0:00:00.000,0:00:05.404
Hi, in this lecture we are going to look[br]at our fourth category of reasons about why

0:00:05.404,0:00:09.470
you'd want to take a course in modeling,[br]why modeling is so important. And that is

0:00:09.470,0:00:12.983
to help you make better decisions,[br]strategize better, and design things

0:00:12.983,0:00:16.948
better. So lets get started, this should[br]be a lot of fun. Alright, so first reason

0:00:16.948,0:00:20.963
why models are so useful. They are good[br]decision aides, they help you make better

0:00:20.963,0:00:25.044
decisions. Let me give you an example.[br]These get us going here. So what you see

0:00:25.044,0:00:29.383
is a whole bunch of different financial[br]institutions, these are companies like

0:00:29.383,0:00:33.054
Bear Sterns, AIG, CitiGroup, Morgan[br]Stanley and this represents the

0:00:33.054,0:00:37.393
relationship between these companies, in[br]terms of how one of their economic success

0:00:37.393,0:00:41.490
depends on another. Now imagine you are[br]the federal government and you've got a

0:00:41.490,0:00:45.340
financial crisis. So a lot of these[br]companies, or some of these companies are

0:00:45.340,0:00:49.546
starting to fail and you've got to decide[br]okay do I bail them out, do I save one of

0:00:49.546,0:00:53.802
these companies? Well now lets use one of[br]these very simple models to help make that

0:00:53.802,0:00:57.957
decision. So to do that we need a little[br]more of an understanding of what

0:00:57.957,0:01:02.254
these numbers represent. So lets look at[br]AIG which is right here. And JP Morgan

0:01:02.254,0:01:07.970
which is right here So now we see a number[br]of 466 between the two of those. What that

0:01:07.970,0:01:12.958
number represents is how correlated JP[br]Morgan success is with AIG success. In

0:01:12.958,0:01:18.140
particular how correlated their failures are. So if[br]AIG has a bad day, how likely is it that

0:01:18.140,0:01:23.451
JP Morgan has a bad day? And we see that[br]it is a really big number. Now if you look

0:01:23.451,0:01:28.828
up here at this 94, this represents the link between Wells[br]Fargo and Lehman Brothers. What that tells

0:01:28.828,0:01:34.139
us is that Lehman Brothers has a bad day,[br]well it only has a small effect on Wells

0:01:34.139,0:01:38.344
Fargo and vice versa. So now you are the[br]government and you got to decide, okay who do I

0:01:38.344,0:01:43.169
want to bail out? Nobody or somebody? Lets[br]look at Lehman Brothers. There's only

0:01:43.169,0:01:48.243
three lines going in and out of Lehman[br]Brothers and one is a 94. I guess four

0:01:48.243,0:01:53.382
lines, one is a 103, one is a 158 and one[br]is a 155. Those are relatively small

0:01:53.382,0:01:58.541
numbers. So if you're the government you[br]say, okay Lehman Brothers has been around

0:01:58.541,0:02:03.616
a long time and its an important company,[br]these numbers are pretty small, if they

0:02:03.616,0:02:08.691
fail it doesn't look like these other[br]companies would fail. But now lets look at

0:02:08.691,0:02:13.386
AIG. We've got a 466, we've got a 441,[br]we've got a 456, we've got a 390 and a

0:02:13.386,0:02:19.336
490. So there are huge numbers associated[br]with AIG. Because there is a huge number

0:02:19.336,0:02:23.171
you basically have to figure, you know[br]what we probably have to prop AIG back up.

