The Inframarginal Returns To College

- Okay, let's, let's get going. For some strange reason, I don't really understand. No, I, I, mid, mid-February hits and our friends from Chicago and Minnesota start to come see us. I don't know why. Migratory

- Patterns. It, it happens every year.

- Our kids like this here, so I don't know, but for whatever reason, Eric, it is wonderful to see you and, but let's find out about the info al returns to college. And we go to, where do we go to Valerie? 1 45. 1 45. Okay.

- Thank you very much for this paper is literally the first time I'm giving it to anybody outside. Those other co-authors of mine is at this moment. So this is very brand new. I would love comments on every part. I got a title there, I don't know if I love that title yet. So even at the end you might be thinking that's kind of the wrong, the wrong way to, to, to, to kind of package the paper. So lemme tell you a little bit about what, what I'm thinking about. So there's a lot of applied micro research that tries to identify what happens to income for people who are right on the margin of a college decision of some sort. And they kind of use admissions data. They kind of look at a very rd, well-identified specification and put, take a look at somebody on one side of a cutoff of admission, compare it to somebody on the other side of the cutoff of admission and say that the returns to college have these huge effects on lifetime income. And I cited two recent papers where you're getting numbers like lifetime income goes up by somewhere between, you know, 10 and 20% depending upon estimations. Then you have a whole bunch of policy makers that come along and sometimes they say, I wanna expand college dramatically. Maybe make it free for everyone citing this research that the returns to college are very, very large when you send people to college. Those policies. And then also understanding other aggregate demand and dynamics I wanna show you in a little while, often confound these marginal effects and they wanna think that they apply to all people. And so what this paper is really going to be about is trying to think of how people away from margins are going to respond to different, different types of policies. So lemme tell you a little bit about the game we're gonna play. So I'm gonna try to assess the returns to college, either some college or maybe a bachelor's degree so we could have associates or bachelor's in the background for individuals away from the margins. So basically with the goal to be better understand potential policy proposals that people put forth to, to expand access to college. The paper's gonna have five parts. I'm gonna start in a modeling sense. So I'm gonna try to develop an equilibrium model of the decision to attend college where there's gonna be rich occupational heterogeneity, there's gonna be rich individual heterogeneity. Some of us are gonna be good at like, you know, carpentry, some of us are gonna be good at lawyering. College is gonna have differential returns for those of us who go to specialize in carpeting or carpentry versus those of us who specialize in lawyering. We're gonna have costs associated with college where money is gonna be one part of cost, but there's also going to be effort and time needed to invest into the, the college decisions. Maybe liquidity constraints, fines or not. And then we're gonna have occupations that are gonna be moving in terms of their demand over time. Some occupations are gonna be going up, some occupations are going down the returns to some occupations when your college might be rising. And that's gonna be kind of the model. We're gonna use a variety of micro data sources to try to pin down key parameters of this model and particularly the elasticities that are gonna drive people on the margin and away from the margin. So a lot of the talk is gonna be taking the model and trying to match it with some micro data moments to help with that. We're gonna show the model is gonna be consistent with a lot of these micro estimates that people have put forth on the marginal returns to to college. Even though we don't target those in any of our, in any of our ways to discipline the parameters, we are then going to use the model to compute the gains welfare gains to individuals of a variety of, you know, potentially realistic but fictitious types of policies. And again, this is all in the early stage who we're willing to get feedback at every part. And I'm just letting you know, you know, some of the estimates were coming in like this morning. So it's something we should take standard errors on on some of this. And then I'm also gonna potentially use the model to explain large trends, which I'm gonna show you on the next slide of how college has been shifting in the aggregate over time. Steve, the

- Counterfactuals, I'm guess principle, you could look at actual events, right? So the GI bill where there is a non

