that,

  • but often, then, the benefits come

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

  • And again, what you need to do is

  • you need to quantify somehow the costs and benefits

  • of certain actions.

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

  • to be able to make a choice.

  • Is that a good idea or a bad idea?

  • Do you want to do this or not?

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

  • of something that's very trivial--

  • purchasing an expensive software.

  • You have to spend some money of doing it.

  • That usually entails negative utility.

  • People don't like to give up money.

  • Second, there's pain and frustration

  • of learning the software.

  • Again, that's often negative utility.

  • And then there's mastery, which is

  • positive utility from knowing or learning the software,

  • until it becomes obsolete.

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

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

  • Well, you determine the value of the utility

  • of costs and benefits somehow.

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

  • And then once you have that, you need

  • to weigh the costs and benefits, and try to aggregate,

  • and try to figure out, is this a good idea or not.

  • There's another choice, which we're actually

  • going to talk about when we talk about welfare

  • and about policies.

  • Overall, it's deactivating a social media account, in part

  • because there's a very nice study that actually

  • studies precisely that.

  • So if you think about deactivating a social media

  • account--

  • Facebook, Twitter, Instagram, whatever people are using--

  • there's different costs and benefits involved.

  • And you can argue about what those are.

  • Part of that is the direct cost of deactivating the account.

  • Often, that's a tedious thing to do.

  • You have to figure out how to do it.

  • Often, companies try to not make it too easy

  • for you to actually do that.

  • You might want to archive some pictures, or whatever,

  • and so on.

  • Often, that's a tedious thing to do.

  • There's often a short-run adjustment cost,

  • where you want to be in touch with your friends.

  • Maybe it's harder to find out where the parties are,

  • or whatever, whatever things are.

  • So often, there's some adjustment cost, likely also

  • negative.

  • And then there is some long-run impact

  • on your social life, on your mental health,

  • on your happiness, and so on, that

  • could be positive or negative.

  • Assuming that perhaps a positive, then again,

  • you have to think about short-run negative costs

  • and benefits.

  • You have to learn about, think about what those are.

  • Again, they might be uncertain.

  • But to the extent that you could tell what they are,

  • then you have costs and benefits at different points in time.

  • And when you make that choice, you

  • have to figure out whether that's

  • worth doing by aggregating them somehow to some point in time

  • and, saying yes, I'll do it, or not.

  • And we'll get back to this in, I think,

  • something like lecture 20 or so, where

  • there is a study that was encouraging people to, in fact,

  • precisely do that, and look at happiness and other outcomes,

  • mental health, and so on, among students.

  • OK, so what are other important choices over time?

  • If you think about almost anything that you can think of,

  • any choice that you make in your life, almost any of these

  • involve some aspects of time.

  • So if you think about investing, saving, borrowing, credit card

  • spending, and so on, that involves choices over time.

  • If you think about education, often, there's

  • costs in the present, benefits in the future.

  • If you think about any sort of health investments--

  • eating healthy, taking your medication,

  • brushing your teeth, exercising, and so on, if you think

  • about sleeping, often sleep involves

  • choices between the present and the future.

  • You think about watching movies at night-- that's fun to do.

  • But often, that comes out like pain on the following

  • day in various forms.

  • Eating patterns as well, dating arguably

  • involves sort of costs and benefits

  • in the present and the future.

  • People make different choices.

  • Again, there's all sorts of other aspects involved as well,

  • including risk, information, and so on.

  • But what I'm pointing out is many choices

  • that people make have some aspects that involve

  • different points in time.

  • And you have to figure out how to weigh these utility

  • streams in some ways accordingly.

  • Now, here's a broad history of how economists

  • have thought about this.

  • And it's interesting to read, in fact.

  • And this is what the Frederick et al. article talks about.

  • In fact, economists sort of went full circle in some way.

  • So it started with a very complicated model

  • of a production, the amount of labor allocated

  • to the production of capital that

  • depends on the effective desire of accumulation,

  • which is a bit of a mouthful.

  • But essentially, there was lots of

  • rich psychological considerations involved

  • in trying to explain how people make choices over time.

  • People thought about self-control, self-restraint,

  • the bequest motive, how much they think about

  • their children, anticipatory utility--

  • people like to save because they like to think they'll be happy

  • in the future--

  • and so on, and so forth.

  • And it was a very complicated model of intertemporal choice

  • that people had been thinking about.

  • At some point, then Bohm-Bawerk, who

  • was an Austrian economist at some point

  • realized or proposed that the interest rate, in some sense,

  • is just a price.

  • So if you think about doing something or saving some money

  • from today until next year, it's really

  • just like choosing between apples and bananas.

  • When you choose between apples and bananas,

  • there's a relative price, which is the price of apples divided

  • by the price of bananas.

  • If you think about choices over time,

  • if you think about consuming $1 today versus $1 next year,

  • the interest rate or 1 plus the interest rate

  • is the relative price of that.

  • So for any dollar that I now consume,

  • I could get 1 plus r dollars in the future.

  • That's just the relative price of consumption

  • now versus in the future.

  • So you could think of--

  • the same way we think about apples and bananas

  • and optimizing between those, the same way we

  • can think about consumption in the present and the future,

  • which are just sort of like different goods over time.

  • And so Irving Fisher, then, came up and said,

  • let's just write down a two-good in difference diagram.

  • This is exactly the indifference diagram

  • that you've seen in like 1401 or other introductory Micro

  • classes.

  • Still, there were actually many psychological factors

  • discussed, like personal factors that determine

  • how much you save, and so on.

  • But it was progress towards that.

  • Now, what is the Fisher diagram?

  • The Fisher diagram looks something like this.

  • This is what you should be familiar with from,

  • again, 1401.

  • What do we see here?

  • What is this?

  • Yes.

  • STUDENT: I guess it traces between [INAUDIBLE]..

  • FRANK SCHILBACH: Right, exactly.

  • So we have here choices between two goods, call them good

  • a and good b.

  • There's a consumption. c a is consumption of good a,

  • c b is a consumption of good b.

  • We have a budget set, essentially,

  • which is determined here by how much your budget's constrained,

  • which is the triangle line that you see there.

  • The slope of that budget set is determined

  • by the relative price.

  • That's essentially the p a divided by p b.

  • And then we have what's called an "indifference curve," which

  • essentially is the curve that makes us indifferent

  • between combinations of two goods.

  • And we choose the point on the budget line

  • that's the furthest out, that gets us

  • in the furthest indifference curve.

  • So that's 1401 that you should be all familiar with.

  • In part, that's what was discussed

  • in recitation on Friday.

  • Now, Fisher then pointed out when

  • you think about choices over time,

  • in fact, that's exactly the same thing.

  • Think about it two periods, period one and period two.

  • We have, essentially, a budget line, again,

  • which is the budget set.

  • Again, that's what was discussed in recitation

  • on Thursday and Friday.

  • The difference here, of course, is then the price.

  • The relative price is determined by the interest rates.

  • So 1 plus r is now essentially the relative price, or 1 over 1

  • plus r, that determines essentially how much we

  • can maximally consume.

  • Again, the triangle that you see here

  • is the potential set that you consume.