0:02:23.171,0:02:27.102
Even if you don't want to because if you[br]don't there is the possibility that this

0:02:27.102,0:02:30.794
whole system will fail. So what we see[br]here is the incredible power of models,

0:02:30.794,0:02:34.581
right to help us make a better decision.[br]The government did let Lehman Brothers

0:02:34.581,0:02:37.745
fail, and terrible for Lehman[br]Brothers, but the economy sort of

0:02:37.745,0:02:41.677
soldiered on. They didn't let AIG fail and[br]we don't know for sure that it would've

0:02:41.677,0:02:45.883
and we don't know for sure that the whole[br]financial you know apparatus United

0:02:45.883,0:02:51.153
States, they propped up AIG and you know[br]we made it, the country made it. It looks

0:02:51.153,0:02:55.533
they've made a reasonable decision.[br]Alright so that is big financial

0:02:55.533,0:03:00.561
decisions. Lets look at something more[br]fun. This is a simple sort of logic puzzle

0:03:00.561,0:03:05.400
that will help us see how models can be[br]useful. Now this is a game called, The

0:03:05.400,0:03:10.346
Monty Hall Problem and its named after[br]Monty Hall was the host of a game show

0:03:10.346,0:03:15.196
called, Lets Make a Deal that aired during[br]the 1970's. Now the problem I'm going to

0:03:15.196,0:03:20.106
describe to you is a characterization of a[br]event that could happen on the show. Its

0:03:20.106,0:03:24.542
one of several scenarios on the show.[br]Here's basically how it works. There's

0:03:24.542,0:03:29.392
three doors. Behind one of these doors is[br]a prize, behind the other two doors there's some, you

0:03:29.392,0:03:34.123
know, silly thing like a goat right, or a[br]woman dressed up in a ballerinas outfit.

0:03:34.123,0:03:38.834
So one of them had something fantastic[br]like a new car or a washing machine. Now

0:03:38.834,0:03:44.322
what you get to do is you pick one door.[br]So maybe you pick door number one, right,

0:03:44.322,0:03:49.810
so you pick door number one. Now Monty[br]knows where the prize is so the two doors

0:03:49.810,0:03:54.592
you didn't pick, one of those always has[br]to go behind it, where you know, silly

0:03:54.592,0:03:59.070
prize behind it. So because one of us[br]always has a silly prize behind it, he

0:03:59.070,0:04:03.898
can always show you one of those other two[br]doors. So you pick door number one, right,

0:04:03.898,0:04:08.552
and what Monty does, you picked one and[br]what Monty does is he then opens up door

0:04:08.552,0:04:13.089
number three and says, here's a goat, then[br]he says, hey, do you want to switch to

0:04:13.089,0:04:19.416
door number two? Well, do you? Alright,[br]that's a hard problem so let's first try

0:04:19.416,0:04:23.835
to get the logic right then we'll right[br]down a formal model. So, it's easier to

0:04:23.835,0:04:28.028
see the logic for this problem by[br]increasing the number of doors. So let's

0:04:28.028,0:04:32.391
suppose there's five doors, and now[br]there's five doors, let's suppose you pick

0:04:32.391,0:04:37.037
this blue door, this bright blue door. The[br]probability that you're correct is 1/5th.

0:04:37.037,0:04:41.343
Right, one of the doors has prize, the[br]probability you're correct is 1/5th. So

0:04:41.343,0:04:46.023
the probability that you're not correct Is[br]4/5ths. So, there's a 1/5th chance you're

0:04:46.023,0:04:50.064
correct. There's a 4/5ths chance you're[br]not. Now let's suppose that Monty

0:04:50.064,0:04:54.218
[inaudible] is also playing this game,[br]because he knows again, he knows the

0:04:54.218,0:04:58.483
answer. So Monty is thinking, okay, well,[br]you know what, I'm gonna show you that

0:04:58.483,0:05:03.624
it's not behind the yellow door. And then[br]he says, you know what else I'm going to

0:05:03.624,0:05:08.565
show you, that it's not behind the pink[br]door. [inaudible]. I'm gonna be nice, I'm

0:05:08.565,0:05:13.630
gonna show you it's not behind the green[br]door. Now he says, do you want to switch

0:05:13.630,0:05:18.525
to the light blue door to the dark blue[br]door. Well in this case, you should start

0:05:18.525,0:05:23.049
thinking, you know initially the[br]probability I was right was only 1/5th And

0:05:23.049,0:05:26.593
he revealed all those other doors that[br]doesn't seem to have the prize. It seems

