WEBVTT 00:00:00.000 --> 00:00:05.404 Hi, in this lecture we are going to look at our fourth category of reasons about why 00:00:05.404 --> 00:00:09.470 you'd want to take a course in modeling, why modeling is so important. And that is 00:00:09.470 --> 00:00:12.983 to help you make better decisions, strategize better, and design things 00:00:12.983 --> 00:00:16.948 better. So lets get started, this should be a lot of fun. Alright, so first reason 00:00:16.948 --> 00:00:20.963 why models are so useful. They are good decision aides, they help you make better 00:00:20.963 --> 00:00:25.044 decisions. Let me give you an example. These get us going here. So what you see 00:00:25.044 --> 00:00:29.383 is a whole bunch of different financial institutions, these are companies like 00:00:29.383 --> 00:00:33.054 Bear Sterns, AIG, CitiGroup, Morgan Stanley and this represents the 00:00:33.054 --> 00:00:37.393 relationship between these companies, in terms of how one of their economic success 00:00:37.393 --> 00:00:41.490 depends on another. Now imagine you are the federal government and you've got a 00:00:41.490 --> 00:00:45.340 financial crisis. So a lot of these companies, or some of these companies are 00:00:45.340 --> 00:00:49.546 starting to fail and you've got to decide okay do I bail them out, do I save one of 00:00:49.546 --> 00:00:53.802 these companies? Well now lets use one of these very simple models to help make that 00:00:53.802 --> 00:00:57.957 decision. So to do that we need a little more of an understanding of what 00:00:57.957 --> 00:01:02.254 these numbers represent. So lets look at AIG which is right here. And JP Morgan 00:01:02.254 --> 00:01:07.970 which is right here So now we see a number of 466 between the two of those. What that 00:01:07.970 --> 00:01:12.958 number represents is how correlated JP Morgan success is with AIG success. In 00:01:12.958 --> 00:01:18.140 particular how correlated their failures are. So if AIG has a bad day, how likely is it that 00:01:18.140 --> 00:01:23.451 JP Morgan has a bad day? And we see that it is a really big number. Now if you look 00:01:23.451 --> 00:01:28.828 up here at this 94, this represents the link between Wells Fargo and Lehman Brothers. What that tells 00:01:28.828 --> 00:01:34.139 us is that Lehman Brothers has a bad day, well it only has a small effect on Wells 00:01:34.139 --> 00:01:38.344 Fargo and vice versa. So now you are the government and you got to decide, okay who do I 00:01:38.344 --> 00:01:43.169 want to bail out? Nobody or somebody? Lets look at Lehman Brothers. There's only 00:01:43.169 --> 00:01:48.243 three lines going in and out of Lehman Brothers and one is a 94. I guess four 00:01:48.243 --> 00:01:53.382 lines, one is a 103, one is a 158 and one is a 155. Those are relatively small 00:01:53.382 --> 00:01:58.541 numbers. So if you're the government you say, okay Lehman Brothers has been around 00:01:58.541 --> 00:02:03.616 a long time and its an important company, these numbers are pretty small, if they 00:02:03.616 --> 00:02:08.691 fail it doesn't look like these other companies would fail. But now lets look at 00:02:08.691 --> 00:02:13.386 AIG. We've got a 466, we've got a 441, we've got a 456, we've got a 390 and a 00:02:13.386 --> 00:02:19.336 490. So there are huge numbers associated with AIG. Because there is a huge number 00:02:19.336 --> 00:02:23.171 you basically have to figure, you know what we probably have to prop AIG back up. 00:02:23.171 --> 00:02:27.102 Even if you don't want to because if you don't there is the possibility that this 00:02:27.102 --> 00:02:30.794 whole system will fail. So what we see here is the incredible power of models, 00:02:30.794 --> 00:02:34.581 right to help us make a better decision. The government did let Lehman Brothers 00:02:34.581 --> 00:02:37.745 fail, and terrible for Lehman Brothers, but the economy sort of 00:02:37.745 --> 00:02:41.677 soldiered on. They didn't let AIG fail and we don't know for sure