1 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 2 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 3 00:00:09,470 --> 00:00:12,983 to help you make better decisions, strategize better, and design things 4 00:00:12,983 --> 00:00:16,948 better. So lets get started, this should be a lot of fun. Alright, so first reason 5 00:00:16,948 --> 00:00:20,963 why models are so useful. They are good decision aides, they help you make better 6 00:00:20,963 --> 00:00:25,044 decisions. Let me give you an example. These get us going here. So what you see 7 00:00:25,044 --> 00:00:29,383 is a whole bunch of different financial institutions, these are companies like 8 00:00:29,383 --> 00:00:33,054 Bear Sterns, AIG, CitiGroup, Morgan Stanley and this represents the 9 00:00:33,054 --> 00:00:37,393 relationship between these companies, in terms of how one of their economic success 10 00:00:37,393 --> 00:00:41,490 depends on another. Now imagine you are the federal government and you've got a 11 00:00:41,490 --> 00:00:45,340 financial crisis. So a lot of these companies, or some of these companies are 12 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 13 00:00:49,546 --> 00:00:53,802 these companies? Well now lets use one of these very simple models to help make that 14 00:00:53,802 --> 00:00:57,957 decision. So to do that we need a little more of an understanding of what 15 00:00:57,957 --> 00:01:02,254 these numbers represent. So lets look at AIG which is right here. And JP Morgan 16 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 17 00:01:07,970 --> 00:01:12,958 number represents is how correlated JP Morgan success is with AIG success. In 18 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 19 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 20 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 21 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 22 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 23 00:01:38,344 --> 00:01:43,169 want to bail out? Nobody or somebody? Lets look at Lehman Brothers. There's only 24 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 25 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 26 00:01:53,382 --> 00:01:58,541 numbers. So if you're the government you say, okay Lehman Brothers has been around 27 00:01:58,541 --> 00:02:03,616 a long time and its an important company, these numbers are pretty small, if they 28 00:02:03,616 --> 00:02:08,691 fail it doesn't look like these other companies would fail. But now lets look at 29 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 30 00:02:13,386 --> 00:02:19,336 490. So there are huge numbers associated with AIG. Because there is a huge number 31 00:02:19,336 --> 00:02:23,171 you basically have to figure, you know what we probably have to prop AIG back up. 32 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 33 00:02:27,102 --> 00:02:30,794 whole system will fail. So what we see here is the incredible power of models, 34 00:02:30,794 --> 00:02:34,581 right to help us make a better decision. The government did let Lehman Brothers 35 00:02:34,581 --> 00:02:37,745 fail, and terrible for Lehman Brothers, but the economy sort of 36 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 37 00:02:41,677 --> 00:02:45,883 and we don't know for sure that the whole financial you know apparatus United 38 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 39 00:02:51,153 --> 00:02:55,533 they've made a reasonable decision. Alright so that is big financial 40 00:02:55,533 --> 00:03:00,561 decisions. Lets look at something more fun. This is a simple sort of logic puzzle 41 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 42 00:03:05,400 --> 00:03:10,346 Monty Hall Problem and its named after Monty Hall was the host of a game show 43 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 44 00:03:15,196 --> 00:03:20,106 describe to you is a characterization of a event that could happen on the show. Its 45 00:03:20,106 --> 00:03:24,542 one of several scenarios on the show. Here's basically how it works. There's 46 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 47 00:03:29,392 --> 00:03:34,123 know, silly thing like a goat right, or a woman dressed up in a ballerinas outfit. 48 00:03:34,123 --> 00:03:38,834 So one of them had something fantastic like a new car or a washing machine. Now 49 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, 50 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 51 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 52 00:03:54,592 --> 00:03:59,070 prize behind it. So because one of us always has a silly prize behind it, he 53 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, 54 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 55 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 56 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 57 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 58 00:04:23,835 --> 00:04:28,028 see the logic for this problem by increasing the number of doors. So let's 59 00:04:28,028 --> 00:04:32,391 suppose there's five