0:05:26.593,0:05:30.316
much more likely that this is the correct[br]door than mine's the correct door and in

0:05:30.316,0:05:33.725
fact it is much more [inaudible]. The[br]probability is 4/5ths it's behind that

0:05:33.725,0:05:37.358
dark blue door and only 1/5th it's behind[br]your door. So you should switch and you

0:05:37.358,0:05:41.037
should also switch in the case of two. Now[br]let's formalize this. This isn't so much,

0:05:41.037,0:05:44.465
this is, we'll use the simple decision[br]three model. To show why in fact you

0:05:44.465,0:05:48.318
should switch. Alright, so let's start[br]out, we'll just do some basic probability.

0:05:48.318,0:05:52.220
There's three doors, you pick door number[br]one, the probability you're right is a

0:05:52.220,0:05:56.319
third and the probability that it's door[br]number two is a third and the probability

0:05:56.319,0:06:00.320
that it's door number three is a third.[br]Now, what we want to do is break this into

0:06:00.320,0:06:04.599
two sets. There's a 1/3rd chance that[br]you're right and there's a 2/3rds chance

0:06:04.599,0:06:09.574
that you're wrong. After you pick door[br]number one, the prize can't be moved. So

0:06:09.574,0:06:14.936
it's either behind door number two, number[br]three or if you got it right, it's behind

0:06:14.936,0:06:20.363
door number one. So let's think about what[br]Monty can do. Monty can basically show you

0:06:20.363,0:06:25.403
if it's behind door number one or door[br]number two, he can show you door number

0:06:25.403,0:06:30.197
three. He can say look, there's the goat.[br]Well if he does that, because he can

0:06:30.197,0:06:34.787
always show you one of these doors,[br]nothing happened to your probability of

0:06:34.787,0:06:39.682
1/3rd. There's a 1/3rd chance you were[br]right before since he can always show you

0:06:39.682,0:06:44.210
a door, there's still only a 1/3rd chance[br]you're right. Right, alternatively,

0:06:44.210,0:06:48.452
suppose that, It was behind door number[br]three well then he can show you door

0:06:48.452,0:06:52.285
number two. He can say the goat's here.[br]So, it's still the case that nothing

0:06:52.285,0:06:56.377
happens to your probability. The reason[br]why when you think about these two sets,

0:06:56.377,0:07:00.313
you didn't learn anything. You learn[br]nothing about this other set right here,

0:07:00.313,0:07:04.301
the 2/3rds chance you're wrong because he[br]can always show you a goat. So your

0:07:04.301,0:07:08.497
initial chan-, your initial probability[br]being correct was 1/3rd, your final chance

0:07:08.497,0:07:12.692
of being correct was probably 1/3rd. So[br]just this sort of idea of drawing circles

0:07:12.692,0:07:16.855
and writing probabilities allows us to see[br]that the correct The correct decision on

0:07:16.855,0:07:20.197
the [inaudible] problem is to switch,[br]right. Just like when we looked at that

0:07:20.197,0:07:23.540
financial decision that the Federal[br]Government had to make with the circles

0:07:23.540,0:07:27.102
and the arrows, you draw that out, and you[br]realize the best decision is to let the

0:07:27.102,0:07:31.069
[inaudible] fail. Bailout AIG. Alright so[br]lets move on a look sort of the next

0:07:31.069,0:07:35.576
reason that models can be helpful and that[br]is comparative statics. What do I mean by

0:07:35.576,0:07:39.547
that? Well here is a standard model from[br]economics, what we can think of is

0:07:39.547,0:07:43.786
comparative statics means you know you[br]move from one equilibrium to another. So

0:07:43.786,0:07:47.971
what you see here is that S is a supply[br]curve, that is a supply curve for some

0:07:47.971,0:07:52.317
good, and D, D1 and D2 are demand curves.[br]So what you see is demand shifting out. So

0:07:52.317,0:07:56.624
when this demand shifts out. In this way[br]what we get is that more goods are sold