that it would've 00:02:41.677 --> 00:02:45.883 and we don't know for sure that the whole financial you know apparatus United 00:02:45.883 --> 00:02:51.153 States, they propped up AIG and you know we made it, the country made it. It looks 00:02:51.153 --> 00:02:55.533 they've made a reasonable decision. Alright so that is big financial 00:02:55.533 --> 00:03:00.561 decisions. Lets look at something more fun. This is a simple sort of logic puzzle 00:03:00.561 --> 00:03:05.400 that will help us see how models can be useful. Now this is a game called, The 00:03:05.400 --> 00:03:10.346 Monty Hall Problem and its named after Monty Hall was the host of a game show 00:03:10.346 --> 00:03:15.196 called, Lets Make a Deal that aired during the 1970's. Now the problem I'm going to 00:03:15.196 --> 00:03:20.106 describe to you is a characterization of a event that could happen on the show. Its 00:03:20.106 --> 00:03:24.542 one of several scenarios on the show. Here's basically how it works. There's 00:03:24.542 --> 00:03:29.392 three doors. Behind one of these doors is a prize, behind the other two doors there's some, you 00:03:29.392 --> 00:03:34.123 know, silly thing like a goat right, or a woman dressed up in a ballerinas outfit. 00:03:34.123 --> 00:03:38.834 So one of them had something fantastic like a new car or a washing machine. Now 00:03:38.834 --> 00:03:44.322 what you get to do is you pick one door. So maybe you pick door number one, right, 00:03:44.322 --> 00:03:49.810 so you pick door number one. Now Monty knows where the prize is so the two doors 00:03:49.810 --> 00:03:54.592 you didn't pick, one of those always has to go behind it, where you know, silly 00:03:54.592 --> 00:03:59.070 prize behind it. So because one of us always has a silly prize behind it, he 00:03:59.070 --> 00:04:03.898 can always show you one of those other two doors. So you pick door number one, right, 00:04:03.898 --> 00:04:08.552 and what Monty does, you picked one and what Monty does is he then opens up door 00:04:08.552 --> 00:04:13.089 number three and says, here's a goat, then he says, hey, do you want to switch to 00:04:13.089 --> 00:04:19.416 door number two? Well, do you? Alright, that's a hard problem so let's first try 00:04:19.416 --> 00:04:23.835 to get the logic right then we'll right down a formal model. So, it's easier to 00:04:23.835 --> 00:04:28.028 see the logic for this problem by increasing the number of doors. So let's 00:04:28.028 --> 00:04:32.391 suppose there's five doors, and now there's five doors, let's suppose you pick 00:04:32.391 --> 00:04:37.037 this blue door, this bright blue door. The probability that you're correct is 1/5th. 00:04:37.037 --> 00:04:41.343 Right, one of the doors has prize, the probability you're correct is 1/5th. So 00:04:41.343 --> 00:04:46.023 the probability that you're not correct Is 4/5ths. So, there's a 1/5th chance you're 00:04:46.023 --> 00:04:50.064 correct. There's a 4/5ths chance you're not. Now let's suppose that Monty 00:04:50.064 --> 00:04:54.218 [inaudible] is also playing this game, because he knows again, he knows the 00:04:54.218 --> 00:04:58.483 answer. So Monty is thinking, okay, well, you know what, I'm gonna show you that 00:04:58.483 --> 00:05:03.624 it's not behind the yellow door. And then he says, you know what else I'm going to 00:05:03.624 --> 00:05:08.565 show you, that it's not behind the pink door. [inaudible]. I'm gonna be nice, I'm 00:05:08.565 --> 00:05:13.630 gonna show you it's not behind the green door. Now he says, do you want to switch 00:05:13.630 --> 00:05:18.525 to the light blue door to the dark blue door. Well in this case, you should start 00:05:18.525 --> 00:05:23.049 thinking, you know initially the probability I was right was only 1/5th And 00:05:23.049 --> 00:05:26.593 he revealed all those other doors that doesn't seem to have the prize. It seems 00:05:26.593 --> 00:05:30.316 much more likely that this is the correct door than mine's the correct door and in 00:05:30.316 --> 00:05:33.725 fact it is much more [inaudible]. The probability is 4/5ths it's behind that 00:05:33.725 --> 00:05:37.358 dark blue door and only 1/5th it's behind your door. So you should switch and you 00:05:37.358 --> 00:05:41.037 should also switch in the case of two. Now let's formalize this. This isn't so much, 00:05:41.037 --> 00:05:44.465 this is, we'll use the simple decision three model. To show why in fact you 00:05:44.465 --> 00:05:48.318 should switch. Alright, so let's start out, we'll just do some basic probability. 