Using Models to Decide, Strategize, and Design

Hi, in this lecture we are going to look
at our fourth category of reasons about why

you'd want to take a course in modeling,
why modeling is so important. And that is

to help you make better decisions,
strategize better, and design things

better. So lets get started, this should
be a lot of fun. Alright, so first reason

why models are so useful. They are good
decision aides, they help you make better

decisions. Let me give you an example.
These get us going here. So what you see

is a whole bunch of different financial
institutions, these are companies like

Bear Sterns, AIG, CitiGroup, Morgan
Stanley and this represents the

relationship between these companies, in
terms of how one of their economic success

depends on another. Now imagine you are
the federal government and you've got a

financial crisis. So a lot of these
companies, or some of these companies are

starting to fail and you've got to decide
okay do I bail them out, do I save one of

these companies? Well now lets use one of
these very simple models to help make that

decision. So to do that we need a little
more of an understanding of what

these numbers represent. So lets look at
AIG which is right here. And JP Morgan

which is right here So now we see a number
of 466 between the two of those. What that

number represents is how correlated JP
Morgan success is with AIG success. In

particular how correlated their failures are. So if
AIG has a bad day, how likely is it that

JP Morgan has a bad day? And we see that
it is a really big number. Now if you look

up here at this 94, this represents the link between Wells
Fargo and Lehman Brothers. What that tells

us is that Lehman Brothers has a bad day,
well it only has a small effect on Wells

Fargo and vice versa. So now you are the
government and you got to decide, okay who do I

want to bail out? Nobody or somebody? Lets
look at Lehman Brothers. There's only

three lines going in and out of Lehman
Brothers and one is a 94. I guess four

lines, one is a 103, one is a 158 and one
is a 155. Those are relatively small

numbers. So if you're the government you
say, okay Lehman Brothers has been around

a long time and its an important company,
these numbers are pretty small, if they

fail it doesn't look like these other
companies would fail. But now lets look at

AIG. We've got a 466, we've got a 441,
we've got a 456, we've got a 390 and a

490. So there are huge numbers associated
with AIG. Because there is a huge number

you basically have to figure, you know
what we probably have to prop AIG back up.

Even if you don't want to because if you
don't there is the possibility that this

whole system will fail. So what we see
here is the incredible power of models,

right to help us make a better decision.
The government did let Lehman Brothers

fail, and terrible for Lehman
Brothers, but the economy sort of

soldiered on. They didn't let AIG fail and
we don't know for sure that it would've

and we don't know for sure that the whole
financial you know apparatus United

States, they propped up AIG and you know
we made it, the country made it. It looks

they've made a reasonable decision.
Alright so that is big financial

decisions. Lets look at something more
fun. This is a simple sort of logic puzzle

that will help us see how models can be
useful. Now this is a game called, The

Monty Hall Problem and its named after
Monty Hall was the host of a game show

called, Lets Make a Deal that aired during
the 1970's. Now the problem I'm going to

describe to you is a characterization of a
event that could happen on the show. Its

one of several scenarios on the show.
Here's basically how it works. There's

three doors. Behind one of these doors is
a prize, behind the other two doors there's some, you

know, silly thing like a goat right, or a
woman dressed up in a ballerinas outfit.

So one of them had something fantastic
like a new car or a washing machine. Now

what you get to do is you pick one door.
So maybe you pick door number one, right,

so you pick door number one. Now Monty
knows where the prize is so the two doors

you didn't pick, one of those always has
to go behind it, where you know, silly

prize behind it. So because one of us
always has a silly prize behind it, he

can always show you one of those other two
doors. So you pick door number one, right,

and what Monty does, you picked one and
what Monty does is he then opens up door

number three and says, here's a goat, then
he says, hey, do you want to switch to

door number two? Well, do you? Alright,
that's a hard problem so let's first try

to get the logic right then we'll right
down a formal model. So, it's easier to

see the logic for this problem by
increasing the number of doors. So let's

suppose there's five doors, and now
there's five doors, let's suppose you pick

this blue door, this bright blue door. The
probability that you're correct is 1/5th.

Right, one of the doors has prize, the
probability you're correct is 1/5th. So

the probability that you're not correct Is
4/5ths. So, there's a 1/5th chance you're

correct. There's a 4/5ths chance you're
not. Now let's suppose that Monty

[inaudible] is also playing this game,
because he knows again, he knows the

answer. So Monty is thinking, okay, well,
you know what, I'm gonna show you that

it's not behind the yellow door. And then
he says, you know what else I'm going to

show you, that it's not behind the pink
door. [inaudible]. I'm gonna be nice, I'm

gonna show you it's not behind the green
door. Now he says, do you want to switch

to the light blue door to the dark blue
door. Well in this case, you should start

thinking, you know initially the
probability I was right was only 1/5th And

he revealed all those other doors that
doesn't seem to have the prize. It seems

much more likely that this is the correct
door than mine's the correct door and in

fact it is much more [inaudible]. The
probability is 4/5ths it's behind that

dark blue door and only 1/5th it's behind
your door. So you should switch and you

should also switch in the case of two. Now
let's formalize this. This isn't so much,

this is, we'll use the simple decision
three model. To show why in fact you

should switch. Alright, so let's start
out, we'll just do some basic probability.