0:07:56.624,0:08:00.993
the quantity goes up, and the price goes[br]up so people want more of something, more

0:08:00.993,0:08:05.307
is gonna get sold and the price is up. So[br]this is where you start seeing how the

0:08:05.307,0:08:09.357
equilibrium moves so this is again a[br]simple example of how. Models help us

0:08:09.357,0:08:13.754
understand how the world will change,[br]equilibrium world, just by drawing some

0:08:13.754,0:08:18.266
simple figures. Alright, reason number[br]three. Counter factuals, what do I mean by

0:08:18.266,0:08:22.837
that? Well you can think you only get to[br]run the world once, you only get to run

0:08:22.837,0:08:27.465
the tape one time. But if we write models[br]of the world we can sort of re-run the

0:08:27.465,0:08:31.919
tape using those models. So here is an[br]example, in April of 2009, The spring of

0:08:31.919,0:08:36.393
2009, the Federal Government decided to[br]implement a recovery plan. Well what you

0:08:36.393,0:08:40.369
see here is sort of the effect, this line[br]right here shows the effect with the

0:08:40.369,0:08:44.446
recovery plan, and this line shows, says,[br]this is what a model shows what would of

0:08:44.446,0:08:48.473
happened without the recovery plan. Now we[br]can't be sure that, that happened, but,

0:08:48.473,0:08:52.142
you know, at least we have some[br]understanding, perhaps, of what the effect

0:08:52.142,0:08:56.322
of recovery plan was, which is great. So[br]these counter factuals are not going to be

0:08:56.322,0:09:00.461
exact, there going to be approximate, but[br]still they help us figure out. After the

0:09:00.461,0:09:05.150
fact whether a policy was a good policy or[br]not. Reason number four. To identify and

0:09:05.150,0:09:09.781
rank levers. So what we are going to do is[br]look at a simple model of contagion of

0:09:09.781,0:09:14.184
failure, so this is a model where one[br]country might fail, so in this case that

0:09:14.184,0:09:18.816
country is going to be England. Then we[br]can ask what happens over time, so you can

0:09:18.816,0:09:23.447
see that initially after England fails, we[br]see Ireland and Belgium fail, and after

0:09:23.447,0:09:27.716
that we see France fail. And after that we[br]see Germany fail. So what this tells us is

0:09:27.716,0:09:31.626
that in terms of its effect on the worlds[br]financial system, London is a big lever,

0:09:31.626,0:09:35.440
so London is something we care about a[br]great deal. Now lets take another policy

0:09:35.440,0:09:39.060
issue, climate change. One of the big[br]things in climate change is the carbon

0:09:39.060,0:09:42.825
cycle, its one of the models that you use[br]all the time, simple carbon models. We

0:09:42.825,0:09:46.832
know that total amount of carbon is fixed,[br]that can be up in the air or down on the

0:09:46.832,0:09:50.645
earth, if it is down on the earth it is[br]better because it doesn't contribute to

0:09:50.645,0:09:54.550
global warming So if you want to think[br]about, where do you intervene, you wanna

0:09:54.550,0:09:58.488
ask, where in this cycle are there big[br]numbers? Right, so you look here in terms

0:09:58.488,0:10:02.678
of surface radiation. That's a big number.[br]Where you think of solar radiation coming

0:10:02.678,0:10:06.717
in, that's a big number coming in. So, you[br]wanna, you think about where you want to

0:10:06.717,0:10:10.806
have a policy in fact, you want to think[br]about it in terms of where those numbers

0:10:10.806,0:10:14.744
are large. So if you look at number, the[br]amount of [inaudible] reflected by the

0:10:14.744,0:10:18.269
surface, that's only a 30, that's not a[br]very big leber. Okay reason five,

0:10:18.269,0:10:22.066
experimental design. Now, what i mean by[br]experimental design, well, suppose you

0:10:22.066,0:10:26.014
want to come up with some new policies.[br]For example, when the Federal Government,

0:10:26.014,0:10:30.161
when they wanted to, when they were trying[br]to decide how to auction off the federal

0:10:30.161,0:10:33.909
airwaves, right, for cell phones, they[br]wanted raise as much money as possible.