00:05:48.318 --> 00:05:52.220 There's three doors, you pick door number one, the probability you're right is a 00:05:52.220 --> 00:05:56.319 third and the probability that it's door number two is a third and the probability 00:05:56.319 --> 00:06:00.320 that it's door number three is a third. Now, what we want to do is break this into 00:06:00.320 --> 00:06:04.599 two sets. There's a 1/3rd chance that you're right and there's a 2/3rds chance 00:06:04.599 --> 00:06:09.574 that you're wrong. After you pick door number one, the prize can't be moved. So 00:06:09.574 --> 00:06:14.936 it's either behind door number two, number three or if you got it right, it's behind 00:06:14.936 --> 00:06:20.363 door number one. So let's think about what Monty can do. Monty can basically show you 00:06:20.363 --> 00:06:25.403 if it's behind door number one or door number two, he can show you door number 00:06:25.403 --> 00:06:30.197 three. He can say look, there's the goat. Well if he does that, because he can 00:06:30.197 --> 00:06:34.787 always show you one of these doors, nothing happened to your probability of 00:06:34.787 --> 00:06:39.682 1/3rd. There's a 1/3rd chance you were right before since he can always show you 00:06:39.682 --> 00:06:44.210 a door, there's still only a 1/3rd chance you're right. Right, alternatively, 00:06:44.210 --> 00:06:48.452 suppose that, It was behind door number three well then he can show you door 00:06:48.452 --> 00:06:52.285 number two. He can say the goat's here. So, it's still the case that nothing 00:06:52.285 --> 00:06:56.377 happens to your probability. The reason why when you think about these two sets, 00:06:56.377 --> 00:07:00.313 you didn't learn anything. You learn nothing about this other set right here, 00:07:00.313 --> 00:07:04.301 the 2/3rds chance you're wrong because he can always show you a goat. So your 00:07:04.301 --> 00:07:08.497 initial chan-, your initial probability being correct was 1/3rd, your final chance 00:07:08.497 --> 00:07:12.692 of being correct was probably 1/3rd. So just this sort of idea of drawing circles 00:07:12.692 --> 00:07:16.855 and writing probabilities allows us to see that the correct The correct decision on 00:07:16.855 --> 00:07:20.197 the [inaudible] problem is to switch, right. Just like when we looked at that 00:07:20.197 --> 00:07:23.540 financial decision that the Federal Government had to make with the circles 00:07:23.540 --> 00:07:27.102 and the arrows, you draw that out, and you realize the best decision is to let the 00:07:27.102 --> 00:07:31.069 [inaudible] fail. Bailout AIG. Alright so lets move on a look sort of the next 00:07:31.069 --> 00:07:35.576 reason that models can be helpful and that is comparative statics. What do I mean by 00:07:35.576 --> 00:07:39.547 that? Well here is a standard model from economics, what we can think of is 00:07:39.547 --> 00:07:43.786 comparative statics means you know you move from one equilibrium to another. So 00:07:43.786 --> 00:07:47.971 what you see here is that S is a supply curve, that is a supply curve for some 00:07:47.971 --> 00:07:52.317 good, and D, D1 and D2 are demand curves. So what you see is demand shifting out. So 00:07:52.317 --> 00:07:56.624 when this demand shifts out. In this way what we get is that more goods are sold 00:07:56.624 --> 00:08:00.993 the quantity goes up, and the price goes up so people want more of something, more 00:08:00.993 --> 00:08:05.307 is gonna get sold and the price is up. So this is where you start seeing how the 00:08:05.307 --> 00:08:09.357 equilibrium moves so this is again a simple example of how. Models help us 00:08:09.357 --> 00:08:13.754 understand how the world will change, equilibrium world, just by drawing some 00:08:13.754 --> 00:08:18.266 simple figures. Alright, reason number three. Counter factuals, what do I mean by 00:08:18.266 --> 00:08:22.837 that? Well you can think you only get to run the world once, you only get to run 00:08:22.837 --> 00:08:27.465 the tape one time. But if we write models of the world we can sort of re-run the 00:08:27.465 --> 00:08:31.919 tape using those models. So here is an example, in April of 2009, The spring of 00:08:31.919 --> 00:08:36.393 2009, the Federal Government decided to implement a recovery plan. Well what you 00:08:36.393 --> 00:08:40.369 see here is sort of the effect, this line right here shows the effect with the 00:08:40.369 --> 00:08:44.446 recovery plan, and this line shows, says, this is what a model shows what would of 00:08:44.446 --> 00:08:48.473 happened without the recovery plan. Now we can't be sure that, that happened, but, 00:08:48.473 --> 00:08:52.142 you know, at least we have some understanding, perhaps, of what the effect 00:08:52.142 --> 00:08:56.322 of recovery plan was, which is great. So these counter factuals are not going to be 00:08:56.322 --> 00:09:00.461 exact, there going to be approximate, but still they help us figure out. After the 00:09:00.461 --> 00:09:05.150 fact whether a policy was a good policy or not. Reason number four. To identify and 00:09:05.150 --> 00:09:09.781 rank levers. So what we are going to do is look at a simple model of contagion of 00:09:09.781 --> 00:09:14.184 failure, so this is a model where one country might fail, so in this case that 00:09:14.184 --> 00:09:18.816 country is going to be England. Then we can ask what happens over time, so you can 00:09:18.816 --> 00:09:23.447 see that initially after England fails, we see Ireland and Belgium fail, and after 00:09:23.447 --> 00:09:27.716 that we see France fail. And after that we see Germany fail. So what this tells us is 00:09:27.716 --> 00:09:31.626 that in terms of its effect on the worlds financial system, London is a big lever, 00:09:31.626 --> 00:09:35.440 so London is something we care about a great deal. Now lets take another policy 00:09:35.440 --> 00:09:39.060 issue, climate change. One of the big things in climate change is the carbon 00:09:39.060 --> 00:09:42.825 cycle, its one of the models that you use all the time, simple carbon models. We 00:09:42.825 --> 00:09:46.832 know that total amount of carbon is fixed, that can be up in the air or down on the 00:09:46.832 --> 00:09:50.645 earth, if it is down on the earth it is better because it doesn't contribute to 00:09:50.645 --> 00:09:54.550 global warming So if you want to think about, where do you intervene, you wanna 00:09:54.550 --> 00:09:58.488 ask, where in this cycle are there big numbers? Right, so you look here in terms 00:09:58.488 --> 00:10:02.678 of surface radiation. That's a big number. Where you think of solar radiation coming 00:10:02.678 --> 00:10:06.717 in, that's a big number coming in. So, you wanna, you think about where you want to 00:10:06.717 --> 00:10:10.806 have a policy in fact, you want to think about it in terms of where those numbers 00:10:10.806 --> 00:10:14.744 are large. So if you look at number, the amount of [inaudible] reflected by the 00:10:14.744 --> 00:10:18.269 surface, that's only a 30, that's not a very big leber. Okay reason five, 00:10:18.269 --> 00:10:22.066 experimental design. Now, what i mean by experimental design, well, suppose you 00:10:22.066 --> 00:10:26.014 want to come up with some new policies. For example, when the Federal Government, 00:10:26.014 --> 00:10:30.161 when they wanted to, when they were trying to decide how to auction off the federal 00:10:30.161 --> 00:10:33.909 airwaves, right, for cell phones, they wanted raise as much money as possible. 