  • And then again, you have a indifference curve

  • that tells us the sets of points that we

  • are indifferent between, good one and good two.

  • And we choose what's furthest out on the indifference curve.

  • So essentially, we can apply any tools

  • that we have from 1401 or any Micro class,

  • from choices between apples and bananas

  • to choices between period one and period two.

  • And so what we're sort of ignoring

  • here is then in period one and period two,

  • how are we going to spend the money?

  • So we think of c1 and c2 as consumption bundles.

  • Think about this like how much money

  • is spent on certain consumption goods in period one

  • versus period two, ignoring whether you buy apples

  • or bananas, just how much money do you want to spend in period

  • one, how much money do you want to spend in period two,

  • ignoring how exactly are you going to divide it,

  • assuming that you're going to get this right in terms

  • of choosing within the period what's best for you.

  • Any questions on that?

  • OK, so that gets us to the workhorse model

  • in economics, which is Samuelson's discounted utility

  • model.

  • Paul Samuelson is a very famous economist who

  • was at MIT for many, many years, one

  • of the founders, if you want, of modern economics,

  • and the MIT Economics Department as it is right now.

  • And what Samuelson proposed was a non-graphical version

  • of that, where he said, let's write down some math.

  • Let's write down the representation.

  • How should we think about utility maximization?

  • And what essentially he was proposing is to say at time t,

  • people maximize their discounted utility, which is just

  • the sum of discounted utility where there is a factor

  • delta, which determines how much we

  • care about the present versus the future.

  • So we have, essentially, these instantaneous utilities, u t,

  • u t plus 1, u t plus 2, and so on.

  • This is your utility at each point in time.

  • Think of time as being discrete.

  • In a sense, time could be years, time

  • could be days, and the like.

  • Think of them perhaps as years for now.

  • There's your t, your t plus 1, your t plus 2,

  • your t plus three, and so on.

  • u t summarizes, in some sense, how you feel in that year

  • overall in terms of utility.

  • That's your utility in that particular period.

  • It could also be daily.

  • It could be how you feel on a certain day,

  • could be hourly, and so on.

  • That's just a matter of definition.

  • And again, u t is a function of all activities that are going

  • on in that particular year.

  • That could be consumption, leisure, all the other things

  • that are going on.

  • That's sort of like in some sense,

  • we abstract away what happens within that particular time

  • period.

  • We're just summarizing all the things

  • you're doing in that year yield to a certain utility.

  • And now the question is, how do we aggregate these utilities?

  • How do we decide between different options

  • when the u t's differ across different options?

  • Now, what's coming in here, then,

  • is the discount factor delta, which you see above,

  • which essentially is telling you how much is util

  • or an amount of utility, a unit of utility,

  • worth in the future compared to the present.

  • And so what you see here is a very simple functional form

  • of doing that.

  • Everything that's in the future is discounted.

  • Usually, we think of delta being smaller than 1.

  • So delta could be something like 0.9, 0.8, or the like.

  • So if you're in period t, period t plus 1 is discounted by 0.9.

  • Period two would be then discounted

  • by 0.9 to the power of 2, and so on, and so forth.

  • And so delta is essentially a very simple way

  • of replacing a very complex psychology, how

  • we think about choices over time,

  • by saying let's just assume that people over time

  • have a constant way of discounting the future.

  • And it's taken on a simple mathematical form

  • of exponentially doing so.

  • Any questions on that?

  • Yes.

  • STUDENT: Why was Samuelson's model adopted so widely?

  • I mean, so it said in the reading

  • that it was very simple and very pretty, but he's very much--

  • it seemed like oversimplified a lot of the research that

  • had been done in the past.

  • Why were people so quick, I guess?

  • FRANK SCHILBACH: Yes.

  • STUDENT: Was it, like, the fashion

  • to have these [INAUDIBLE]?

  • FRANK SCHILBACH: Yeah, so I think

  • one has to think a little bit about where things are coming

  • from, in the sense that to start with,

  • nobody had formalized some of these choices

  • that people were making.

  • In some sense, Samuelson was, like, OK,

  • we have to assume something.

  • So let's assume exponential discounting.

  • That's a simple thing to do.

  • So let me just make that assumption as a first pass.

  • He actually never thought this is the right model,

  • or this is a normative model how people should behave,

  • or the like.

  • That was all coming later.

  • He was just proposing something that's tractable.

  • And for tractability, he was proposing that.

  • Now, it's important to understand

  • for a lot of behavioral economics,

  • a lot of neoclassical economics, the traditional economics,

  • simplicity is good.

  • So usually, we like to simplify a lot of choices.

  • And when things are simple, you can, in a tractable way,

  • analyze things in the world.

  • And for many problems in the world,

  • like for example, economic growth,

  • or like how the economy evolves as a whole,

  • and so on, some of these, the exponential discounting model

  • might actually be the right model in some ways.

  • Or if you think about how managers of firms,

  • or whatever, et cetera, behave, in some ways

  • that might be the right-- or the economy

  • as a whole-- that might be the right model overall.

  • So in some sense, the answer is kind of like, A,

  • some choices are actually explained reasonably well

  • with exponential discounting.

  • B, it was simple and easy to do, and you had to start somewhere.

  • And then C, I guess people tend to stick to traditional things.

  • So in some ways, once you have written down a model,

  • and people have written papers and invested their career

  • in it, they tend to defend that, where in fact, maybe that's not

  • the right thing to do, and become dogmatic about it.

  • But that's now changing.

  • And exactly as you say, there's problems with this model,

  • and we're going to talk about those right now.

  • Now let me tell you a little bit about some definitions,

  • just to be clear what we're talking about.

  • So one is, what's a "discount function,"

  • what's a "discount rate," and what's a "discount factor?"

  • So these are just definitions.

  • A discount function essentially is

  • when you have a stream of future utilities, u t, u t plus 1,

  • u t plus 2, and so on, and so forth, you

  • have to write down a function how

  • to weigh these in the future.

  • So d of tau, as I'm calling it, is essentially

  • giving you this discount function

  • that specifies essentially all the weights

  • that you're putting on future utilities and future periods.

  • That could be that functional form.

  • Could be anything.

  • That's just a very general definition.

  • Now, what's the discount rate?

  • It's essentially the rate of decline

  • of the discount function.

  • We call that rho and rho of tau, which essentially

  • is just the derivative with respect to time

  • divided by the discount function at that point in time.

  • And the negative of that, because we think usually as

  • positive as in the discount function tends to decline,

  • as in stuff that's further away in the future

  • you put less weight on than stuff that's closer to you

  • or closer to the present.

  • And so again, rho of tau specifies

  • the rate at which value a util declines with delay.

  • And then finally, what does exponential discounting do?

  • Exponential discounting specifies a specific functional

  • form of the discount function.

  • What does that mean?

  • Essentially, we just take the discount function, d of tau,

  • and what Samuelson was doing then was essentially

  • just proposing a specific functional form, saying,

  • OK, let's try that one.

  • That's a simple thing to do.

  • Why do you choose that one?

  • Well, it's delta to the power of tau.

  • The discount factor now is delta.

  • This is essentially when you think about two periods,

  • how much weight do you put on each of those periods.

  • Let me just go back for a second.

