13   1   Path Dependence

13 1 Path Dependence

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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