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.