- Exactly. So going back in time. So I haven't done any of those kind of things. So I'm gonna use micro data in in in some things. We haven't done that going back in time yet, but those, that's exactly on our, on our agenda. You're gonna see, you know, I am, I would say 85% of the ingredients in the model. I think I've got kind of want, but there's gonna be other things. So first I'm trying to get the model in the playground set up. So the model is really trying to, the goal in part is to drive to develop this playground. But then once we do that, I'm gonna feel much more comfortable, you know, going back in time also removing policies. There's currently a lot of policies already existing about subsidies to college. So what happens, you know, are those cost effective or not? So the playground is gonna be hopefully designed to, to, to explain that John, you had some

- Not too much on on the stuff you're not gonna do, but yeah, this, do you get in or not? People who don't get into one college, go to another college. Exactly. So, so

- You're gonna have some margins like that in our model as well. And so the data they use exactly that identification. So some of those papers I cited are basically in Texas there's like, you know, I'm gonna make up a number like 35 different public schools. You're on the margin for one of them. If you don't go to this school, you go to another. So some of that number is going to what type of college you go to as well as whether you go to a four year versus a two year versus none at all. And so all of that is gonna be confounded in those estimates. I'm gonna try to replicate some of that in the spirit of our model. Once I kind of, you know, two slides away, I'm gonna show you kind of start doing the model. Anish,

- When you talk about college for your college is everything beyond high school. So it's like two years. It's C college associate

- Degrees. Yes. So I am going to have two college types in the model. Again, I'll get there very soon. One is going to be a bachelor's degree plus in the other, I'm gonna call some college, which is gonna be a bundle of other things, which is gonna be two year degrees and some certificates as well as people starting college and dropping out, which I don't have in the model at this moment. I'm gonna tell you there's gonna be some of that part of the real world that I don't have a handle on yet in how I'm going to pay and take, take that into, into the model instead of the data. The data I know with how I'm doing that in the model. We'll see, once I get the model up and running, it'll be a lot clear what I do and don't have and I'll try to get there in a second. First, Paula, how,

- How do you think about which occupations would remain? Like where is that coming from?

- Yeah, we're gonna have a big part of that in the talk. That's gonna be the talk.

- What about people coming from outside the us?

- None of that's gonna be in the model or anything in the data

- That could

- Feed into productivity. Yep. So when I restrict the data, I'm gonna be looking at native born, when we start talking about immigrants coming through again, we can think about how that changes. None of that's gonna be there today. But those are all gonna be things. But again, once I get in, I'm gonna Shelly tell you what I'm gonna be doing and it'll be a lot easier what I have and then I'm gonna do it. But a lot of the elements question is the paper. Once I set up the model, how do I bring this in the data? What are the occupations? How am I gonna estimate, you know, kind of the primitives in the model, how am I gonna estimate the elasticities in the model? That's gonna be the guts of the paper. And then my counterfactuals, we're gonna spend like four minutes at the end and I'll show you what it produces. But a lot of the guts is going to be what I'm doing. Paula,

- I I, I'm wondering what you can play with quality of college.

- Hmm. You're gonna see what I could do in the model and then we'll go with the data. Let me give it a few minutes in the model there is going to be stuff, let me just kind of, I'll defer that in in a second. There's gonna be bachelor's but there's gonna be bachelor's for STEM stuff versus bachelor's for other type of stuff. So there's gonna be quality across occupations bins but not so much Harvard versus any, most of the world doesn't go to that top end anyways. But when we start thinking about that top bin, you know, I, we'll see once I get into the model, I think it'll be helpful for me once I kind of lay out what I have for then you telling me all the things that I'm missing. That could be first order. Before I get to that, I'm gonna do two more things before the model slide is coming in two. But I just wanted to kind of show you one pattern that has been on my mind for a long time that helped motivated even me thinking about this project. Adrian and I were kicking this around, I don't know, seven years ago, five years ago, two years ago. And we kind of abandoned, this is the share of men 25 to 34 who have a bachelor's degree in the, in the United States from from the CPS and what you can see basically very little movement in that bachelor's here. Claudia Godin has written about this before this period, huge increase but in the last, you know, 75 to 2000 and change, no movement at all. But on the flip side, starting in the mid two thousands, this thing shot up by about 10 percentage points. And just in the back of your mind, if we look at things like skill premiums, which aren't about the margin, they're about the average, the skill premium move like crazy in the first period. It hasn't done anything in the last period. And so part of my mind is having this framework, not only could I think about policies, but also just thinking about these aggregate trends and things like what happens when a whole manufacturing sector shrinks by a large amount. You know, where do people reallocate and maybe they have to go to other, you know, marginal jobs on the return. And so those are gonna be in the background. I haven't made much progress on that but that is a launching off point in the back of my mind as well. Lemme just tell you one thing what I find and then we'll get right into it and I'll take Paul's question after that.

