We live in a complex world with diverse people, firms, and governments whose behaviors aggregate to produce novel, unexpected phenomena. We see political uprisings, market crashes, and a never ending array of social trends. How do we make sense of it? Models. Evidence shows that people who think with models consistently outperform those who don't. And, moreover people who think with lots of models outperform people who use only one. Why do models make us better thinkers? Models help us to better organize information - to make sense of that fire hose or hairball of data (choose your metaphor) available on the Internet. Models improve our abilities to make accurate forecasts. They help us make better decisions and adopt more effective strategies. They even can improve our ability to design institutions and procedures. In this class, I present a starter kit of models: I start with models of tipping points. I move on to cover models explain the wisdom of crowds, models that show why some countries are rich and some are poor, and models that help unpack the strategic decisions of firm and politicians. The models covered in this class provide a foundation for future social science classes, whether they be in economics, political science, business, or sociology. Mastering this material will give you a huge leg up in advanced courses. They also help you in life. Here's how the course will work. For each model, I present a short, easily digestible overview lecture. Then, I'll dig deeper. I'll go into the technical details of the model. Those technical lectures won't require calculus but be prepared for some algebra. For all the lectures, I'll offer some questions and we'll have quizzes and even a final exam. If you decide to do the deep dive, and take all the quizzes and the exam, you'll receive a Course Certificate. If you just decide to follow along for the introductory lectures to gain some exposure that's fine too. It's all free. And it's all here to help make you a better thinker!
Solow Growth Model
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From the course by University of Michigan
Model Thinking
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From the lesson
Tipping Points & Economic Growth
In this section, we cover tipping points. We focus on two models. A percolation model from physics that we apply to banks and a model of the spread of diseases. The disease model is more complicated so I break that into two parts. The first part focuses on the diffusion. The second part adds recovery. The readings for this section consist of two excerpts from the book I'm writing on models. One covers diffusion. The other covers tips. There is also a technical paper on tipping points that I've included in a link. I wrote it with PJ Lamberson and it will be published in the Quarterly Journal of Political Science. I've included this to provide you a glimpse of what technical social science papers look like. You don't need to read it in full, but I strongly recommend the introduction. It also contains a wonderful reference list.
Meet the Instructors
Scott E. PageProfessor of Complex Systems, Political Science, and Economics
Center for the Study of Complex Systems
Hi, we just took in a very simple growth model and in that growth model we saw that
well, growth stopped, right. Once we got to 144 machines and an output of 120, we
no longer got any growth. So we use that very simple model to get at. A really
important fact, that without innovation, if technology stays fixed, growth will
stop. Now, sure the labor supply could get bigger, we could have more workers or
something like that. But holding the amount of labor fixed and holding that
technology fixed, if we've got a fixed savings rate, and a fixed rate of
depreciation, there's no more growth at some point. We're gonna go up, up, up, up,
up, and then stop. Well. That hasn't been human experience right. Economic well
being continue to go way up right and GDP continues to go up, and so what's driving
that. Well to get at that we're gonna look at a deeper model, richer model known as
the solo growth model. And what's nice about this model and I love about this
model, we're just gonna add one variable. We're just going to add one more variable
to our other model, and that's suddenly going to give us a way to include
innovation. Now, just to make this, you know. More interesting [laugh], maybe more
real. These models are developed by real people. Right, and so, the speaker model's
developed again by Bob Solo. And Bob Solo is an economist at MIT. And here's Bob
right here. And this is Bob actually testifying before the House Science
Technology committee on the need to have multiple models to understand the economy.
