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.