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.