- And John did we just think of that as there was a skill premium, people said, oh let's go to college, takes a while to fill

- In. It could be, I mean again, we're gonna think, you know, if the skill premium moves in the 90 and then people move 15 years later, there could be hysteresis in people's, this is, you know, 25 years. If I shrink this to 25 to 30 year olds, you get very things. It seems like somewhere in the early parts of, you know, the great recession, you get this kind of shift and you'll, you can't see it exactly here 'cause there's stuff, but when I get into actual, you know, kind of enrollment data, but let's put that aside because again, I'm not gonna be able to make much progress on that today. Let tell you kind of first of all what I am going to do, which is I'm gonna just, these are the takeaways that I think at the end of today I'll be able to say something about first, which is, you know, policies that dramatically reduce the cost of college education will have very little effect on college completion or individual out there given the cost. These broad policies have a very large negative rate of return to the extent that there are effects, they tend to come to transferring resources to people who had already gone to college, which tend to be higher income people. The model can, as I said, replicate these marginal returns to people going to college in terms of income. But in terms of actual utility in our model, it doesn't move too much even though income does because these papers that focus on looking at the income returns don't realize that college is costly in a variety of different ways beyond tuition. And then the model is gonna shift, shoot out that the tuition is actually a small part of overall college costs for most individuals. It's gonna be things like, you know, can you, you know, the dis utility is studying or can you take four years off of no income or a whole bunch of these other things that are gonna be large component of of the cost. And so at the end it's, this is the marginal info, marginal thing. It's gonna be many people have small income gains from college because their comparative an absolute advantage isn't even gonna be in college stuff that's gonna be enhanced by college and that there's gonna be lots of costs out there beyond tuition that are also going to be hard for us to move, you know, effect with policies like just reducing tuition. I don't have a good sense of what those costs are yet. I mean as I get to the end of the paper you'll see me speculating a little bit about what these other costs might be. So that's gonna be kind of the stuff that I'm going to be leaning towards with that's gonna come outta the model for today. I think it could do other things. I just haven't done that, like explaining those times Sherry things that I wanted to get to. I just haven't gotten to those yet. Okay. Paula, you had some Perfect.

- Yes. Hello. I'm just wondering if we were to take like this slide and analogize it to high school, you go back in time, like what would, would your model be able to make the

- Same like compulsory high school? I, that is a great question and I don't know the answer to that yet. And so I'm gonna come in and let me see in one slide we'll get to the model where people are going to have some skills on the pre precipice of a college decision. How they get those skills. I'm relatively silent about but in the back of my mind, investments are made in elementary school and preschool. If you're, you know, you know Jim Heckman, you know, early in life and how those skills get formatted and you know, to be like a carpenter, you need some think skills. Now where did those skills come from? How much of it was given during the high school period? I don't have a a a sense of it is a great question that I have no answers for right now.

- Could just on your last part of the previous slide. So you're finding not much advantage. Yeah, but the, the on the margin guys did is that because the, the margin first got an advantage and then we lowered the standards and and now we're quickly into the territory of people?