Right, so this is a group of economists here and we're standing up and we're
swearing to tell the truth, the whole truth, and nothing but the truth about why
models are important to understand where growth comes from. And in this particular
case, to prevent things like, you know, the home mortgage crisis, which cost us
all a lot of money. Alright, so how does Solo's model work? What does Bob's model
do? Well, what Bob does is this wonderful thing. He includes. Includes one more
variable. So everything's the same as before, [inaudible] labor, capital,
depreciation, savings. But we're gonna include this thing A of T which stands for
technology. So when A is low technology is low when A is high technology is high it's
better so A's just going to be the parameter we can tune to effect sort of
how much or how good is the technology in the economy so for making cocoanut picking
machines [laugh] right A is really small and if we're making incredibly cool you
know laser pointers and IPhones and stuff like that, technology is great. Okay, so
this is it. Very simple formula. Output is just equal to the technology at that time,
times capital to some. Beta. And L to sum one minus. Now wait a minute. This also
got a little more complicated. Now I got these betas here. Now before I had square
roots. Well, if beta equals one half. Right, so beta is a half. Then this is
just the square root of labor times the square root of capital. Right? Easy. If
beta gets bigger than a half, that means that capital matters a little bit more. If
beta gets less than a half, then that means that capital matters a little bit
less. So depending on the technology, it could be that it's a capital intensive
technology so that beta would be big. Doesn't use that much capital and beta
tends to be relatively small. So, you can estimate different [inaudible] betas for
different manufacturing processes or even for different countries, right? And a half
was just a convenience we assumed. So that's actually something that we take
models to beta, you go and estimate and figure out what is beta. And for us, if
we're just trying to get the ideas here, right? And we're going to take beta equals
a half. So let's go back, and just to remind ourselves of where we were before,
right? Remember our total output was ten because we [inaudible] a hundred workers,
so ten times the square root of N. We had a savings rate of 30%. And we added a
depreciation at a quarter. And we went through and we did all that stuff we saw
the equilibrium where the investment was exactly equal the depreciation. When we
got to that happened we put an output of 120 which required 144 machines, right? So
that meant that we were going to invest in 36 new machines but we'd lose 36 machines
to depreciation. So that was our equilibrium. Now we want to say well, what
would innovation do? Well, innovation would do, was, would we'd put an A in
front of this. Now have an A in front of this ten times the square root of m. So,
let's do that and let's see what happens. So now we're going to say the output it.
Two times ten times the square root of eleven. So what we're going to do is,
we're going to assume that somebody had a technological innovation and our coconut
machines are now, somehow like, everything's twice as good, or twice as
productive. Okay, well now let's, let's walk through the math. So, what's our
investment gonna be? Investment is gonna be 0.3. Times twenty the squared of M. So
that's gonna be six times the squared of M. And what's our depreciation? Well,
that's gonna be one-fourth M, right? So that's just M over four. And so we just
have to set these things equal again, right? So six squared of M equals M over
four. So that means 24. Square root of M, equals M. So that means 24, equals square
root of M. So that means M equals. Right? So our equilibrium is gonna be m is equal
496. And output, right, is gonna be two times ten times the square root of 496,
which is 24, right? So that's 24 times ten which is 240, which is 480, right. So our
output 480. Before it was 120, and now it's 480. So, think about it. Productivity
doubled, right, [inaudible] our technology got twice as good. But long run GDP went
up by four. But why is that, well let's look back at our numbers here. Okay, we
became twice as productive so that means if we had kept the number of machines at a
144, we now would have an output of 28, 240. Right, so we would have doubled where
we were at. But we didn't. Keep the number machines at 144 when the technology are
better we actually increase the number machines to 496. So when you have a
technological change two things happen. First you just get more productive you get
more stuff, second because you?re getting more stuff it makes sense to invest in
more machines. So there's this multiplier effect so that means productivity goes up
by two right. Output eventually the long run, long run [inaudible] goes up by four
right, and this is what you think of as sort of as a innovation multiplier because
it happens were there's these two effects, right. Labor and capital become more
productive. So that, boom, you just get more stuff. But second of all, because
they're more productive it makes sense to invest in more machines so then you get
even more stuff. So there's this multiplier. Well, let's think about it.