  • Here, when you think about going from u t to u t plus 1,

  • you just add an additional delta.

  • And going from u t plus 1 to u t plus 2, you add another delta,

  • and so on.

  • That gives you essentially the relative weights

  • between two adjacent periods.

  • Now crucially, as you see here in that functional form,

  • this is constant.

  • So every time you have a time period, you go to the future,

  • you add another delta.

  • And that's an assumption.

  • So that's a very convenient thing to do.

  • In part what it tells you, then, is also

  • that the discount rate is constant over time.

  • Again, so that you could do some math,

  • and calculate the discount rate, if you do that,

  • you'll find out that the discount

  • rate is minus log delta, which is approximately 1 minus delta.

  • That is to say, not only is the discount factor constant,

  • but also the discount rate is constant.

  • And that's an assumption, again, that's made by Samuelson.

  • So you can do that math.

  • We can also do some of that in recitation in case

  • you have questions.

  • Now let me give you an example on how

  • does that help us think about how

  • people make choices over time.

  • Student Amy considers writing a term paper today

  • so as to give herself a free evening in the future.

  • So this is essentially the idea that the student now, tonight,

  • has some stuff to do.

  • There's some opportunity costs right now.

  • An outside option-- she could watch TV,

  • she could meet her friends, or whatever,

  • or she could write her a paper right now.

  • The paper, if you write the paper right now,

  • it comes at a utility cost of minus 1,

  • costs 1 util because the other activities

  • would be more fun to do it.

  • She'd rather watch movies.

  • However, if, instead, she also has some other stuff

  • to do tonight, so she doesn't really

  • have a free evening if she doesn't write the paper,

  • but she just prefers not to write it right now.

  • Now, if she writes the paper right now,

  • she will get a free evening sometime

  • in the future in a few days from now.

  • And that would be a lot more fun.

  • She could go out.

  • She could do whatever other things she likes to do.

  • She could go to the symphony or whatever she likes doing.

  • The instantaneous benefit, the utility of getting a free unit,

  • is 4/3 utils, so it's higher than the cost right now.

  • But it's in the future, in some future evening.

  • Suppose Amy's daily discount factor is 0.9.

  • Now, what does she do?

  • How do we think about this now?

  • So the daily discount factor is 0.9.

  • Is she going to do it if the free evening is tomorrow?

  • Yes.

  • STUDENT: [INAUDIBLE].

  • FRANK SCHILBACH: And that's positive or negative?

  • It's positive.

  • Exactly.

  • But it's exactly right.

  • So you have to think about she gets the immediate costs right

  • now, which is minus 1, the benefits of 4/3 on the future.

  • Since her daily discount factor is 0.9,

  • she's going to discount that by 0.9.

  • That's still larger than 1.

  • So she decides to do that.

  • That's how she weighs, essentially,

  • the present and the future.

  • Now, in two periods, she does the exact same thing.

  • But two periods are now further away in the future.

  • So she discounts it by delta to the power of 2.

  • And that gives her, again, something

  • that's larger than 0, if I got the math right.

  • So still she's willing to do it, if the free night

  • comes two nights from now.

  • If it's in three periods, however, turns out

  • then minus 1 plus delta to the power of 3 times 4/3

  • is, in fact, smaller than 0.

  • So she will not do it.

  • So essentially, when she thinks about costs and benefits,

  • it depends a lot on how far away are the benefits in the future.

  • The further they're away in the future, the more they get

  • discounted, and the less likely she's

  • doing something that will cost her utility now and yield

  • benefits in the future.

  • Now, of course that's highly stylized.

  • Yeah.

  • STUDENT: [INAUDIBLE]

  • FRANK SCHILBACH: Correct.

  • Correct.

  • So what I'm assuming here, I was not

  • saying, when is the best time of doing that.

  • What I was assuming is choice between today

  • versus in a few days from now.

  • There was no option of saying today, actually,

  • I'd rather do it tomorrow.

  • We'll get to that.

  • I was just giving you an example of a very simple choice

  • between today versus sometime in the future, and then

  • another choice between today versus tomorrow, today

  • versus in two days from now, today

  • versus three days from now, assuming that other days are

  • not an option for now.

  • We'll get to-- so procrastination,

  • you need several days.

  • We'll get to that later.

  • So again, the bottom line-- one second-- the bottom line

  • is she will do it if the nice evening comes the next period

  • or in two periods, but not if it comes later.

  • Yeah.

  • STUDENT: Doesn't in all the periods

  • she gets more utility if she rather gets a free day today

  • and she switches the options, so she can [INAUDIBLE]??

  • FRANK SCHILBACH: Yes.

  • Yeah, so what I'm assuming here-- and this is, again,

  • an assumption-- is that the free night cannot--

  • so I was saying a little bit, but perhaps not clearly--

  • she has something to do tonight anyway,

  • so she can't really have a free night.

  • Maybe she needs to call her friends and so on.

  • So that option is not available right now.

  • You're exactly right.

  • If the free night came tonight, she would do that, and then

  • do the stuff later, because she prefers

  • the present over the future.

  • But I was assuming that away for simplicity.

  • But in general, as it happens, many choices

  • are often in the form of either current costs

  • and future benefits, and then you'd

  • rather defer those things.

  • You only do that, essentially, if the benefits

  • are sufficiently high.

  • Other options are current benefits and future costs,

  • and then the entire thing is essentially flipped.

  • So now, the next question, then, you

  • might have is to say, well, how do we actually estimate delta?

  • So we see people doing choices, but in some sense

  • in the real world, we actually don't

  • know what somebody's delta is.

  • So how can we actually estimate people's delta over all?

  • Let's stick with the stylized example.

  • What do we need to estimate delta in this specific example?

  • Well, you would need several choices over time,

  • and then essentially, you need to know

  • what the costs and benefits of those choices are.

  • And if you knew that, then you could

  • learn about what delta is.

  • Let me just write this down for you.

  • Suppose we didn't know Amy's delta,

  • but we knew that u tau's for all periods

  • for the different options that she has.

  • So how could we estimate this from the above data?

  • So we learned, essentially, over here,

  • suppose we see this behavior overall.

  • What we get is several inequalities involving delta

  • and involving u t's or u tau's that people choose

  • in different points in time.

  • So once we have these inequalities,

  • then we can essentially just estimate what is delta.

  • We just back out what delta is from these choices.

  • So what do we do?

  • Well, we can just essentially do the math.

  • It's very simple.

  • And what we'll find is, for example, if you

  • see that the behavior that we just saw,

  • which was essentially that she does it

  • when the free night comes one day from now

  • or two days from now, that gives us two inequalities,

  • the first two inequalities that are written down,

  • which is essentially delta must be larger than 3/4,

  • delta must be larger than 3/4 to the power of 1/2,

  • which is about 0.87.

  • And then we have a third choice, where she doesn't do it

  • if the free night comes three nights from now, which gives us

  • another inequality, which tells us

  • delta must be lower than 0.91.

  • So if you saw those choices, but if you

  • knew the utility of a person, you could then

  • back out what delta is.

  • And delta in this case would be between 0.87 and 0.91.

  • Does this make sense or any questions about that?

