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!
Path Dependence
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En provenance du cours de University of Michigan
Model Thinking
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Path Dependence & Networks
In this set of lectures, we cover path dependence. We do so using some very simple urn models. The most famous of which is the Polya Process. These models are very simple but they enable us to unpack the logic of what makes a process path dependent. We also relate path dependence to increasing returns and to tipping points. The reading for this lecture is a paper that I wrote that is published in the Quarterly Journal of Political Science
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Scott E. PageProfessor of Complex Systems, Political Science, and Economics
Center for the Study of Complex Systems
Hi. In this set of lectures, we're going to talk about path dependence. Now loosely
speaking, path dependence means what happens now depends on what happened along
the path to get here, like history. So history matters. So this will be different
than our Markov process models where we found that history doesn't matter at all.
What we're going to do in these lectures is frame them around a simple class of
models known as urn models. And these urn models are going to help us flush out a
lot of the logic behind what causes path dependence, what really is path
dependence, and also distinguish between different types of path dependence. So for
example, an outcome, what happens today could be path dependent. In addition the
equilibrium what happens in the long run the distribution over all possible
outcomes could also be path dependent. So we're going to flash those things out. So
when we talk about path dependents, what do we mean? One of the most famous example
of path dependence involves the typewriter keyboard that's probably in front of most
of you, many of you right now. This typewriter keyboard, this standard
configuration [inaudible] is called the QWERTY typewriter keyboard. And that's
because if you look across the top row of keys starting on the left, you see the
word QWERTY. It's not really a word, but you see those letters. Now initially,
there were lots of different keyboard configurations, but it turned out that the
path through which history played out, that QWERTY ended up getting locked in due
to a process of what we're gonna call increasing returns. The more people that
had QWERTY. [inaudible] the more people want [inaudible] and the more typewriters
that got built with [inaudible] and it got locked in so that everybody uses the
accordion typewriter. Or at least nearly everybody. Now typewriters are one thing
but path dependence occurs in a lot of situations, so let's first define what we
mean. So like path dependence what I mean is that the outcome probably. What's going
to happen depends on the path, the sequence of previous outcomes. So what
happens in the past has an impact on it. It doesn't necessarily determine, that's
why I'm saying probabilities here. It affects. What's likely to happen now. So
the past matters. History matters. And what are cases where this is true, where
history matters. Well, there's a lot of them. They're easy to think of. So for
example, we think of choices over technology. A QWERTY keyboard is a simple
technology, but if you think of things like whether you have alternating current
or direct current, that's an example of one process winning out over another.
Gasoline cars versus electric cars. And now electric cars are rising back up. So
again, technological choice can depend on the history. Other examples, the law. How
the law evolves over time depends on what has sort of become law in the past. So
precedent plays a large role in law and as precedent plays a large. Drawn law. That
means past outcomes influence current outcomes. It's even the case of where they
give institutional choices. Do you have a single pair of healthcare system? Do you
have a multi-pair healthcare system? Do you have a situation where you have
defined benefits to your pension funds or is it defined contributions where you
basically have to put in a certain amount each period? You get another institutional
choices that can be path dependent. They can depend on previous institutional
choices. And finally, even if we look broadly something like economic success,
can depend on sequences of past outcomes. So current outcomes. So how well the
economy's doing now, what the population size is, can depend on previous evidence.
Let me give an example of that. I live in Ann Arbor, Michigan, which is a beautiful
town nestled along the Huron River, about 50 miles just west of Detroit. If you go
about 40 miles west of Ann Arbor, you're gonna run into a town called Jackson. Now
Ann Arbor featured, for a long time, the world's largest public university, the
University of Michigan, where I teach. Just down the road in Jackson, they have
the world's largest four-walled prison. I often joke with kids that three wall
prisons aren't very big, because people can escape. There's like a huge prison,
Jackson State Prison, is enormous. Now these are choices that were made in the
past, and they had drastic implications for how the life of those cities, the
economic success of those cities played out. Let?s just look at population
numbers. So notice if you look at Jackson in the 1920s and 1930s, you see a huge
increase in population, 54 percent in the 1920s. This was a period when there was a
lot of crime in the United States, and prisons were good business. [inaudible] be
in. But if you look in 1940 and 1950, you see minus ten percent and 2.9 Percent.
Now, we're suddenly sending people off to war. Those people are coming back from
war, and what you get is a decrease in the population. Let's look at Ann Arbor. So
Ann Arbor's doing fine during the 20s, and 30s. But during 1940, right, it slips down
to 10.7 percent again, because everybody's off to war. But then when they come back
to war, this is the thing to focus on, there's the GI Bill. And all these young
men can get educated. And you see a massive increase in the city of Ann
Arbor's population. And so now [inaudible] these two cities Jackson started out at
31.000. Now it's only 36.000. And Argus started out at 14.000. And ten years ago
it's at a 114.000. So what you see is, in Argus's path and Jackson?s path, went in
very different ways because of these choices they made. One chose the
university and one chose the prison. When people talk about path dependence, they
often talk about increasing returns. So let's think of the case of [inaudible]
University. [inaudible] think, you build this university, and then other
educational things, like hospitals, law schools that weren't originally part of
the university, they join in. And eventually, you grow and grow and grow
through what's called a virtuous cycle, with good building on good. And
[inaudible] you can think of increasing returns. ?Cause the more [inaudible], the
more [inaudible]. So it's just success on top of success. When people talk about
increasing returns, they often equate it with path dependence. They say path
dependence is increasing returns. It's increasing returns as path dependence.
We're gonna see that that's in fact not true. That there's logically completely
separate concepts and we're gonna see that through the use of a model. Another thing
that we're gonna distinguish from path dependence is chaos. Now chaos I've got
written next to this SESTIC. This stands for extreme sensitivity to initial
conditions. So, when I think of chaos what I think of I've got two points, A and B.
That are really close to each other to start. But A heads off this way, and B
heads off this way. It means their paths diverge from very similar starting points.
That's what we think of as chaos. Path dependence means the path that they
followed along the way matters. So chaos deals with initial points, path dependence
deals with the path. Now, when we talk about path dependence, what's interesting
is we're thinking about a situation where there's a dynamic process. Where there's a
state in this period, and a state in the next period, and a state in the next
period, and so on. It's gonna sound a lot like a Markov process. We've, remember, in
Markov processes, that the path didn't. Matter. Starting point didn't matter.
History didn't matter. So there has to be something in these path dependent
processes that violates the assumptions of the markup process. What it's gonna be is
the fix transition probabilities. Remember in our markup processes the transition
probabilities had to be fixed. In the models that we construct, these urn
models, what we're gonna see is the transition probabilities change, and
that's why history can matter. Alright, so there's a quick overview of what we're
gonna cover. We're gonna start out by just talking about what path dependence is,
then we're gonna construct these Urn models to try and make sense of all sorts
of different types of path dependence we can see, and what causes path dependence,
and flush out the difference between path dependent outcomes, when individual event
in path dependent equilibria sort of long run distributions depend on the path, and
then we're gonna see differences between things like path dependence, tipping
points, and Markov processes, and chaos. Okay. Let's get started. Thanks.
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