- Yeah, so there's, there's both of those. So there's two parts of this and we'll kind of try to decompose it ish later on. So the marginal person is really the marginal and they get an income gain but there's an offsetting cost in utility. So their margin, even the margin, even the margin people aren't gonna gain much in utility. And then when you're far away these people actually lose quite a bit when you kind of, you know, they don't take it up but if you force 'em to go to college, they would actually be worse off. You know, you take somebody who might be a good manufacturer or a good carpenter and then that's where they're comparing advantage is and you force 'em someplace else. It is, they pay the cost without much of the benefits. But lemme kinda get, again, I wanna get into the model and then kind of go Steve. Yeah one more high

- Level conceptual issue with table. It's not clear that people are on the margin know they're on the margin. Exactly. And I think it's the case that in that period where men stopped increasing their college attendance rate, there was a big increase in the share of men who went to college and didn't finish. So, which is also kind of supportive of this idea, these people don't really have an idea of whether they're suited for college Exactly or not. That could be to fact that our education system may no longer give people very may no good prepare them. Yep. And give them good signals.

- Yes.

- So in your framework, are you going to assume people kind of know where they are in the distribution or are you gonna allow for the possibility that they're wrong

- Today? I am not going to do that, but embedded the way the model's going to take that is gonna put this in some of these cost parameters. So at the end when I start trying to figure out where these costs come of from, it could be this uncertainty could be part of it because starting and stopping could be. Now as I to Anna's question early on, you know I'm gonna have bachelor's high school and a sum college and the sum college is gonna be a mix of people who purposefully get an associate's degree from people who try and start. And I think one direction that we need to go to in the model is maybe distinguishing between those two because it does make a difference. And then I think Steve's kind of question comes in and it maybe get a little bit more about this information call start of people who start and stop, which is huge. So in the data of the sum college, the share of them who actually have an associate's degree is like, you know, not even a third. It might even be a little bit less than a than a third. So most of them are starters and stoppers and so, and our model is gonna load somewhere onto these costs of getting those people go to go to college.

- So, but going back to John question to some extent what you're telling us also is that the previous literature was underestimating the cost.

- Yes. I

- Think in a big

- Way and as Rick knows, all of 'em will have a footnote somewhere and say hey this is the return to college, the whole paper's about that. And then there'll be a footnote that's, oh by the way, just so you know, we don't include any of the utility stuff that actually could be important for slowing people down. So every one of these papers has that footnote but you again, but they still say look at the, this is the income return and then they take that as the utility term in narrative even though they will always apologize that this is income is not utility. So, and again some of these are my colleagues at Chicago Jo Mount Joy and again I talked to Jack about it, he's like Oh no I said that in footnote 76 that there's, you know, and again he does and he's not, again it is income is not utility but you know, okay, so lemme kind of just give you, I'm gonna give you a few slides of just the ingredients in the model. I'm gonna give you a couple of functional forms of utility and wages and then we'll go into how I'm going to discipline the key elements of this model. So this is kind of the broad kind of model the individuals are gonna be indexed by. There's gonna be rich occupational heterogeneity, I'll define those on the next two slides. I just wanna say, and we've already talked about this, there's gonna be three education co choices in the model education. One means you don't go to any college education, two goes, you go to some college in the Anna sense that I talked about before could be an associates could be starting in dropping out and education three is you got a bachelor's of more and those are gonna be the three choices people could make in the model conditional on your after. In addition to your education, you're gonna choose which sector to work in and there's gonna be a bunch of sectors out there. Some of 'em are gonna be manufacturing, some of 'em are gonna be lawyering and then they're gonna have to make some effort decisions about how much effort to spend in any of their educational co choices accumulating human capital. Okay? The model is static in the sense there's gonna be none of this dynamics of dropouts or anything in the sense every time I'm gonna do it, you think about it as repeated cross sections. When I have time in the model, it's gonna be 25 year olds today they're gonna make some decisions. 10 years later a different set of 25 year olds are gonna do that. So time in our model is gonna be different cohorts. Yeah John.