  • So all I was doing here is to say,

  • suppose we didn't know delta, but we just

  • saw the Amy's choices.

  • What can we learn about her delta

  • if we knew what the utilities are at each point in time?

  • And if you do that, from this behavior

  • we get these inequalities.

  • And we can then back out what the delta is.

  • Now in reality, we actually don't

  • know what the u tau's are.

  • We don't know what utility is for different options

  • from people.

  • So if you see people's behavior, we can't actually

  • estimate the delta from that.

  • So what could we do instead, or what kinds of choices

  • can we make or can we elicit?

  • Yes.

  • STUDENT: If you can do it with money,

  • there are different options.

  • You have a chance to win [INAUDIBLE]..

  • FRANK SCHILBACH: Right.

  • And what additional assumptions do we need for that?

  • So that's exactly right.

  • That's exactly what people have done a lot.

  • So this is Rick Thaler again, a Nobel Prize winner

  • who has done exactly that in 1981,

  • getting people to start with hypothetical monetary choices.

  • So say suppose-- this is kind of what

  • I was asking you at the beginning in the first class.

  • I was asking you different numbers,

  • but what x makes you indifferent between $15 today

  • and x dollars in a month, a year, and 10 years from now?

  • What do we need to assume for that now?

  • Or what other assumptions do we need?

  • How do we go from money to your utility?

  • STUDENT: There's an old study [INAUDIBLE]..

  • FRANK SCHILBACH: Exactly.

  • I need to assume something that's quite important.

  • I need to assume utility is linear in money,

  • either to say I'm just looking at that specific problem,

  • u of X equals X. Or slightly more complicated,

  • but in principle the same, marginal utility

  • is constant over time.

  • And that's sort of related.

  • For our purposes, what we're going

  • to assume for now is just to say your utility

  • is linear in money.

  • You have X equals X.

  • And then what you can do is if I give you an amount Y--

  • Y is $15-- and then I ask you what

  • makes you indifferent between X dollars in, say,

  • a month or a year from now?

  • I'm just going to write down an equation, which essentially

  • is to say u of Y, which is the utility of getting

  • the $15 right now--

  • is you're indifferent between that because you just told me

  • so, and u of X, which X is the amount that you just told me.

  • And now I need to discount that by delta

  • to the power of t, which is because it's in the future,

  • you need to discount that.

  • Once I know that, I know essentially everything

  • on the left-hand side and the right-hand side of the equation

  • except for the delta.

  • I can just back out delta from that.

  • So what we're going to do is we're going to just use, then,

  • the linearity assumption of the utility

  • is linear in money, which is like u of Y equals Y,

  • and u of X equals X.

  • We take logs on both sides and rearrange,

  • and then get rho, which is, again, the discount rate,

  • equals minus log delta.

  • And that's log of X divided by Y and divided

  • by t, which is the time period that I'm asking you about.

  • That's a simple algebra and rearranging things.

  • We talked about a little bit in recitation

  • and in the problem set as well.

  • But is it clear what we're doing here?

  • Are there any questions about that?

  • So just to summarize what I'm doing here,

  • I'm just asking you between different choices over time.

  • I'm assuming a utility function of money.

  • So I'm imposing on you in some way--

  • and it might be a good or a bad assumption--

  • but I'm essentially assuming how you value money

  • at different points in time.

  • And with that assumption, then, I

  • can back out from your choices over time

  • how much you discounting utility in the future.

  • And then the rest is just rearranging and doing

  • some math.

  • So now, how do you do that?

  • Here's an example of how to do that, then, for Y equals 15

  • and X equals 20.

  • So if you told me that what makes

  • you indifferent between $15 now and X in a month,

  • if you told me $20, I can just write down the equation,

  • and I get essentially a delta of 0.003.

  • The reason being that if you are indifferent

  • between $15 and $20 right now, you're

  • discounting, essentially, anything

  • that's in the future by 3/4.

  • Essentially $20 in a month from now or 3/4 as much--

  • or the money in the future is 3/4 as much worth for you

  • than the money right now.

  • That's the 20 versus 15 in a month from now.

  • And then I have to do this every month.

  • So every month, it's 3/4 to the power of 12

  • will give you something like 0.03 as delta.

  • So I'm just calculating the yearly discount factor

  • using your monthly choice.

  • Yeah.

  • STUDENT: [INAUDIBLE].

  • FRANK SCHILBACH: Right.

  • So usually, what people do is yearly discount factors.

  • So usually the delta is yearly.

  • That's just a convention.

  • You could also do it monthly, or daily, or whatever.

  • So what I'm doing is yearly discount factors,

  • partially because I want to make them comparable across choices.

  • But you could similarly also just do

  • the monthly one, or whatever.

  • And a lot of economic analyses, yearly is the frequency.

  • When it comes to your problem set questions,

  • it's going to be daily, because students

  • tend to think in days, not necessarily in years.

  • STUDENT: [INAUDIBLE].

  • FRANK SCHILBACH: Right.

  • So in some sense, this is what we're getting here

  • in some ways in saying--

  • here I'm asking you about--

  • so you see the choice here, and these are actually real choices

  • that people have made.

  • When I ask you now between Y dollars, $15, right now

  • and X dollars in 10 years from now,

  • people tend to give different answers.

  • And one constant finding there is

  • that people tend to be more patient when

  • it comes to longer run choices compared to shorter run

  • choices.

  • I'm calculating the same discount factor.

  • And what I just told you earlier is in the exponential

  • discounting model, the discount factor delta

  • should be constant over time.

  • Should be the same whether you decide

  • between today and tomorrow, between a year from now

  • and a year and a day from now, or between any time

  • in the future.

  • But what we find or tend to find in these kinds of choices

  • is that people's discount factor is

  • a lot higher in the future compared to in the present.

  • I'll get back to that.

  • So actually, your question is exactly on point.

  • When eliciting choices between different days versus months

  • versus years, you get a lot different answers

  • depending on what you ask.

  • OK.

  • So now, we can say-- and this is exactly what you're asking--

  • let's see.

  • When you do this in different settings, what kinds of answers

  • do you actually get.

  • And what you see here is here's people's choices of delta

  • and different types of experiments people have done.

  • This is different years of publication.

  • But overall, what do you see is essentially,

  • these estimates are all over the place.

  • So you think we know what delta is.

  • We think it's 0.9, or 0.8, or 0.95, or whatever.

  • But in fact, when you look at people's choices

  • in different types of experiments,

  • these choices tend to be all over the place.

  • So that's not a good sign for a model,

  • because you're trying to identify a parameter that

  • fits many settings.

  • Well, here, it seems to be that these choices are essentially

  • all over the place, which tells you already maybe something is

  • wrong in this model that we should try to fix.

  • Now, one thing I already said here

  • is to say, when you look at short-run

  • versus long-run choices, we tend to find that people are really

  • impatient in the short run.

  • However, people are patient in the long run.

  • There's lots to learn from this experiment in various ways,

  • in part about strategies to overcome self-control problems.

  • For example, a lot of kids are trying

  • to manage their attention, are looking at,

  • and looking away, and so on.

  • But mostly, I think the key part you

  • learn is how painful it can be to resist.

  • In the short run, there's lots of essentially

  • short-run discounting or essentially

  • short-run impatience that we see in the world.