00:10:33.909 --> 00:10:37.956 Well to test auction designer were best they ran some experiments. Well the thing 00:10:37.956 --> 00:10:41.953 you want to do, you want to think about, so here is the example of the experiment 00:10:41.953 --> 00:10:45.851 and what you see is, this is a round from some auction and these are different 00:10:45.851 --> 00:10:49.967 bidders and, you know, the cost for. That they paid. What you can do, you want to 00:10:49.967 --> 00:10:54.353 think, how do I run the best possible experiment, the most informative possible 00:10:54.353 --> 00:10:58.570 experiment? And one way to do that, right, is to construct some simple models. 00:10:58.570 --> 00:11:02.703 Alright, six, reason six. Institutional design, now this is a biggie and this is 00:11:02.703 --> 00:11:07.211 one that means a lot to me. The person you see at the top here, this is Stan Rider he 00:11:07.211 --> 00:11:11.720 was one of my advisors in graduate school and the man at the bottom is Leo Herwicks, 00:11:11.720 --> 00:11:15.746 he was one of my mentors in graduate school and Leo won the nobel prize in 00:11:15.746 --> 00:11:20.074 economics. Leo won the nobel prize for, which is A field known as mechanism 00:11:20.074 --> 00:11:24.947 design. Now this diagram is called the Mount Rider, named after Stan Rider in the 00:11:24.947 --> 00:11:29.636 previous picture and Ken Mount, one of his co-authors. And let me explain this 00:11:29.636 --> 00:11:33.839 diagram to you because it's very important. What you see here is this 00:11:33.839 --> 00:11:38.468 theta, here. What this is supposed to represent is the environment, the set of 00:11:38.468 --> 00:11:43.280 technologies, people's preferences, those types of things. X over here represents 00:11:43.280 --> 00:11:47.298 the outcomes, what we want to have happen. So how we want to sort of use our 00:11:47.298 --> 00:11:51.799 technologies and use our labor and use you know, whatever we have at our disposal to 00:11:51.799 --> 00:11:55.979 create good outcomes. Now this arrow here is sort of , it's what we desire, it's 00:11:55.979 --> 00:12:00.212 like if we could sit around and decide collectively what kind of outcomes we'd 00:12:00.212 --> 00:12:04.391 like to have given the technology, this is what we collectively decide, this is 00:12:04.391 --> 00:12:07.981 something called a social choice correspondence or a social choice 00:12:07.981 --> 00:12:12.147 function. Sort of, what would be the ideal outcome for society? The thing is that 00:12:12.147 --> 00:12:16.334 [inaudible] doesn't get the ideal outcome because what happens is [inaudible] wants 00:12:16.334 --> 00:12:20.371 though. Because the thing is to get those outcomes you have to use mechanisms and 00:12:20.371 --> 00:12:24.358 that what this m stands for, mechanisms. So a mechanism might be something like a 00:12:24.358 --> 00:12:28.688 market, a political institution, it might be a bureaucracy. What we want to ask is, 00:12:28.688 --> 00:12:33.867 is the outcome we get to the mechanism, right, which goes like this is that equal 00:12:33.867 --> 00:12:38.982 to the outcome that we would get, right, ideally and the better mechanism is, the 00:12:38.982 --> 00:12:44.091 closer it is to equal to what we ideally want. Example: so my with my undergraduate 00:12:44.091 --> 00:12:48.829 students for a homework assignment one time I said, suppose we allocated classes 00:12:48.829 --> 00:12:52.249 by a market So, you know, if you had to bid for classes, would that be a good 00:12:52.249 --> 00:12:55.647 thing or a bad thing? Well, currently the way we do it is there's a hierarchy. So 00:12:55.647 --> 00:12:58.872 seniors, you know fourth year students register first and then juniors then 00:12:58.872 --> 00:13:02.098 sophomores and then freshmen. And the students were asking, should we have a 00:13:02.098 --> 00:13:05.323 market? And