- But the general thing in the choice of what kind of degree to get, if I get a grievance studies degree versus accounting, it's gonna make a big differe.

- And so you're gonna see that, gimme a second when I define this lawyering human capital investments are going to be very different than manufacturing human capital investments in the model. So gimme a two more slides just on notation and then you'll see kind of where the heterogeneity is in in, in the model. So lemme talk about the individual heterogeneity first. This is gonna be what people are gonna be born with in the model. People are gonna be born with four sets of things. They're gonna be born with this absolute advantage. How good I am at everything. They're gonna be born. I'm gonna call that alpha going forward that's gonna be drawn from some distribution that has some dispersion of sigma alpha. Okay, that's gonna be very important. That's gonna tell me how many people are on the margin as how these distributions are. So this slide is really going to be determining these parameters is gonna be the most important part of this paper. 'cause it's gonna determine who's on the margin at different places. And I'm gonna show you a variety of micro data ways that we're gonna try to pin down these parameters. People are also gonna be born with comparative advantage in a Roy sense. Some of us are gonna be good at lawyering conditional on our absolute advantage. And some of us are gonna be good at manufacturing. There's, there's gonna be capital O occupations later on. It's gonna be six in your mind, something countable and people are gonna get a draw on each of those occupations. Alpha makes me better in everything. The fee is gonna make me relatively better in some versus others. So absolute and comparative advantage are gonna be in the background of the model. And then we're gonna draw some costs that are idiosyncra idiosyncratic to us about how costly it is to get a bachelor's degree or how costly it is to get some college. We again could be an associates or dropouts and those are gonna be two parameters epsilon, which are gonna be determining how costly idiosyncratically it is for us to go to those margins. That's what we're born with. So we're gonna be born with a productivity overall, A productivity in each of the sectors in these two cost parameters eventually. I haven't done that today. I tried the model wasn't converging quite yet. If I had another four days I could allow some correlations between these things. But right in today I'm not going to have that. I'm gonna show you where that's gonna be needed on things I don't match overly well in the micro data kind of. Well and I think these correlations could be important. So I think the data's gonna be screaming for the fact that some of us who have high absolute advantage, maybe because of investments we make in high school might be relatively better in lawyering than we are in manufacturing in a comparative as that vantage defense. I don't have any of that today. Okay, here's some of the choices people are gonna make. They're gonna make this capital s I'll show you a utility function in a second. This is gonna be the effort you're gonna put in to accumulating human capital. So I'm gonna call your accumulated hap human capital. Think about the time investment in studying in college. That's gonna be capital S. It's gonna be individual specific and it's gonna depend on not only what education but what occupation I give. I might have to study harder to be a lawyer than I do to be a fine arts major. And then our skill is going to be that human capital multiplied by our absolute advantage. Occupations are gonna differ in some productivity that's gonna be beta and there's gonna be, for every occupation, it's gonna be how productive that occupation is. That's gonna be, we might have manufacturing decline over time and I'm gonna view that as a decline in productivity and manufacturing or lawyering get more productive over time. And then each occupation is going to have a different return to human capital. So think about the return to human capital and each occupation is human capital. I get if I'm high school, the human capital I get if I'm some college or the human capital I get, if I have a bachelor's degree that'll be a gamma for bachelor's, a gamma for high school and a gamma for some college. And those are gonna differ by occupation. The return to me getting bachelor's degree might be relatively small in manufacturing compared to lawyering. I might definitely need a bachelor's degree by definition 'cause they won't take me in any other in any other way. So these parameters are gonna move over time and that's gonna move people's choices about what occupations should potentially sort to. So occupations are gonna be defined by their productivities, by the returns to different human capital and they're gonna have different costs and average. So the epsilons where the idiosyncratic parts of costs, these caps are gonna be the average parts of cost that's gonna include tuition. And then they might just be hard on average to be a lawyer. You know you might need more time and you might need five years versus four years and bachelor's to be a lawyer. And so those are gonna be the average costs that are gonna be common to all of us that are gonna be embedded in these caps. They're gonna be occupation and education specific. The kappa for a high school, we're just normalizing to one. Steve,

- That's so interesting. What's driving those changing?