  • And if you think about it, often it's very hard in the short run

  • to resist.

  • Often when you think about in the future,

  • it's much easier to do so.

  • When you think about choices that you

  • might face in your life--

  • be it marshmallows or something else--

  • would you rather have one marshmallow right now versus

  • two marshmallows in an hour, you might say,

  • well, maybe one marshmallow looks actually pretty good.

  • Let's just take that one marshmallow right now.

  • And a lot of these kids, I guess, opted for doing so.

  • When I ask you instead, would you

  • like to have a marshmallow in a week from now

  • versus two marshmallows in a week from now and an hour,

  • it almost becomes ridiculous.

  • Of course you're going to take two marshmallows

  • in a week and an hour from now.

  • What does it matter in terms of when exactly you

  • get the marshmallow?

  • When I ask you the same questions about one marshmallow

  • in a year from now versus two marshmallows in a year

  • and an hour from now, it becomes very obvious that of course, I

  • want the two marshmallows-- unless you

  • think in a year from now, you might be on a diet.

  • But the exponential discounting model

  • has precisely that assumption.

  • The assumption is that how much you discount

  • an hour in this case does not vary depending

  • on whether it's right now, whether it's

  • in a week from now, versus whether it's

  • in a year from now.

  • And the short-run discounting essentially

  • tends to violate that assumption,

  • in part because it leads to pretty absurd implications,

  • as I'm going to show you in a bit.

  • So what other evidence in the world

  • do we have about short-run impatience,

  • other than the marshmallows?

  • Yes.

  • STUDENT: [INAUDIBLE] get concentrated.

  • FRANK SCHILBACH: Right.

  • There's lots of-- I think among you guys,

  • not that many people smoke, but lots of smokers would say,

  • oh, I'd love to stop smoking in the future.

  • I really want to quit.

  • But then they find it very hard to do right now.

  • And maybe next time in the future,

  • I will quit, and so on, and so forth.

  • Lots of people try, and then fail, and so on.

  • And in part, it's like the short-run impatience

  • or short-run difficulty to do that

  • compared to maybe the long-run desires of wanting to do so.

  • We'll get back to smoking, actually,

  • at some point in the future.

  • But that's exactly a great example of that.

  • That's also true for other drugs, other addictions,

  • and so on.

  • Actually, some of the social media,

  • or computers, or phones, or whatever,

  • you can also think of like that being sort

  • of addictive in a sense.

  • In the short run, it's very hard to get away from that.

  • But in the very long run, it would be nice thing to do.

  • Often, then, there's short-run impatience involved.

  • Yeah.

  • STUDENT: Taking a break now versus [INAUDIBLE]..

  • FRANK SCHILBACH: Yeah, so a break now always

  • seems like a great idea.

  • And then in the future, you're going

  • to work really hard and so on.

  • And then the future comes, and again,

  • taking a break right now seems really appealing.

  • Yeah.

  • STUDENT: Aggressive driving.

  • FRANK SCHILBACH: Oh, that's interesting.

  • Can you say more?

  • STUDENT: In the short run, you're impatient.

  • You're concerned about your [INAUDIBLE]

  • so you might try to get to the destination faster.

  • Or just in general, people try to get to the destination as

  • fast as possible [INAUDIBLE].

  • FRANK SCHILBACH: Right.

  • So of course, there's also other factors involved,

  • including risk and the like.

  • You might think-- you underestimate how risky it is,

  • and you might think, oh, I might be overconfident,

  • that you're never going to have an accident.

  • But exactly as you say, in the short run, essentially

  • there's some short-run benefits, which is

  • like I could be there faster.

  • It's kind of annoying to drive, and so on, and so forth.

  • The costs are in the future in some sense, so uncertain.

  • You might crash and so on, and you

  • might be impatient in the very short run.

  • That's right.

  • But I think that's a little tricky as an example

  • because there's all these other factors.

  • I do think, however, that short-run impatience is

  • involved in that as well.

  • Yes.

  • STUDENT: I think credit cards are also a good example.

  • Like, you can buy this now with a credit card instead

  • of saving to buy the thing.

  • FRANK SCHILBACH: Yes.

  • So a lot of essentially choices of money over time,

  • you can see the choices that I was asking you guys in class.

  • That essentially shows some short-run impatience as well.

  • There's perhaps even more salient payday loans

  • that you might be familiar with.

  • So payday loans are essentially a very interesting phenomenon,

  • where essentially, there are workers

  • who get their paycheck by the end of the month

  • or the beginning of the month, but then

  • on the 20th of the month or sometime earlier, they

  • would like to have some money earlier than that.

  • So you can essentially just say, give me

  • some money at a very high interest rate,

  • and once my payday comes, I'm going to pay you back.

  • The interest rates are usually enormous.

  • Usually it's something like up to 5,000 annualized compound

  • interest, which is insane.

  • These are huge interest rates.

  • It's also an enormous industry in the US.

  • It's more stores than McDonalds and Starbucks combined,

  • which I'm not sure how many stores there are,

  • but I think there's lots of them.

  • And people pay huge interest rates,

  • and it's a huge industry of doing that.

  • What's kind of funny about payday loans, in some ways,

  • is actually in some ways, it's an odd thing of the world--

  • that's sort of an aside--

  • as in workers have worked already for 20 days.

  • In some sense, the employer owes them money.

  • But instead, they're essentially taking loans

  • from a salary that's actually, in some sense,

  • theirs already anyway in various ways.

  • But that's just an aside.

  • So that's a huge industry.

  • You were saying something similar,

  • which is credit card debt.

  • Usually there, the annual interest rate

  • is lower than that.

  • It's something like 20% in many cases, sometimes also higher.

  • There's lots of credit card debt in the US.

  • And you can think of this as like essentially

  • signs of short-run impatience.

  • What you see is people wanting to spend money now

  • on various things.

  • And they get the gains of doing that.

  • The cost of that comes sometime in the future when you actually

  • have to pay it back.

  • Finally, there's also some evidence of payday effects.

  • These are often involved in things like people,

  • for example, who get food stamps or any other monthly

  • or other cash transfers-- that people

  • get either food stamps or money at some point

  • conditional/unconditional cash transfers

  • at the beginning of the month.

  • And then usually, there's these cycles in consumption

  • or also expenditures, where at the beginning of the month,

  • people live large and have lots of money.

  • Same is also true for graduate students on their stipends.

  • The first weeks or months after getting your paychecks

  • often is really great.

  • And then it sort of declines over the course of that cycle.

  • The same is also true, by the way,

  • for farmers and harvest cycles in India and other places.

  • And then usually towards the end of the cycle,

  • people either are hungry, or have low caloric intake,

  • or are just not very happy.

  • That's a very common phenomenon.

  • And at the heart of that, there is some short-run impatience,

  • in the sense of at the beginning of the month,

  • you're really impatient, want to consume

  • some stuff, and discount what's in the end of the cycle, what's

  • further away, where the costs are coming, then,

  • in terms of not having enough resources or money

  • available anymore.

  • Here's some examples of payday loans.

  • I was wondering what this woman--

  • this is from wonga.com.