doors, and now there's five doors, let's suppose you pick 60 00:04:32,391 --> 00:04:37,037 this blue door, this bright blue door. The probability that you're correct is 1/5th. 61 00:04:37,037 --> 00:04:41,343 Right, one of the doors has prize, the probability you're correct is 1/5th. So 62 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 63 00:04:46,023 --> 00:04:50,064 correct. There's a 4/5ths chance you're not. Now let's suppose that Monty 64 00:04:50,064 --> 00:04:54,218 [inaudible] is also playing this game, because he knows again, he knows the 65 00:04:54,218 --> 00:04:58,483 answer. So Monty is thinking, okay, well, you know what, I'm gonna show you that 66 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 67 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 68 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 69 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 70 00:05:18,525 --> 00:05:23,049 thinking, you know initially the probability I was right was only 1/5th And 71 00:05:23,049 --> 00:05:26,593 he revealed all those other doors that doesn't seem to have the prize. It seems 72 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 73 00:05:30,316 --> 00:05:33,725 fact it is much more [inaudible]. The probability is 4/5ths it's behind that 74 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 75 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, 76 00:05:41,037 --> 00:05:44,465 this is, we'll use the simple decision three model. To show why in fact you 77 00:05:44,465 --> 00:05:48,318 should switch. Alright, so let's start out, we'll just do some basic probability. 78 00:05:48,318 --> 00:05:52,220 There's three doors, you pick door number one, the probability you're right is a 79 00:05:52,220 --> 00:05:56,319 third and the probability that it's door number two is a third and the probability 80 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 81 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 82 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 83 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 84 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 85 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 86 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 87 00:06:30,197 --> 00:06:34,787 always show you one of these doors, nothing happened to your probability of 88 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 89 00:06:39,682 --> 00:06:44,210 a door, there's still only a 1/3rd chance you're right. Right, alternatively, 90 00:06:44,210 --> 00:06:48,452 suppose that, It was behind door number three well then he can show you door 91 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 92 00:06:52,285 --> 00:06:56,377 happens to your probability. The reason why when you think about these two sets, 93 00:06:56,377 --> 00:07:00,313 you didn't learn anything. You learn nothing about this other set right here, 94 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 95 00:07:04,301 --> 00:07:08,497 initial chan-, your initial probability being correct was 1/3rd, your final chance 96 00:07:08,497 --> 00:07:12,692 of being correct was probably 1/3rd. So just this sort of idea of drawing circles 97 00:07:12,692 --> 00:07:16,855 and writing probabilities allows us to see that the correct The correct decision on 98 00:07:16,855 --> 00:07:20,197 the [inaudible] problem is to switch, right. Just like when we looked at that 99 00:07:20,197 --> 00:07:23,540 financial decision that the Federal Government had to make with the circles 100 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 101 00:07:27,102 --> 00:07:31,069 [inaudible] fail. Bailout AIG. Alright so lets move on a look sort of the next 102 00:07:31,069 --> 00:07:35,576 reason that models can be helpful and that is comparative statics. What do I mean by 103 00:07:35,576 --> 00:07:39,547 that? Well here is a standard model from economics, what we can think of is 104 00:07:39,547 --> 00:07:43,786 comparative statics means you know you move from one equilibrium to another. So 105 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 106 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 107 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 108 00:07:56,624 --> 00:08:00,993 the quantity goes up, and the price goes up so people want more of something, more 109 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 110 00:08:05,307 --> 00:08:09,357 equilibrium moves so this is again a simple example of how. Models help us 111 00:08:09,357 --> 00:08:13,754 understand how the world will change, equilibrium world, just by drawing some 112 00:08:13,754 --> 00:08:18,266 simple figures. Alright, reason number three. Counter factuals, what do I mean by 113 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 114 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 115 00:08:27,465 --> 00:08:31,919 tape using those models. So here is an example, in April of 2009, The spring of 116 00:08:31,919 --> 00:08:36,393 2009, the Federal Government decided to implement a recovery plan. Well what you 117 00:08:36,393 --> 00:08:40,369 see here is sort of the effect, this line right here shows the effect with the 118 00:08:40,369 --> 00:08:44,446 recovery plan, and this line shows, says, this is what a model shows what would of 119 00:08:44,446 --> 00:08:48,473 happened without the recovery plan. Now we can't be sure that, that happened, but, 120 00:08:48,473 --> 00:08:52,142 you know, at least we have some understanding, perhaps, of what the effect 121 00:08:52,142 --> 00:08:56,322 of recovery plan was, which is great. So these counter factuals are not going to be 122 00:08:56,322 --> 00:09:00,461 exact, there going to be approximate, but still they help us figure out. After the 123 00:09:00,461 --> 00:09:05,150 fact whether a policy was a good policy or not. Reason number four. To identify and 124 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 125 00:09:09,781 --> 00:09:14,184 failure, so this is a model where one country might fail, so in this case that 126 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 127 00:09:18,816 --> 00:09:23,447 see that initially after England fails, we see Ireland and Belgium fail, and after 128 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 129 00:09:27,716 --> 00:09:31,626 that in terms of its effect on the worlds financial system, London is a big lever, 130 00:09:31,626 --> 00:09:35,440 so London is something we care about a great deal. Now lets take another policy 131 00:09:35,440 --> 00:09:39,060 issue, climate change. One of the big things in climate change is the carbon 132 00:09:39,060 --> 00:09:42,825 cycle, its one of the models that you use all the time, simple carbon models. We 133 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 134 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 135 00:09:50,645 --> 00:09:54,550 global warming So if you want to think about, where do you intervene, you wanna 136 00:09:54,550 --> 00:09:58,488 ask, where in this cycle are there big numbers? Right, so you look here in terms 137 00:09:58,488 --> 00:10:02,678 of surface radiation. That's a big number. Where you think of solar radiation coming 138 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 139 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 140 00:10:10,806 --> 00:10:14,744 are large. So if you look at number, the amount of [inaudible] reflected by the 141 00:10:14,744 --> 00:10:18,269 surface, that's only a 30, that's not a very big leber. Okay reason five, 142 00:10:18,269 --> 00:10:22,066 experimental design. Now, what i mean by experimental design, well, suppose you 143 00:10:22,066 --> 00:10:26,014 want to come up with some new policies. For example, when the Federal Government, 144 00:10:26,014 --> 00:10:30,161 when they wanted to, when they were trying to decide how to auction off the federal 145 00:10:30,161 --> 00:10:33,909 airwaves, right, for cell phones, they wanted raise as much money as possible. 146 00:10:33,909 --> 00:10:37,956 Well to test auction designer were best they ran some experiments. Well the thing 147 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 148 00:10:41,953 --> 00:10:45,851 and what you see is, this is a round from some auction and these are different 149 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 150 00:10:49,967 --> 00:10:54,353 think, how do I run the best possible experiment, the most informative possible 151 00:10:54,353 --> 00:10:58,570 experiment? And one way to do that, right, is to construct some simple models. 152 00:10:58,570 --> 00:11:02,703 Alright, six, reason six. Institutional design, now this is a biggie and this is 153 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 154 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, 155 00:11:11,720 --> 00:11:15,746 he was one of my mentors in graduate school and Leo won the nobel prize in 156 00:11:15,746 --> 00:11:20,074 economics. Leo won the nobel prize for, which is A field known as mechanism 157 00:11:20,074 --> 00:11:24,947 design. Now this diagram is called the Mount Rider, named after Stan Rider in the 158 00:11:24,947 --> 00:11:29,636 previous picture and Ken Mount, one of his co-authors. And let me explain this 159 00:11:29,636 --> 00:11:33,839 diagram to you because it's very important. What you see here is this 160 00:11:33,839 --> 00:11:38,468 theta, here. What this is supposed to represent is the environment, the set of 161 00:11:38,468 --> 00:11:43,280 technologies, people's preferences, those types of things. X over here represents 162 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 163 00:11:47,298 --> 00:11:51,799 technologies and use our labor and use you know, whatever we have at our disposal to 164 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 165 00:11:55,979 --> 00:12:00,212 like if we could sit around and decide collectively what kind of outcomes we'd 166 00:12:00,212 --> 00:12:04,391 like to have given the technology, this is what we collectively decide, this is 167 00:12:04,391 --> 00:12:07,981 something called a social choice correspondence or a social choice 168 00:12:07,981 --> 00:12:12,147 function. Sort