- Nope. I mean again, in the back of my mind, but in the model I'm gonna treat 'em as God is just moving all of these things around. So those are gonna be the exogenous driving forces in the model is going to be that lo bottom row, those six parameters and everything else is gonna be the endogenous sorting in the background

- Structure of the model. Be kind of interesting to project later on. It

- Would be fantastic. What you're gonna see is they are going to load onto things like manufacturing's going down over time. The model is going to see the beta for that is going to be moving around. But right now I'm taking the, those are gonna be the driving forces in the model. So the game I'm playing, those are the driving forces. There's sorting from those four things that people got and the whole game is how those things move around and how people resort. And then I'm gonna start later in the paper. Shocking the Kappas, let's reduce the cost of going to college. Some part of that is gonna be tuition. How do people resort? And that's gonna be what I'm gonna do in my counteracts. Yeah Luigi.

- So each occupation is gonna be

- Inogen. I'm gonna show you on the next slide Endogen, I'm gonna show you on the next slide what is going to be the wage function and the average wages are gonna be endogenous to these things and the sorting, okay? These things are gonna be primitives though in in the wage function. So next slide is utility, the slide after that is wages which will enter utility, then the model's done and then we'll just go into how I wanna discipline those parameters. Yes,

- It might be on this wage slide, but given that we're concerned about the kind of time and effort cost of attending college, you think of the occupation returns to working as the of an effort cost of working. So I'm gonna have, you're gonna see when I do the

- Function, there's gonna be both the the, the wage is gonna have the, the gamblers gonna be the returns plus it's going to include all the sorting, which is gonna be a function of kappa and your effort is going to be in there as well. So gimme one more slide but it all of that will be in there. So I wanted to lay it down in words kind of what are the primitives and then I'm gonna show you two functional forms. So functional form for utility and a functional form for wages. And then the model is essentially over. Okay? And that'll just show you, it could simplify to a discreet choice kind of framework where people can sort a after that, okay? So here is our utility function. Individuals are gonna get utility out of their wage, which will be endogenous on the next slide. That wage will then be a function of I my own stuff like how my absolute and comparative advantage plus stuff like what education I get, what occupation I go to. And then time as I told you, I'm gonna have time because these things are gonna be moving around over over time. These driving forces on the last slide, nice and easy, you're gonna get some disutility from effort you have to put in to accumulating human capital. That's gonna be this s and then, so think about one minus S as being your leisure and s being how much effort you have to put in into getting human capital. And so think about a pre preor where you're doing your schooling and then you're gonna have to make this, make this choice, this effort I'm gonna show you on a first order condition is going to then depend on the education you go to, the occupation or you go to and how those things move over time. The drivers at that there is gonna be a utility parameter,

- Just the S function got a T subgroup.

- Oh because all the things are gonna be moving around over time. I, I should probably drop the T like it's gonna depend upon like the occupations are gonna move with their productivity over time. So I should probably make this a static model and then just allow these things to change over time. I'm, I, as I was writing the slides, I find the, the t's going in and that's why I had the apology slide that it's really just to say of cross section 'cause there's no, there's no dynamics in the model. It's just the things that I'm gonna make my, my choice of things that are gonna drive my F today. Those things are gonna change over time. And so our model Bs is gonna change over time. Okay? The pitchforks, I don't know how to say that are gonna be the utility parameters and my distil utility and I'm also gonna allow that potentially to differ by education. It might be more costly on average to get college education for four years or bachelor's than it is for two years. I think I can normalize that parameter and I think it would just reload onto the CAPAs someplace else. I'm playing with that, I haven't done that yet. Hey, what do we got Kevin?