Productivity are up by two. Total it up. Eventually in the long run, not
immediately. Gotta build up all of those machines. It goes up by four. Well that
leads to a puzzle and here's where models are really useful. Is it additive, or is
it multiplicative? Here's the issue with two. It could be that productivity went up
by two. And so we get two plus two, and, so [inaudible] by four. Or it could be we
get 2X2, two squared is the reason productivity went up by four. So we wanna
figure out, is this additive effect, right? The machine effect plus the
productivity effect. Or is it multiplicative, is it 2X2? Well, to make
sense of that, what we can do is, we can increase the multiplier to three. Because
if it's additive then we get six, and if it's multiplicative, we get nine. Right so
if we make this three times as productive we're going to ask in the long run do we
end up with six times as much stuff or do we end up with nine times as much stuff
and again this is [inaudible] why do we model we model to get the logic right okay
without the model. It'd be very hard to figure out, is this gonna go by six, or is
this gonna go by nine. Heck, we might not have even have got the second effect of
more machines. Right, so the model was only useful just to giving us that. Now
it's gonna tell us the magnitude of the effect. 'Kay, just to get our bearings
again, let's remember where we started from. We start from an existing technology
where it's just the square root of labor times the square root of machines. We see
100 units of labor. So it's ten times the square root of M. We save 30 percent and
invest that in new machines. Right, so that's gonna be three times the square
root of M. We lose a quarter of our machines to depreciation, so that's just M
over four. We set those things equal. We get m equals 144, we get output of 120.
That's our equilibrium. Now we wanna say lets triple it okay so let?s suddenly
assume there's an A that comes in that's got a value of three, so now we're going
to get three times ten times the squared of M [inaudible] 30 times the squared of M
and let?s see what happens okay so what's our total investment going to be? Well
that's going to be 0.3 times 30 times the squared of M so that's going to be nine.
Times the square root of M. What's our depreciation? Well, that's still just M
over four. So let's set these equal. Nine times the square root of M equals M over
four, so that means 36 squared of M equals M. So that means 36 equals the square root
of M. So is equal to 36 squared, right? So M, we just keep it as 36 squared. Right?
So N equals 36 squared. What's total output gonna be? So if we've got 36
squared machines, which is a big number, what's output gonna be? Well, output is
three times ten times the square root of 36 squared. So that's three times ten
times 36. Well, three times 36 is 108, so that's 1,080. So what happened when we
made ourselves three times as productive? Well. Total output went up nine times. So
what we see, remember what was our question? Our question was, is it
additive? Are we gonna get three plus three are six. Or multiplicative, three
times three are nine? The answer is, it's gonna be multiplicative. We're gonna three
times three is nine. Two effects multiplied on top of one another. Right,
the first one is we just get more stuff. The second one is we invest in more
machines. And those two effects get multiplied together. So becoming three
times more effective means we get nine times in the long run equilibrium. So let
me summarize for a second. In the simple growth model, growth stopped. Right? At
some point we got to 144 machines and then we no longer had any growth. When we go to
the Solow growth model, what happens is, if we can continue to increase that A,
right? So, if we can continue to increase our productivity, then growth can
continue. That sort of begs the question. Where do increases in A come from? And
this has led to what people call endogenous growth models. So an endogenous
growth model, labor can go to things like picking coconuts. Labor can also go to
things like, investing in new technologies, research and design, and
those sorts of things, to try and increase that A parameter. So what we can think of
is before all of our labor went to increasing cap, picking coconuts, right?
Now, that labor could also go to doing research on new coconut picking machines.
What you get in indigenous growth model is how much labor goes into actually making
stuff, and how much goes into research and design and thinking, right. It's a choice
variable. In the model, right, and you solve for how much of that you get. Quick
summary, right. Growth ceases without innovation, if that's true. Everybody
should be pro innovation. And in fact, most people are. Right, so here's two
quotes. Here's a fun little quiz. One of these quotes is from President Obama, who
is a democrat. The other quote is from President Reagan. I want you to try and
guess which quote came from Obama, and which quote came from Reagan. All right?
So both Reagan are pro innovation, right? They, they are, because they are pro GDP
growth, because [inaudible] gonna lift those people out of poverty. Right? We
wanna make everyone better off. Because if we can lift people out of poverty, we make
people happier. And what we've learned is the way to do that, right, is. First, by
investing in capital. Right? Because that makes us, you know, all do better. We get
to the 144 machines. But at some point then growth stops and then you need
investment in technology. Then investment in technology leads to innovation which
raises the whole thing up and we get this multiplier effect. Right? We get the
increased productivity and then we also get the incentives to produce more
machines. Right? Which raises our statement [inaudible] even more. So that's
the E, in essence what growth theory is. Thanks.
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