0:10:33.909,0:10:37.956
Well to test auction designer were best[br]they ran some experiments. Well the thing

0:10:37.956,0:10:41.953
you want to do, you want to think about,[br]so here is the example of the experiment

0:10:41.953,0:10:45.851
and what you see is, this is a round from[br]some auction and these are different

0:10:45.851,0:10:49.967
bidders and, you know, the cost for. That[br]they paid. What you can do, you want to

0:10:49.967,0:10:54.353
think, how do I run the best possible[br]experiment, the most informative possible

0:10:54.353,0:10:58.570
experiment? And one way to do that, right,[br]is to construct some simple models.

0:10:58.570,0:11:02.703
Alright, six, reason six. Institutional[br]design, now this is a biggie and this is

0:11:02.703,0:11:07.211
one that means a lot to me. The person you[br]see at the top here, this is Stan Rider he

0:11:07.211,0:11:11.720
was one of my advisors in graduate school[br]and the man at the bottom is Leo Herwicks,

0:11:11.720,0:11:15.746
he was one of my mentors in graduate[br]school and Leo won the nobel prize in

0:11:15.746,0:11:20.074
economics. Leo won the nobel prize for,[br]which is A field known as mechanism

0:11:20.074,0:11:24.947
design. Now this diagram is called the[br]Mount Rider, named after Stan Rider in the

0:11:24.947,0:11:29.636
previous picture and Ken Mount, one of his[br]co-authors. And let me explain this

0:11:29.636,0:11:33.839
diagram to you because it's very[br]important. What you see here is this

0:11:33.839,0:11:38.468
theta, here. What this is supposed to[br]represent is the environment, the set of

0:11:38.468,0:11:43.280
technologies, people's preferences, those[br]types of things. X over here represents

0:11:43.280,0:11:47.298
the outcomes, what we want to have happen.[br]So how we want to sort of use our

0:11:47.298,0:11:51.799
technologies and use our labor and use you[br]know, whatever we have at our disposal to

0:11:51.799,0:11:55.979
create good outcomes. Now this arrow here[br]is sort of , it's what we desire, it's

0:11:55.979,0:12:00.212
like if we could sit around and decide[br]collectively what kind of outcomes we'd

0:12:00.212,0:12:04.391
like to have given the technology, this is[br]what we collectively decide, this is

0:12:04.391,0:12:07.981
something called a social choice[br]correspondence or a social choice

0:12:07.981,0:12:12.147
function. Sort of, what would be the ideal[br]outcome for society? The thing is that

0:12:12.147,0:12:16.334
[inaudible] doesn't get the ideal outcome[br]because what happens is [inaudible] wants

0:12:16.334,0:12:20.371
though. Because the thing is to get those[br]outcomes you have to use mechanisms and

0:12:20.371,0:12:24.358
that what this m stands for, mechanisms.[br]So a mechanism might be something like a

0:12:24.358,0:12:28.688
market, a political institution, it might[br]be a bureaucracy. What we want to ask is,

0:12:28.688,0:12:33.867
is the outcome we get to the mechanism,[br]right, which goes like this is that equal

0:12:33.867,0:12:38.982
to the outcome that we would get, right,[br]ideally and the better mechanism is, the

0:12:38.982,0:12:44.091
closer it is to equal to what we ideally[br]want. Example: so my with my undergraduate

0:12:44.091,0:12:48.829
students for a homework assignment one[br]time I said, suppose we allocated classes

0:12:48.829,0:12:52.249
by a market So, you know, if you had to[br]bid for classes, would that be a good

0:12:52.249,0:12:55.647
thing or a bad thing? Well, currently the[br]way we do it is there's a hierarchy. So

0:12:55.647,0:12:58.872
seniors, you know fourth year students[br]register first and then juniors then