There's three doors, you pick door number
one, the probability you're right is a

third and the probability that it's door
number two is a third and the probability

that it's door number three is a third.
Now, what we want to do is break this into

two sets. There's a 1/3rd chance that
you're right and there's a 2/3rds chance

that you're wrong. After you pick door
number one, the prize can't be moved. So

it's either behind door number two, number
three or if you got it right, it's behind

door number one. So let's think about what
Monty can do. Monty can basically show you

if it's behind door number one or door
number two, he can show you door number

three. He can say look, there's the goat.
Well if he does that, because he can

always show you one of these doors,
nothing happened to your probability of

1/3rd. There's a 1/3rd chance you were
right before since he can always show you

a door, there's still only a 1/3rd chance
you're right. Right, alternatively,

suppose that, It was behind door number
three well then he can show you door

number two. He can say the goat's here.
So, it's still the case that nothing

happens to your probability. The reason
why when you think about these two sets,

you didn't learn anything. You learn
nothing about this other set right here,

the 2/3rds chance you're wrong because he
can always show you a goat. So your

initial chan-, your initial probability
being correct was 1/3rd, your final chance

of being correct was probably 1/3rd. So
just this sort of idea of drawing circles

and writing probabilities allows us to see
that the correct The correct decision on

the [inaudible] problem is to switch,
right. Just like when we looked at that

financial decision that the Federal
Government had to make with the circles

and the arrows, you draw that out, and you
realize the best decision is to let the

[inaudible] fail. Bailout AIG. Alright so
lets move on a look sort of the next

reason that models can be helpful and that
is comparative statics. What do I mean by

that? Well here is a standard model from
economics, what we can think of is

comparative statics means you know you
move from one equilibrium to another. So

what you see here is that S is a supply
curve, that is a supply curve for some

good, and D, D1 and D2 are demand curves.
So what you see is demand shifting out. So

when this demand shifts out. In this way
what we get is that more goods are sold

the quantity goes up, and the price goes
up so people want more of something, more

is gonna get sold and the price is up. So
this is where you start seeing how the

equilibrium moves so this is again a
simple example of how. Models help us

understand how the world will change,
equilibrium world, just by drawing some

simple figures. Alright, reason number
three. Counter factuals, what do I mean by

that? Well you can think you only get to
run the world once, you only get to run

the tape one time. But if we write models
of the world we can sort of re-run the

tape using those models. So here is an
example, in April of 2009, The spring of

2009, the Federal Government decided to
implement a recovery plan. Well what you

see here is sort of the effect, this line
right here shows the effect with the

recovery plan, and this line shows, says,
this is what a model shows what would of

happened without the recovery plan. Now we
can't be sure that, that happened, but,

you know, at least we have some
understanding, perhaps, of what the effect

of recovery plan was, which is great. So
these counter factuals are not going to be

exact, there going to be approximate, but
still they help us figure out. After the

fact whether a policy was a good policy or
not. Reason number four. To identify and

rank levers. So what we are going to do is
look at a simple model of contagion of

failure, so this is a model where one
country might fail, so in this case that

country is going to be England. Then we
can ask what happens over time, so you can

see that initially after England fails, we
see Ireland and Belgium fail, and after

that we see France fail. And after that we
see Germany fail. So what this tells us is

that in terms of its effect on the worlds
financial system, London is a big lever,

so London is something we care about a
great deal. Now lets take another policy

issue, climate change. One of the big
things in climate change is the carbon

cycle, its one of the models that you use
all the time, simple carbon models. We

know that total amount of carbon is fixed,
that can be up in the air or down on the

earth, if it is down on the earth it is
better because it doesn't contribute to

global warming So if you want to think
about, where do you intervene, you wanna

ask, where in this cycle are there big
numbers? Right, so you look here in terms

of surface radiation. That's a big number.
Where you think of solar radiation coming

in, that's a big number coming in. So, you
wanna, you think about where you want to

have a policy in fact, you want to think
about it in terms of where those numbers

are large. So if you look at number, the
amount of [inaudible] reflected by the

surface, that's only a 30, that's not a
very big leber. Okay reason five,

experimental design. Now, what i mean by
experimental design, well, suppose you

want to come up with some new policies.
For example, when the Federal Government,

when they wanted to, when they were trying
to decide how to auction off the federal

airwaves, right, for cell phones, they
wanted raise as much money as possible.