  • Apparently, they are advertising with grandmothers,

  • because you wonder what this woman is doing there.

  • But what you see here on the right-hand side is essentially,

  • the interest rates are something in the 1,000%.

  • These are the annualized interest rates.

  • These are enormous interest rates.

  • Usually people take many loans of that.

  • They also take repeated loans.

  • So it's not just as an emergency where people take a loan,

  • but people tend to roll over these loans over and over

  • again, and actually pay lots and lots of money

  • to these companies.

  • There's often very high credit card APRs,

  • which 20%, 25%, and so on are very common.

  • Again, lots of people have lots of credit card debt.

  • And often, it's again, not just to deal with shocks.

  • You might say, well, if you have a health

  • shock or some other shock in the family,

  • if people get perhaps unemployed for a short period of time,

  • maybe that makes sense to deal with that shock.

  • But often, people tend to roll over

  • this interest for many, many cycles,

  • and keep paying these really high interest rates.

  • Now, in some sense, that's just empirical evidence.

  • That's just a fact that these things exist.

  • However, when you think that through,

  • you get very absurd implications of this short-run impatience.

  • So what I showed you now is several pieces of evidence

  • of short-run impatience.

  • Now taking the exponential discounting model

  • very seriously, we're going to think about some

  • of these implications of what does

  • the exponential discounting model say and imply from that.

  • And one way to think about this is the money

  • now versus later choices.

  • As I told you before, when you look at number one here,

  • I was asking you about what makes

  • you indifferent between $100 now and $X in two weeks.

  • And the median student was saying something $120, $115.

  • And you can think about what does that imply

  • for the yearly delta.

  • Well, it implies for the yearly delta that it's about 5/6.

  • So you're indifferent between $100

  • now versus $120 in the future.

  • So that must mean the future is 5/6 as much worth

  • as the present is for you right now.

  • Now, that's fine.

  • Excuse me, that was the two weeks

  • that was I was asking you about, $100 now versus X

  • dollars in 2 weeks from now.

  • So the two-week delta is 5/6.

  • Now you can think about what does that

  • mean for your four-week delta.

  • Well, it's 5/6 to the power of 2.

  • So that's essentially you're indifferent between $100 now

  • and $144 in four weeks from now.

  • You're also indifferent between $100 now

  • and $11,400 in a year from now.

  • And you're also indifferent between $100 now

  • and I don't even know what that number is,

  • but a very, very large number.

  • So if you think the discount factor is delta,

  • and you just roll that forward, you

  • get essentially absurd implications,

  • the reason being that we assume the discount factor

  • is constant.

  • And so that, then, essentially, if you

  • are reasonably impatient between the present and any time

  • in the near future, like two or four weeks from now,

  • that must imply that you really, really

  • don't care about what's happening in five

  • years from now, and so on.

  • Now, that's completely unrealistic.

  • The discount factor for two-week delays in the future

  • must be, in some ways, higher than the discount

  • factor for two-week delays in the present.

  • And that's essentially what the quasi-hyperbolic, or the model

  • I'm going to propose to you in the next class,

  • is going to try and explain.

  • So why is that unrealistic?

  • Well, we know for many situations in the world,

  • people care a lot about the future.

  • People save for retirement.

  • People invest in education.

  • People exercise, often.

  • People do problem sets.

  • People brush their teeth.

  • People eat healthy, and so on.

  • People invest a lot in the future,

  • in stuff that happens four or five, six, seven, 10

  • years from now.

  • So they care a lot about the future in some ways.

  • Yet we find the short-run impatience.

  • So now we need to find some model that can bridge this gap.

  • And so another way to put this is

  • when you look at the evidence that we have in terms

  • of my time horizon, when you look at discount

  • factors conducted in studies such as the one

  • that I just showed you, or using real-world decisions, what you

  • see usually is that the discount factor in the very short run

  • tends to be very small.

  • This is what you see on the left-hand side of the graph.

  • When you look at further in the future,

  • the discount factor tends to be higher.

  • Or another way to put this is the estimated delta increases

  • by time horizon.

  • Again, that's a violation of the exponential discounting model.

  • So that's the first piece of evidence.

  • The second one is preference reversal,

  • dynamic inconsistency.

  • What I mean by that is dynamic consistency

  • is essentially the property that when

  • you make a choice for the future between two future periods,

  • and when the future then comes absent new information

  • or any other things that have happened,

  • you will stick to that choice.

  • A formal decision or a definition

  • here is, the action a person thinks

  • she should take in the future always

  • coincides with the action that she actually prefers

  • to take once the time comes.

  • So if I make a plan to exercise tomorrow,

  • or if I make a plan to eat salad tomorrow,

  • I'm going to actually do that.

  • I'm not going to be, actually watching movies

  • seems like a good idea, or the potato chips instead

  • look better.

  • I have perfect foresight in what I'm

  • going to plan for the future.

  • I know my future preferences.

  • And my future preferences for what I want for the future

  • coincide with what I actually want in the future, as well.

  • And so put differently, there's no intrapersonal conflicts.

  • That is to say what I want for the future is also

  • what my future self wants for itself.

  • And so that's closely connected to the assumption

  • of exponential discounting-- that is to say exponential

  • discounting has the assumption that how much I care between

  • the present and the future is always--

  • the weight is always determined by delta,

  • and that delta doesn't change over time.

  • So when I think now about what I want

  • in the future, between a year from now

  • and two years from now, the difference

  • between those or the discounting will always be delta.

  • Once the future comes, the difference

  • between a year from then and--

  • at the time, then, it will be like the present

  • and a year from now-- will also be delta.

  • So there's no difference there.

  • So what's the formal argument of the exponential discounting

  • model?

  • Well, it is essentially if at time 0,

  • I prefer an action A over an action B,

  • suppose there's different actions.

  • There's action A and action B that I

  • can do starting in period one.

  • Well, if I prefer action A over action B, on the left-hand side

  • there's the utilities associated with that.

  • There's u0 plus delta times u1 A of action

  • A plus delta squared of u2 of action A, and so on.

  • If I prefer that over action B, well, it

  • must be that I prefer the stream of utility

  • on the left-hand side to the stream of utility

  • on the right-hand side.

  • But now that implies if I take away the u0, because they're

  • the same on both sides, because I'm

  • making choices for the future, and then divide by delta, what

  • I get is essentially, again, an equality that at time 1, again,

  • I still prefer option A over option B. That is to say,

  • if I prefer option A over option B

  • at time 0, that implies essentially

  • that I also prefer option A over option B at time 1.

  • So that essentially is another way to say it,

  • is that the exponential discounting factor

  • implies time and consistency.

  • Any questions about that?

  • So what examples do we have that violate this property?

  • We already talked about this a bit in the previous classes,

  • but just remind ourselves.

  • Yes.

  • STUDENT: The betting on how much weight

  • you lose when you're on a diet.

  • You make sure that you'll want to change your behavior.

  • FRANK SCHILBACH: Exactly.

  • So dieting in general seems a great example of saying,

  • I really would like to lose some weight,

  • or have some target weight, or some target

  • exercising, or a certain behavior of eating

  • and exercising or combined.

  • And I really would like to do that.

  • For now-- I mean, I think about the future.