0:12:58.872,0:13:02.098
sophomores and then freshmen. And the[br]students were asking, should we have a

0:13:02.098,0:13:05.323
market? And their first reaction is yes,[br]because markets work. Right. You have

0:13:05.323,0:13:08.764
this, you know, you have a market, what[br]you get here is sort of what you expect to

0:13:08.764,0:13:12.076
get. Right, what you'd like to get, so[br]it's sort of equal. But when they thought

0:13:12.076,0:13:15.430
about choosing classes, everybody goes,[br]wait a minute, markets may not work well

0:13:15.430,0:13:18.581
and the reason why is, you need to[br]graduate. And so seniors need specific

0:13:18.581,0:13:22.216
courses and that's why we let seniors[br]register first and if people could bid for

0:13:22.216,0:13:25.896
courses then the fraction that had a lot[br]of money might bid away the courses from

0:13:25.896,0:13:30.054
seniors and people might never graduate[br]from college so a good institution markets

0:13:30.054,0:13:35.047
may be good in some settings they may not[br]be in others. The way we figure that out

0:13:35.047,0:13:39.796
is by using models. Reason seven: To help[br]choose among policies in institutions.

0:13:39.796,0:13:43.686
Simple example. Suppose [inaudible] a[br]market for pollution permits or a cap and

0:13:43.686,0:13:47.268
trade system. We can write down simple[br]model and you can tell us which one is

0:13:47.268,0:13:50.942
going to work better. Or here is another[br]example, this is picture of the city of

0:13:50.942,0:13:54.616
Ann Arbor and if you look here you see[br]some green areas, right, what these green

0:13:54.616,0:13:58.244
things are... Is green spaces. Their is a[br]question should the city of Ann Arbor

0:13:58.244,0:14:01.919
create more green spaces. You might think[br]of course, green space is a good thing.

0:14:01.919,0:14:05.686
The problem is when you, if you buy up a[br]bunch of green space like this area here

0:14:05.686,0:14:09.268
is all green. What can happen is people[br]could say lets move next to that, lets

0:14:09.268,0:14:12.756
build little houses all around here[br]because it is always going to be green,

0:14:12.756,0:14:17.350
and that can actually lead to more sprawl.[br]So what can seem like really good simple

0:14:17.350,0:14:21.921
ideas may not be good ideas if you[br]actually construct a model to think

0:14:21.921,0:14:26.325
through it. [sound] okay, we've covered a[br]lot. So, let's give a quick summary here.

0:14:26.325,0:14:30.558
How can models help us? Well first thing[br]they can do is become real time decision

0:14:30.558,0:14:34.790
makers. They can help us figure out when[br]we intervene and when we don't intervene.

0:14:34.790,0:14:38.957
Second, they can help us with comparative[br]status. We can figure out, you know what,

0:14:38.957,0:14:42.963
what's likely to happen, right, if we make[br]this choice. Third, they can help us with

0:14:42.963,0:14:46.672
counter-factuals, they can you know[br]appresent a policy, we can sort of run a

0:14:46.672,0:14:50.580
model and think about what would have[br]happened if we hadn't chosen that policy

0:14:50.580,0:14:54.684
Fourth, we can use them to identify and[br]rank levers. Often as you've got lots of

0:14:54.684,0:14:58.892
choices to make models can figure out[br]which choice might be the best or the most

0:14:58.892,0:15:02.840
influenced. Fifth, they can help us with[br]experimental design. They can help us

0:15:02.840,0:15:06.841
design experiments in order to develop[br]better policies and better strategies.

0:15:06.841,0:15:10.633
Sixth, they can help us design[br]institutions themselves figuring out if we

0:15:10.633,0:15:14.478
have a market here, should we have a[br]democracy, should we use a bureaucracy.

0:15:14.478,0:15:18.582
And seventh, finally, they can help us[br]choose among policies and institutions so

0:15:18.582,0:15:22.842
if we are thinking about one policy or[br]another policy we can use models to decide

0:15:22.842,0:15:25.596
among the two. All right. Thank you.