Hi. In this lecture, we're going to talk about a famous model from social science, and this model is the Schelling Spatial Segregation Model. Shellings model was developed by a man named Thomas Shelling who's an economist at the University of Maryland. What Shelling was trying to do was he trying to sort of understand an empirical phenomenon. And that under, that empirical phenomenon that he was interested in was segregation. And two types of segregation [inaudible] primarily interested in. One was racial segregation, the other was segregation by income. So let's look at some pictures of each. So what you see is a picture of New York City. Each red dot in this graph represents a city block that's majority Caucasian or White. This blue dot represents a city block that's majority Afro American, this yellow dot represents a city block that's majority of Latino and each green dot represents a city block that is majority Asian some could be Koreans, could be Japanese, could be Chinese American but it's cross [inaudible] by the census. When you look at this picture what you see is incredible racial segregation alright. Now, the same is true if you look by income. So, here's, again a picture of New York City. Each red dot represents someone that's very wealthy each light blue dot represents someone whose poor and the moderately blue dots represent someone in the middle class. So you get this picture, what you see is segregation by income, and it's also, you know, fairly stark, not as stark as the racial segregation, but it's pretty stark. So this is what Shelling wanted to understand. You wanna construct a model to make sense of this. Now you might say you don't need a model. Why do we need a model? It's obvious. Look, people maybe they're racist, people don't like to live with people who don't look like them and that's why we get segregation. Well, that's what Shelling set out to explore and he set out to explore that using a model. So. What kind of model he constructs. He constructs what we call, remember, an agent based model, so remember, an agent based model. You've got three things. You've got these agents, which in this case will be people. All right, that's part one. Then you have their behaviors. You have to say, okay, what rules do they follow. That's part two. And then the third part is, you just add them up. You just aggregate it and you see what happens when all these people are following these rules, what do we get at the aggregate level. Okay, so what's Schelling's model about? [inaudible] model's about people choosing where to live. So you can think, when you think about people choosing where to live. Well, you think about, okay, I'm gonna buy a house, what kind of house do I wanna buy? Do I wanna buy this beautiful craftsmen house? Do I wanna buy a Spanish style house? Do I wanna live in an apartment, those sorts of questions. Well, [inaudible] abstracted away from all that. And he said, okay, let's, I wanna think about this in a different way. I wanna think about people living in a city, living in someplace, and deciding, should I stay here or should I move? So, here's how he did it. He thought of each person as being located on a checker board. So, what he did, is he described the whole city, whether it's New York, or Detroit, or Houston, as a giant checker board. And each checker board can having a person living there, or it can be blank. So, in this picture that we see here. Right? What we've got is we've got a person living at S. So this is our person right here. And there's eight neighbors, one through eight. And one of those neighborhoods is blank, right. If you look at number three here, right, there's no one living there. So she's got a total of seven neighbors. Now let's let red represent rich people and gray represent poor people. And so this is a rich person. And if we look at here, she's got three neighbors who are rich like her, but then she's got four neighbors who aren't. So in total, three out of her seven neighbors. Are the same as her and she got to decide: okay, is three out of seven enough? If three out of seven of my neighbors are like me, should I stay or should I go? Where this is where Shellingham writes down the rules and he calls this a threshold based rule. So each person has a threshold and they decide based on this threshold: Do I stay where I'm at or do I move? So, one rule would be Three-sevenths is good enough. So maybe your rule is 33 percent so 33 percent of my neighbors are like me I'll stay but if fewer than 33 percent are like me then I'll move, so this woman here she looks and she counts three of her seven neighbors are like her so she stays but one of her neighbors moved out. And now there are only two out of seven neighbors like her, then she'd move. So this is the model. That's all there is to it. So there's people, they've got neighborhoods, and they have to decide whether to stay or to move, and then we ask, what happens. Now when Shelling ran his model he did it on, using paper and pencil on an airplane actually, and he wrote out a big checkerboard and he just used, I think, nickels and pennies to represent the different income groups. We've got some advantages Shelling didn't have, we're going to use a computer program called NetLogo. And this is free software. We've used it before, right? So, lets go to our NetLogo model. Okay, here it is, our model. Now remember three parts nature makes model, the agents, the rule, and then the aggregate behavior. So, if these, if you look at this [inaudible] Lego model, the first thing you see here is this number up on the top. And that tells us number of agents. We can set this up. And [inaudible] blue agents and yellow agents, where the blue agents be rich and the yellow agents be poor. And that is randomly set up on this grid. We got a behavior, right. Behavior was the percent similar wanted, so it's 30 percent right now. People want 30 percent of their neighbors to look like them. And then we've got the aggregation, which we are going to be covered in these two graphs. So the aggregation is going to tell us what's the percentage similar; so how many people are like you in your neighborhood of eight and then the percentage on happy, how many people aren't having their threshold met. Alright so starting at 30 percent and, notice we start off 50 percent similar. And only sixteen percent are unhappy. Now 50 percent similar makes sense. Because people are randomly set out there. So half should be like [inaudible] and half should be not. Okay so here we go. If we let this one. What happens is the n went up with 72 percent similar. And nobody's unhappy so the system goes to an equilibrium, but what's interesting about this if you look at this seven, 72 percent of a person's neighbors are like them even though people are incredibly tolerant they only need 30 percent of the people. In their neighborhood to be like them, and you end up with 70 percent of the people in your neighborhood like you. So here's the deep insight from [inaudible] model. What you see at the macro level, segregation like this, may not in fact represent what's going on at the micro level because these are pretty tolerant people, right. These are very tolerant people. All they want is a third of the people to look like them and they'll be okay. But if that's their rule, you end up with 70 percent of people looking like you. But what if we make them just slightly less tolerant? And so we move this up to, let's say 40%. And we set this up. Now, again we started with 49.5 percent of people unhappy. And remember it's 30 percent of people unhappy. But 49 percent of people are similar to you. And if we let this go. What we end up now is 80 percent of the people end up being similar. To their neighbors, right? So, you get, a person neighbors are, 80 percent of them are similar to them. So you get even more segregation. But what's interesting is if we ramp this up even more, lets say to 52%, let's just make it a little over 50%. Now over 60 percent of people are unhappy. That's because over 60 percent of people have 50 percent or fewer neighbors like them. And if we run this, we get unbelievable segregation. Right? Now, what's incredible about this is that 52 percent isn't that intolerant, if you think about it, you're sort of [inaudible], I just want to be in a majority. I actually might prefer a racially mixed neighborhood, or an income-mixed neighborhood, but. If I do that, what I end up with is 94 percent of my neighbors will be like me. And if you look closely at this picture, what you see is that there's sort of like little islands of empty space, the black regions are empty space, between the blue and yellow regions. So these people are really segregating. Now you could say, so this is sort of surprising. And again, we get these amazing results from showing that at the macro level, we get segregation, but at the micro level, people are pretty tolerant. Now, remember how we though about why we get segregation. ?Cause we think that, well, people are, you know, people don't wanna hang out with poor people. What if we assume that rich people don't wanna hang out with poor people. So let's crank this way up. And poor people don't wanna hang out with rich people, so let's crank this way up to 80%. So now, people want 80 percent of their neighbors to be like them. And if they're not, they're gonna move. Well, we should get massive segregation here, right? Even worse than before. Okay. We don't. We don't even get an equilibrium. We get this sort of, completely random process, right? Everybody's still hanging out in neighborhoods that are still 50 percent of people are similar. The reason why is, if you don't want anybody in your neighborhood to be like you, well, it's hard to find a place to live. You know, cuz you move someplace else where there's gonna be someone who's not like you and then you're going to want to move again. So if people really were incredibly racist or incredibly biased based on income, then we might not see this variation we see. We might see people moving all the time, churning, churning, churning, churning to avoid being around anyone like them. So what Schelling's model tells us, right, again, and this really sort of. Very simple way, that happen at that macro level. Segregation by race, by income, by all sorts of other things, may not be, right? Because of the fact that, at the micro level, people are that intolerant. So the micro and the macro. May not [inaudible]. Okay so that's the big lesson right. Micro motives need not be equal to [inaudible] micro behavior. And in fact. Showing [inaudible] book The book he's famous for. Micro motives and micro behavior and reminding us that what we see out there in the world. Need not imply that that's, so the [inaudible] need not imply what we think about the micro level of behaviors of individuals. Okay, so let's, let's flesh out [inaudible] a little bit more. Because one of the things that interesting about it is what people sometimes call the tipping phenomena in [inaudible] model. So remember when we set it up, only fifteen percent of people wanted to move. So let's suppose I've got some person, you know, and they're sitting in some neighborhood, and there's only two sevenths of her neighbors are like her, so she moves. But when she moves, she can cause other people to move. So let's look at this person here who's sitting in a neighborhood where there's two of her seven neighbors are like her. Now let's suppose that she's happy with that. She's cool with that. She's gonna stay with two of her seven neighbors being just like her. But what happens is, this person leaves. Person number five leaves the system. Right. Move to someplace else because that person didn't have enough neighbors like her to feel comfortable. But when that person leaves, that's going to cause her to leave. Right, so that's an exodus tip, one person leaves causing another person to leave, okay? There's also a genesis tip. Let's suppose she's living in this neighborhood and she's got, in this case right, she's got two out of seven neighbors who look like her and what happens is, someone moves into the neighborhood who is not like her and now she's only got two out of eight. And so now there's too many poor people living in the neighborhood and she says you know what, because of that, I'm out of here. This would be a genesis tip. Somebody moves in, causes her to move. So those are the two things that cause tips in Shelling's models, genesis tips and exodus tips. So people moving out cause other people to move out and people moving in cause some people who are currently living there to want to move out. Alright, so when you look at a city, then, like New York, or Detroit, or Houston, or LA, or Chicago, or Philadelphia. [inaudible] maps for any one of these cities, they look exactly like this. Not exactly, [inaudible] the same sort of patterns of racial segregation. In some [inaudible] cases, even more pronounced. Now what we could infer from that would be that, at the micro level, people are very racist. People don't feel comfortable living in neighborhoods with people like them. Well, what's interesting is if you poll people, if you ask them, people actually say, no, I'd like to live in a mixed income, mixed race neighborhood. Yet. They sorta may want it to be a little bit more like the maybe 30, 40 percent like them. Well if that's what people what at the micro level, you know, to be in sort of mixed neighborhoods, it's not what they get. What they get is pictures like this. And that's what's so surprising about Shelling's model. The macro behavior, right, doesn't want, the micro behavior doesn't produce sort of macro level behavior. That's consistent with what they want. Alright. So, that's Schelling's model, and, in the next lecture we're gonna go into more detail about sort of how do we measure segregation, and then, we'll talk about some of the fertility of Schelling's model, and how we can apply it to other settings as well. Thank you.