  • Often at New Year's or certain points

  • of the year, our birthdays and so on,

  • people think, OK, I'm going to do this.

  • I have great plans and so on.

  • They have certain preferences for the future.

  • But then the future comes a week or a month from then.

  • People don't follow through.

  • Exactly.

  • That's essentially a clear example

  • of a preference reversal, which is essentially

  • another way of saying preferences

  • are dynamically inconsistent.

  • Any other example?

  • Yes.

  • STUDENT: [INAUDIBLE] say we should

  • do something, kind of like this is, like,

  • what we want our future to be.

  • [INAUDIBLE]

  • FRANK SCHILBACH: Exactly.

  • So that's true for, did you say exercising?

  • STUDENT: Yeah.

  • FRANK SCHILBACH: Yeah, for exercising, exactly.

  • I'll show you some examples of people, for example, signing up

  • for gyms that pay yearly membership fees,

  • and so on, that tend to be very expensive.

  • The idea often is then they think

  • about they will go to the gym weekly, or daily, or whatever.

  • And then under that assumption for your preferences

  • for the future, then it makes a lot of sense.

  • But then if you then not actually go,

  • or if your preferences are different,

  • then it turns out to be different in the future, that's

  • a pretty bad idea.

  • Yes, you were saying.

  • STUDENT: So consider apples or bananas.

  • If I'm choosing [INAUDIBLE].

  • FRANK SCHILBACH: Yeah, to be clear,

  • if you just start eating apples because you

  • had too many bananas in the past, that's

  • not what we were talking about.

  • So it's not about people's past choices

  • affecting future choices through some form of habit formation,

  • or people getting bored, or tired, or the like.

  • But it's about if I today choose today I want bananas,

  • tomorrow I want apples, and then tomorrow I'm actually saying,

  • actually, I don't like apples, I really like bananas,

  • then that would be a violation.

  • But it needs to be something that's essentially

  • either new information or some new options or so on that

  • become available.

  • In the example that you're mentioning,

  • there was none of that.

  • So that's not quite what we're talking about.

  • More common is-- and there's a paper that does this, in fact,

  • with Dutch employees by Read and van Leeuwen that essentially

  • asked people about next week first.

  • So it asked them about-- this is actually

  • an actual company, where workers were asked, after lunch,

  • would you like to have a snack?

  • And what snack would you like to have?

  • Would you like to have apples or chocolate?

  • When you're asked to do that today for next week,

  • 74% chose fruit or apples, essentially.

  • So lots of people tend to want to be virtuous in the future,

  • eat healthily, and so on.

  • When you ask them then the same question--

  • so then in the actual experiment, what

  • they did is then they went back to the workers, and said,

  • oh, I forgot your choice.

  • Why don't you choose again.

  • Let us know.

  • That was a little bit cheating, but then essentially,

  • 70% of people, when it comes for the same day, choose chocolate.

  • And here's none of that, in the sense

  • of there's no habit formation, there's

  • no people ate too many apples and now they

  • really want chocolate.

  • That was only one choice.

  • And so now, when I make some choices

  • for the future and the future comes,

  • I should stick to that choice.

  • Similarly, there's movie choices.

  • It used to be--

  • you guys are probably too young for this--

  • Netflix used to send you movies to your home.

  • But often what lots of people had was this issue--

  • they had great plans of watching highbrow, or high culture,

  • and often sad or deep movies in the future.

  • There's really things they wanted

  • to watch, be it The Piano or Schindler's List

  • and so on, which by some category

  • we might call highbrow.

  • But instead, when the present comes,

  • people often like to watch essentially lowbrow movies

  • like comedies, and so on and so forth,

  • for example, Four Weddings and a Funeral, Speed, and so on,

  • so action movies or the like.

  • And then what would happen in Netflix

  • often is you would get all these movies that you'd really

  • love to watch in the future, but never in the present,

  • then get stuck with them.

  • And there's, in fact, an example or a paper

  • who does this, which essentially elicits people's preferences

  • for what they would like to watch in the present

  • versus in the future.

  • And what you see, essentially, is

  • people tend to systematically pick

  • for the present, for tonight, people

  • tend to watch or want to watch lowbrow movies.

  • Action, rom com, or whatever sounds really good for tonight.

  • When you think about what would you like to watch next week,

  • people tend to pick highbrow movies instead.

  • And there's lots of examples of that kind.

  • And so just to summarize, these preference reversals,

  • again, these are not really possible in the exponential

  • discounting model.

  • That should not occur.

  • That's by assumption not possible in that model,

  • as I just showed you before, yet we see plenty

  • of examples in the real world.

  • Now, the third piece of evidence is demand for commitment.

  • That's really closely related to that.

  • So one example here is demand for commitment

  • is essentially when you know that your future preferences

  • will be different from your present preferences,

  • you might engage in commitment devices.

  • What does that mean?

  • You might want to change the prices of your options

  • in the future.

  • And particularly, you might want to take away

  • some options in the future.

  • One example is Ulysses and the Sirens.

  • Who knows that story or can tell me what it is?

  • Yes.

  • STUDENT: So basically, there are these Sirens,

  • and they're singing and [INAUDIBLE]..

  • But [INAUDIBLE] but it's hard to tear yourself from [INAUDIBLE]..

  • So he had [INAUDIBLE] tied to the ship

  • so that he wouldn't be able to.

  • FRANK SCHILBACH: Yes, exactly.

  • So here's Ulysses.

  • I think he was on his way back from his long journey.

  • He knew that the Sirens were going to come.

  • He knew that his preferences would change in the future--

  • that he would not be able to resist

  • their power or their songs.

  • And so what he did is he asked his crew

  • to bind him to the mast so he would not

  • be able to leave the ship, even if he wanted to in the future.

  • And that's demand for commitment because he was taking away

  • some options in the future, with a goal

  • to change his future behavior, knowing that his preferences

  • would change in the future.

  • If you wonder why the guys who are rowing

  • are not leaving the ship.

  • They had wax in their ears.

  • I don't know why Ulysses couldn't use the wax either,

  • but anyway--

  • So that's one example of a commitment device.

  • There's another one, which is sort of financial advice

  • that people often get, which is the following--

  • cut up your credit card and store the cards.

  • If possible, get rid of all your credit cards

  • or put temptation out of reach.

  • If you really can't do without a credit card,

  • limit yourself to one.

  • Put it in a tub of water, and stick it in the freezer.

  • And so the idea here is if you really

  • have self-control problems, well,

  • when you want to buy something really quickly,

  • when temptation sort of takes over,

  • you have to limit your options in some ways.

  • So in some sense, have you some cool down period.

  • It takes a while to get your credit card out of the freezer.

  • I don't know.

  • I asked my wife about is this a thing?

  • And she was saying, well, haven't you watched

  • "Confessions of a Shopaholic?"

  • I have not.

  • If you want to watch that video, you

  • see, in fact, apparently that is, in fact, a thing.

  • But the idea of having some cool down period,

  • which essentially is to deal with essentially

  • short-run impatience, comes in many settings

  • and many variations.

  • In fact, for example, if you'd like to get married,

  • often you have to go to some office

  • and declare that you would like to get married, and then

  • wait for another three days or something

  • until you actually get married.