their first reaction is yes, because markets work. Right. You have 00:13:05.323 --> 00:13:08.764 this, you know, you have a market, what you get here is sort of what you expect to 00:13:08.764 --> 00:13:12.076 get. Right, what you'd like to get, so it's sort of equal. But when they thought 00:13:12.076 --> 00:13:15.430 about choosing classes, everybody goes, wait a minute, markets may not work well 00:13:15.430 --> 00:13:18.581 and the reason why is, you need to graduate. And so seniors need specific 00:13:18.581 --> 00:13:22.216 courses and that's why we let seniors register first and if people could bid for 00:13:22.216 --> 00:13:25.896 courses then the fraction that had a lot of money might bid away the courses from 00:13:25.896 --> 00:13:30.054 seniors and people might never graduate from college so a good institution markets 00:13:30.054 --> 00:13:35.047 may be good in some settings they may not be in others. The way we figure that out 00:13:35.047 --> 00:13:39.796 is by using models. Reason seven: To help choose among policies in institutions. 00:13:39.796 --> 00:13:43.686 Simple example. Suppose [inaudible] a market for pollution permits or a cap and 00:13:43.686 --> 00:13:47.268 trade system. We can write down simple model and you can tell us which one is 00:13:47.268 --> 00:13:50.942 going to work better. Or here is another example, this is picture of the city of 00:13:50.942 --> 00:13:54.616 Ann Arbor and if you look here you see some green areas, right, what these green 00:13:54.616 --> 00:13:58.244 things are... Is green spaces. Their is a question should the city of Ann Arbor 00:13:58.244 --> 00:14:01.919 create more green spaces. You might think of course, green space is a good thing. 00:14:01.919 --> 00:14:05.686 The problem is when you, if you buy up a bunch of green space like this area here 00:14:05.686 --> 00:14:09.268 is all green. What can happen is people could say lets move next to that, lets 00:14:09.268 --> 00:14:12.756 build little houses all around here because it is always going to be green, 00:14:12.756 --> 00:14:17.350 and that can actually lead to more sprawl. So what can seem like really good simple 00:14:17.350 --> 00:14:21.921 ideas may not be good ideas if you actually construct a model to think 00:14:21.921 --> 00:14:26.325 through it. [sound] okay, we've covered a lot. So, let's give a quick summary here. 00:14:26.325 --> 00:14:30.558 How can models help us? Well first thing they can do is become real time decision 00:14:30.558 --> 00:14:34.790 makers. They can help us figure out when we intervene and when we don't intervene. 00:14:34.790 --> 00:14:38.957 Second, they can help us with comparative status. We can figure out, you know what, 00:14:38.957 --> 00:14:42.963 what's likely to happen, right, if we make this choice. Third, they can help us with 00:14:42.963 --> 00:14:46.672 counter-factuals, they can you know appresent a policy, we can sort of run a 00:14:46.672 --> 00:14:50.580 model and think about what would have happened if we hadn't chosen that policy 00:14:50.580 --> 00:14:54.684 Fourth, we can use them to identify and rank levers. Often as you've got lots of 00:14:54.684 --> 00:14:58.892 choices to make models can figure out which choice might be the best or the most 00:14:58.892 --> 00:15:02.840 influenced. Fifth, they can help us with experimental design. They can help us 00:15:02.840 --> 00:15:06.841 design experiments in order to develop better policies and better strategies. 00:15:06.841 --> 00:15:10.633 Sixth, they can help us design institutions themselves figuring out if we 00:15:10.633 --> 00:15:14.478 have a market here, should we have a democracy, should we use a bureaucracy. 00:15:14.478 --> 00:15:18.582 And seventh, finally, they can help us choose among policies and institutions so 00:15:18.582 --> 00:15:22.842 if we are thinking about one policy or another policy we can use models to decide 00:15:22.842 --> 00:15:25.596 among the two. All right. Thank you.