Well to test auction designer were best
they ran some experiments. Well the thing

you want to do, you want to think about,
so here is the example of the experiment

and what you see is, this is a round from
some auction and these are different

bidders and, you know, the cost for. That
they paid. What you can do, you want to

think, how do I run the best possible
experiment, the most informative possible

experiment? And one way to do that, right,
is to construct some simple models.

Alright, six, reason six. Institutional
design, now this is a biggie and this is

one that means a lot to me. The person you
see at the top here, this is Stan Rider he

was one of my advisors in graduate school
and the man at the bottom is Leo Herwicks,

he was one of my mentors in graduate
school and Leo won the nobel prize in

economics. Leo won the nobel prize for,
which is A field known as mechanism

design. Now this diagram is called the
Mount Rider, named after Stan Rider in the

previous picture and Ken Mount, one of his
co-authors. And let me explain this

diagram to you because it's very
important. What you see here is this

theta, here. What this is supposed to
represent is the environment, the set of

technologies, people's preferences, those
types of things. X over here represents

the outcomes, what we want to have happen.
So how we want to sort of use our

technologies and use our labor and use you
know, whatever we have at our disposal to

create good outcomes. Now this arrow here
is sort of , it's what we desire, it's

like if we could sit around and decide
collectively what kind of outcomes we'd

like to have given the technology, this is
what we collectively decide, this is

something called a social choice
correspondence or a social choice

function. Sort of, what would be the ideal
outcome for society? The thing is that

[inaudible] doesn't get the ideal outcome
because what happens is [inaudible] wants

though. Because the thing is to get those
outcomes you have to use mechanisms and

that what this m stands for, mechanisms.
So a mechanism might be something like a

market, a political institution, it might
be a bureaucracy. What we want to ask is,

is the outcome we get to the mechanism,
right, which goes like this is that equal

to the outcome that we would get, right,
ideally and the better mechanism is, the

closer it is to equal to what we ideally
want. Example: so my with my undergraduate

students for a homework assignment one
time I said, suppose we allocated classes

by a market So, you know, if you had to
bid for classes, would that be a good

thing or a bad thing? Well, currently the
way we do it is there's a hierarchy. So

seniors, you know fourth year students
register first and then juniors then

sophomores and then freshmen. And the
students were asking, should we have a

market? And their first reaction is yes,
because markets work. Right. You have

this, you know, you have a market, what
you get here is sort of what you expect to

get. Right, what you'd like to get, so
it's sort of equal. But when they thought

about choosing classes, everybody goes,
wait a minute, markets may not work well

and the reason why is, you need to
graduate. And so seniors need specific

courses and that's why we let seniors
register first and if people could bid for

courses then the fraction that had a lot
of money might bid away the courses from

seniors and people might never graduate
from college so a good institution markets

may be good in some settings they may not
be in others. The way we figure that out

is by using models. Reason seven: To help
choose among policies in institutions.

Simple example. Suppose [inaudible] a
market for pollution permits or a cap and

trade system. We can write down simple
model and you can tell us which one is

going to work better. Or here is another
example, this is picture of the city of

Ann Arbor and if you look here you see
some green areas, right, what these green

things are... Is green spaces. Their is a
question should the city of Ann Arbor

create more green spaces. You might think
of course, green space is a good thing.

The problem is when you, if you buy up a
bunch of green space like this area here

is all green. What can happen is people
could say lets move next to that, lets

build little houses all around here
because it is always going to be green,

and that can actually lead to more sprawl.
So what can seem like really good simple

ideas may not be good ideas if you
actually construct a model to think

through it. [sound] okay, we've covered a
lot. So, let's give a quick summary here.

How can models help us? Well first thing
they can do is become real time decision

makers. They can help us figure out when
we intervene and when we don't intervene.

Second, they can help us with comparative
status. We can figure out, you know what,

what's likely to happen, right, if we make
this choice. Third, they can help us with

counter-factuals, they can you know
appresent a policy, we can sort of run a

model and think about what would have
happened if we hadn't chosen that policy

Fourth, we can use them to identify and
rank levers. Often as you've got lots of

choices to make models can figure out
which choice might be the best or the most

influenced. Fifth, they can help us with
experimental design. They can help us

design experiments in order to develop
better policies and better strategies.

Sixth, they can help us design
institutions themselves figuring out if we

have a market here, should we have a
democracy, should we use a bureaucracy.

And seventh, finally, they can help us
choose among policies and institutions so

if we are thinking about one policy or
another policy we can use models to decide

among the two. All right. Thank you.