  • Often, the idea is people sometimes come to their senses

  • and it takes a few days.

  • So what do these examples show?

  • Well, they show that people have a tendency

  • for immediate gratification.

  • And they tend to discount quite heavily

  • in short-term decisions.

  • Now, what does the demand for commitment then show?

  • It's we, in fact, tend to disapprove of this tendency

  • beforehand.

  • That is to say we know that in the future,

  • we might be impatient.

  • We don't like that.

  • And because of that, we bind ourselves to the mast,

  • or we freeze our credit cards, or some people, at least, do.

  • And so all of these decision makers

  • are time inconsistent in the sense

  • that when they make certain choices for the future, what

  • they will want to choose in the future will be different.

  • And knowing that, they will restrict their options.

  • That is to say, different selves want different things.

  • So then what's the heart of the issue?

  • Well, the heart of the issue is that there

  • are conflicts rooted between short and long-run patience.

  • What we want in the short run is different from what

  • we want in the long run.

  • That is to say when we think ahead of the future,

  • we tend to be very patient.

  • There's all sorts of good things we want to do in the future.

  • When the time actually comes, when

  • we think about the present, we tend to be impatient.

  • Now the issue with exponential discounting,

  • then, is the exponential discounting model

  • has only one parameter which captures

  • essentially discounting.

  • But it can sort of--

  • by assumption, the discounting needs

  • to be the same across all time horizons.

  • That is to say, it can only match one of those two things,

  • but not both.

  • It can only match either your short-run discounting, but then

  • the long-run discounting is off, or you

  • can try to match the long-run discounting,

  • but then the short-run discounting is off.

  • So what that tells us, we need two parameters

  • to deal with that.

  • So what we want, and I'll talk about this

  • a lot more in the next class or in the next few minutes.

  • And then in the next class, we want a model

  • that has greater patience for trade-offs in the future

  • than for trade-offs in the present.

  • And then we want another model.

  • So one is we want different levels of patience

  • over different time horizons, and we

  • want a model that explains or helps us

  • explain dynamic inconsistency.

  • So what is that model?

  • So I just showed you before the exponential discounting model.

  • That's just what I showed you before,

  • but that's exactly the same, where essentially,

  • your discounted or lifetime utility is essentially

  • what's given here, where we have delta.

  • It's between 0 and 1.

  • And delta is a short-term discount factor

  • and it's a long-run discount factor.

  • If I'm trying to decide between t and t plus 1,

  • the difference between that is essentially delta.

  • And if I decide between t plus 3 and t plus 4,

  • it's also delta that regulates this factor.

  • Now, what does the quasi-hyperbolic discounting

  • model do?

  • It has another parameter.

  • And this parameter is called beta.

  • And beta governs, essentially, short-run discounting,

  • while delta is the long-run discount factor.

  • What is that telling us?

  • Essentially, beta discounts anything that's in the future.

  • So essentially, if you look at the equation now,

  • anything that's in the future, that's not period t,

  • is discounted by beta.

  • And then within any future periods,

  • we have another discount factor that's essentially

  • the long-run discount factor.

  • That's delta.

  • Now, why does that help us?

  • It helps us because now we can essentially

  • separate short-run and long-run discounting.

  • You can say short-run discounting is governed by beta

  • and long-run discounting is governed by delta.

  • And now we can match a lot of facts

  • that we couldn't match earlier.

  • Any questions on that?

  • Yeah.

  • STUDENT: Yeah, I was wondering if the evidence [INAUDIBLE]

  • was comparable to this.

  • Because if you have a beta that really discounts

  • any future consumption, would the commitment device

  • [INAUDIBLE].

  • Because many [INAUDIBLE].

  • FRANK SCHILBACH: So you're asking two separate questions

  • here.

  • So one question is, can we explain,

  • in theory, commitment devices?

  • Can we explain essentially-- can we write down

  • a theory that says you should be at least

  • under some assumptions, under some parameters,

  • willing to engage in commitment devices

  • to demand for commitment?

  • The answer is yes, depending a little bit on your naivete

  • and sophistication, which we're going to get to.

  • But so you in principle, at least,

  • can in theory write down a version of this model that

  • predicts demand for commitment.

  • You're asking a separate question,

  • which is are these commitment devices actually going to help?

  • So A, are some people are going to make use of these commitment

  • devices, and B, are they going to help?

  • The answer is maybe.

  • In many situations, in fact, no.

  • The reason being often people then--

  • they might demand commitment but then not follow through

  • in various ways, which can be then explained

  • by people are sort of overconfident

  • when it comes to their self-control problems.

  • We're going to talk about this next time.

  • So the idea here is that people might understand that they

  • have self-control problems.

  • They might demand commitment devices.

  • They might say, I'd like to have a commitment device to help me,

  • but they might underestimate how bad their self-control problems

  • actually are.

  • So then they demand a commitment device

  • that's actually kind of helpful but not quite enough,

  • that's not powerful enough.

  • They demand that commitment device,

  • but then they actually fail and do

  • the thing they want to do anyway, and essentially

  • have to pay money, or other things like that.

  • We'll talk about that.

  • But that's not a theoretical problem.

  • That's an empirical problem, in the sense of in principle,

  • commitment devices should help.

  • They might not be able to do so in practice.

  • Let me tell you a little bit more

  • about specifics of the model.

  • And then we're going to talk about this in more detail

  • next time.

  • So usually, we tend to assume that beta is lower

  • than 1 and delta is close to 1.

  • So for example, we think beta is 2/3, or 3/4, or the like,

  • and delta equals 1.

  • So then your discounted utility becomes something like this.

  • So relative to the current period,

  • all future periods are worth much less.

  • So everything in the future, essentially, you

  • discount by 2/3.

  • And then within any future periods,

  • you don't discount very much anymore.

  • Usually, we think delta is 0.99, 0.95, or the like.

  • So there's some discounting in the future.

  • You care more about stuff that's one year from now compared

  • to 10 years from now or 30 years from now,

  • but not that much differently.

  • You care a lot about whether stuff is in the present

  • versus in two weeks from now or in a year from now.

  • And so then similarly, if beta equals 1/2 and delta equals 1,

  • then again, your discount function--

  • this is the d of tau that I was writing down earlier--

  • is essentially you care about the present 1,

  • and then everything in the future is 1/2.

  • So again, relative to the present,

  • all future periods are worth less, weighed 1/2.

  • And then all discounting takes place between the present

  • and the immediate future.

  • So then again, what we can explain now

  • is essentially short run impatience.

  • I'm essentially impatient between the present

  • and the future.

  • Anything that's in the future is essentially far away

  • or gets the weight of, in this case, 1/2 or 2/3 or the like.

  • I can also explain long-run patience,

  • because essentially across the years in the future,

  • there's no discounting happening anymore.

  • People tend to be relatively patient.

  • And so then, decisions, of course,

  • are very sensitive to the timing of costs and benefits.

  • We're going to talk about that next time.

  • So as I said in the email I sent you, readings until Wednesday

  • are the [INAUDIBLE] paper.

  • We're going to discuss or finish the same set of slides

  • that I've given you now.

  • Let me know if you have any questions.

  • Thank you.

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