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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Â something called a social choice correspondence or a social choice

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Â among the two. All right. Thank you.

Â