of, what would be the ideal outcome for society? The thing is that 169 00:12:12,147 --> 00:12:16,334 [inaudible] doesn't get the ideal outcome because what happens is [inaudible] wants 170 00:12:16,334 --> 00:12:20,371 though. Because the thing is to get those outcomes you have to use mechanisms and 171 00:12:20,371 --> 00:12:24,358 that what this m stands for, mechanisms. So a mechanism might be something like a 172 00:12:24,358 --> 00:12:28,688 market, a political institution, it might be a bureaucracy. What we want to ask is, 173 00:12:28,688 --> 00:12:33,867 is the outcome we get to the mechanism, right, which goes like this is that equal 174 00:12:33,867 --> 00:12:38,982 to the outcome that we would get, right, ideally and the better mechanism is, the 175 00:12:38,982 --> 00:12:44,091 closer it is to equal to what we ideally want. Example: so my with my undergraduate 176 00:12:44,091 --> 00:12:48,829 students for a homework assignment one time I said, suppose we allocated classes 177 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 178 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 179 00:12:55,647 --> 00:12:58,872 seniors, you know fourth year students register first and then juniors then 180 00:12:58,872 --> 00:13:02,098 sophomores and then freshmen. And the students were asking, should we have a 181 00:13:02,098 --> 00:13:05,323 market? And their first reaction is yes, because markets work. Right. You have 182 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 183 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 184 00:13:12,076 --> 00:13:15,430 about choosing classes, everybody goes, wait a minute, markets may not work well 185 00:13:15,430 --> 00:13:18,581 and the reason why is, you need to graduate. And so seniors need specific 186 00:13:18,581 --> 00:13:22,216 courses and that's why we let seniors register first and if people could bid for 187 00:13:22,216 --> 00:13:25,896 courses then the fraction that had a lot of money might bid away the courses from 188 00:13:25,896 --> 00:13:30,054 seniors and people might never graduate from college so a good institution markets 189 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 190 00:13:35,047 --> 00:13:39,796 is by using models. Reason seven: To help choose among policies in institutions. 191 00:13:39,796 --> 00:13:43,686 Simple example. Suppose [inaudible] a market for pollution permits or a cap and 192 00:13:43,686 --> 00:13:47,268 trade system. We can write down simple model and you can tell us which one is 193 00:13:47,268 --> 00:13:50,942 going to work better. Or here is another example, this is picture of the city of 194 00:13:50,942 --> 00:13:54,616 Ann Arbor and if you look here you see some green areas, right, what these green 195 00:13:54,616 --> 00:13:58,244 things are... Is green spaces. Their is a question should the city of Ann Arbor 196 00:13:58,244 --> 00:14:01,919 create more green spaces. You might think of course, green space is a good thing. 197 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 198 00:14:05,686 --> 00:14:09,268 is all green. What can happen is people could say lets move next to that, lets 199 00:14:09,268 --> 00:14:12,756 build little houses all around here because it is always going to be green, 200 00:14:12,756 --> 00:14:17,350 and that can actually lead to more sprawl. So what can seem like really good simple 201 00:14:17,350 --> 00:14:21,921 ideas may not be good ideas if you actually construct a model to think 202 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. 203 00:14:26,325 --> 00:14:30,558 How can models help us? Well first thing they can do is become real time decision 204 00:14:30,558 --> 00:14:34,790 makers. They can help us figure out when we intervene and when we don't intervene. 205 00:14:34,790 --> 00:14:38,957 Second, they can help us with comparative status. We can figure out, you know what, 206 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 207 00:14:42,963 --> 00:14:46,672 counter-factuals, they can you know appresent a policy, we can sort of run a 208 00:14:46,672 --> 00:14:50,580 model and think about what would have happened if we hadn't chosen that policy 209 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 210 00:14:54,684 --> 00:14:58,892 choices to make models can figure out which choice might be the best or the most 211 00:14:58,892 --> 00:15:02,840 influenced. Fifth, they can help us with experimental design. They can help us 212 00:15:02,840 --> 00:15:06,841 design experiments in order to develop better policies and better strategies. 213 00:15:06,841 --> 00:15:10,633 Sixth, they can help us design institutions themselves figuring out if we 214 00:15:10,633 --> 00:15:14,478 have a market here, should we have a democracy, should we use a bureaucracy. 215 00:15:14,478 --> 00:15:18,582 And seventh, finally, they can help us choose among policies and institutions so 216 00:15:18,582 --> 00:15:22,842 if we are thinking about one policy or another policy we can use models to decide 217 00:15:22,842 --> 00:15:25,596 among the two. All right. Thank you.