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Hi. In this set of lectures, we're going
to talk about path dependence. Now loosely

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speaking, path dependence means what
happens now depends on what happened along

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the path to get here, like history. So
history matters. So this will be different

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than our Markov process models where we
found that history doesn't matter at all.

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What we're going to do in these lectures
is frame them around a simple class of

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models known as urn models. And these urn
models are going to help us flush out a

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lot of the logic behind what causes path
dependence, what really is path

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dependence, and also distinguish between
different types of path dependence. So for

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example, an outcome, what happens today
could be path dependent. In addition the

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equilibrium what happens in the long run
the distribution over all possible

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outcomes could also be path dependent. So
we're going to flash those things out. So

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when we talk about path dependents, what
do we mean? One of the most famous example

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of path dependence involves the typewriter
keyboard that's probably in front of most

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of you, many of you right now. This
typewriter keyboard, this standard

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configuration [inaudible] is called the
QWERTY typewriter keyboard. And that's

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because if you look across the top row of
keys starting on the left, you see the

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word QWERTY. It's not really a word, but
you see those letters. Now initially,

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there were lots of different keyboard
configurations, but it turned out that the

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path through which history played out,
that QWERTY ended up getting locked in due

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to a process of what we're gonna call
increasing returns. The more people that

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had QWERTY. [inaudible] the more people
want [inaudible] and the more typewriters

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that got built with [inaudible] and it got
locked in so that everybody uses the

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accordion typewriter. Or at least nearly
everybody. Now typewriters are one thing

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but path dependence occurs in a lot of
situations, so let's first define what we

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mean. So like path dependence what I mean
is that the outcome probably. What's going

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to happen depends on the path, the
sequence of previous outcomes. So what

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happens in the past has an impact on it.
It doesn't necessarily determine, that's

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why I'm saying probabilities here. It
affects. What's likely to happen now. So

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the past matters. History matters. And
what are cases where this is true, where

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history matters. Well, there's a lot of
them. They're easy to think of. So for

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example, we think of choices over
technology. A QWERTY keyboard is a simple

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technology, but if you think of things
like whether you have alternating current

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or direct current, that's an example of
one process winning out over another.

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Gasoline cars versus electric cars. And
now electric cars are rising back up. So

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again, technological choice can depend on
the history. Other examples, the law. How

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the law evolves over time depends on what
has sort of become law in the past. So

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precedent plays a large role in law and as
precedent plays a large. Drawn law. That

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means past outcomes influence current
outcomes. It's even the case of where they

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give institutional choices. Do you have a
single pair of healthcare system? Do you

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have a multi-pair healthcare system? Do
you have a situation where you have

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defined benefits to your pension funds or
is it defined contributions where you

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basically have to put in a certain amount
each period? You get another institutional

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choices that can be path dependent. They
can depend on previous institutional

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choices. And finally, even if we look
broadly something like economic success,

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can depend on sequences of past outcomes.
So current outcomes. So how well the

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economy's doing now, what the population
size is, can depend on previous evidence.

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Let me give an example of that. I live in
Ann Arbor, Michigan, which is a beautiful

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town nestled along the Huron River, about
50 miles just west of Detroit. If you go

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about 40 miles west of Ann Arbor, you're
gonna run into a town called Jackson. Now

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Ann Arbor featured, for a long time, the
world's largest public university, the

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University of Michigan, where I teach.
Just down the road in Jackson, they have

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the world's largest four-walled prison. I
often joke with kids that three wall

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prisons aren't very big, because people
can escape. There's like a huge prison,

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Jackson State Prison, is enormous. Now
these are choices that were made in the

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past, and they had drastic implications
for how the life of those cities, the

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economic success of those cities played
out. Let?s just look at population

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numbers. So notice if you look at Jackson
in the 1920s and 1930s, you see a huge

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increase in population, 54 percent in the
1920s. This was a period when there was a

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lot of crime in the United States, and
prisons were good business. [inaudible] be

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in. But if you look in 1940 and 1950, you
see minus ten percent and 2.9 Percent.

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Now, we're suddenly sending people off to
war. Those people are coming back from

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war, and what you get is a decrease in the
population. Let's look at Ann Arbor. So

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Ann Arbor's doing fine during the 20s, and
30s. But during 1940, right, it slips down

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to 10.7 percent again, because everybody's
off to war. But then when they come back

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to war, this is the thing to focus on,
there's the GI Bill. And all these young

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men can get educated. And you see a
massive increase in the city of Ann

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Arbor's population. And so now [inaudible]
these two cities Jackson started out at

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31.000. Now it's only 36.000. And Argus
started out at 14.000. And ten years ago

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it's at a 114.000. So what you see is, in
Argus's path and Jackson?s path, went in

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very different ways because of these
choices they made. One chose the

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university and one chose the prison. When
people talk about path dependence, they

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often talk about increasing returns. So
let's think of the case of [inaudible]

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University. [inaudible] think, you build
this university, and then other

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educational things, like hospitals, law
schools that weren't originally part of

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the university, they join in. And
eventually, you grow and grow and grow

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through what's called a virtuous cycle,
with good building on good. And

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[inaudible] you can think of increasing
returns. ?Cause the more [inaudible], the

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more [inaudible]. So it's just success on
top of success. When people talk about

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increasing returns, they often equate it
with path dependence. They say path

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dependence is increasing returns. It's
increasing returns as path dependence.

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We're gonna see that that's in fact not
true. That there's logically completely

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separate concepts and we're gonna see that
through the use of a model. Another thing

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that we're gonna distinguish from path
dependence is chaos. Now chaos I've got

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written next to this SESTIC. This stands
for extreme sensitivity to initial

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conditions. So, when I think of chaos what
I think of I've got two points, A and B.

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That are really close to each other to
start. But A heads off this way, and B

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heads off this way. It means their paths
diverge from very similar starting points.

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That's what we think of as chaos. Path
dependence means the path that they

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followed along the way matters. So chaos
deals with initial points, path dependence

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deals with the path. Now, when we talk
about path dependence, what's interesting

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is we're thinking about a situation where
there's a dynamic process. Where there's a

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state in this period, and a state in the
next period, and a state in the next

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period, and so on. It's gonna sound a lot
like a Markov process. We've, remember, in

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Markov processes, that the path didn't.
Matter. Starting point didn't matter.

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History didn't matter. So there has to be
something in these path dependent

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processes that violates the assumptions of
the markup process. What it's gonna be is

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the fix transition probabilities. Remember
in our markup processes the transition

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probabilities had to be fixed. In the
models that we construct, these urn

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models, what we're gonna see is the
transition probabilities change, and

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that's why history can matter. Alright, so
there's a quick overview of what we're

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gonna cover. We're gonna start out by just
talking about what path dependence is,

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then we're gonna construct these Urn
models to try and make sense of all sorts

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of different types of path dependence we
can see, and what causes path dependence,

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and flush out the difference between path
dependent outcomes, when individual event

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in path dependent equilibria sort of long
run distributions depend on the path, and

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then we're gonna see differences between
things like path dependence, tipping

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points, and Markov processes, and chaos.
Okay. Let's get started. Thanks.