- I object to the assumption that

- I knew you would this,

- There's always dis utility to the studying. Yeah.

- So what this is going to do through the lens of the model is going to generate why we get paid in some in some wages. There's gotta be some cost we gotta make in order to invest in the effort and in the model, just so you can tell, to Ken's point, this is going to generate why lawyers are gonna get paid more than teachers because on average you have to be compensated on average for the additional effort to be a lawyer versus teacher averages you. I'm saying what this is gonna help me in the averages. So, and then the idiot, the epsilons are in the background. So there's nothing that says your cost couldn't be negative for you idiosyncratically. And so that's what I would say. Yeah. What did

- I, I'm assuming it's immeasurable how you calculate the opportunity cost of gonna college. Oh you know, that's a real tough one. Yeah. And moreover, the opportunity cost of going to college given this alpha parameter you have in there is really high for, I mean it's like athletes, right? Yeah. You leave that one year, become a pro football player. Yeah. You know, and so that's, I don't know how that's incorporated in there and I don't know if we can,

- Yeah. So I'm not gonna have the dropout decision but to, the key part is the opportunity cost is going to be loaded into this Kappas as well. And so there's a fee part and the kappa that is pinning those kind of, or not the feedback, the pitchfork and the ca, these are gonna be pinning these things down and I think our model's gonna spit out large numbers for those. And then I think part of what we're gonna do is we can measure the tuition part that's countable for people. Everything else, how do we unpack it? And so we haven't done the unpacking yet. And so you'll see that at the end. I'm gonna get in a few minutes, I'm gonna show you how large these CAPAs are gonna be. And one part is the opportunity cost that's gonna be embedded. How we discipline the non tuition part is something that I'm, I'm working on in real time and I would love thoughts A as as as we get to to the end of that, as we go through. Yeah,

- I'm, I'm curious, so there is this utility from studying or utility, this utility whatever, is there a, this utility from working? Because in principle you could imagine that I'm trading off studying really hard, now I get a better job, it's gonna have lower this utility. Do you allow for some of these?

- So all of that is going to be embedded into the wages and the gamma. So on the one side so that I don't worry about who the model is gonna be robust to that, that what them don't have in the model, which is going to be an extensive margin of labor supply. So I'm gonna have everybody working now for lots of things that's not gonna matter. But when I'm gonna do some of the counterfactuals, we're gonna move down like the demand for manufacturing. We know some of that is gonna show up on people not working and that's going to then lead to some selection in the average wages that my model is not going to be accounting for. And so that is something on our to-do list is to add one more draw of a dis utility of labor to try to get a labor supply curve. We'll have a a basically a dip. We have estimates of that. I don't worry about disciplining that parameter. There's a huge literature on estimating labor supply elasticities, but that margin isn't in here right now. So let me then talk to again, the cost in this function. Your utility will be reduced if you go to college. So an indicator variable I is if you go to a college of type E, and if you do, you gotta pay the cost capa. And as we've all been talking about these cap CAPA's, the way it's set up is gonna include all of the average costs, the opportunity cost, the tuition, the, the average psychic cost that's gonna be in the background, the information cost that Steve did, this is gonna be these, everything's gonna load onto this and you're gonna have to pay your dis utility cost as well. The epsilon which we draw. So there's a systematic component of the cost and the idiosyncratic post to the cost. You only pay those when you go to college. That's our utility

- Shut down this channel. You get a system where basically people would go to community college because it'll still be a relatively low cost and there is some advantage or other words. It's really this part that is driving this huge cost.

- And so like the cost part, let me, I'm gonna show you, I'm gonna back out these CAPAs, I'm gonna show you some numbers and it's gonna come up with some number, like for the, you know, the average across these, it's gonna be something like 300,000 bucks. We know the tuition on average estimates like 14,000 a year. Net of fee. Net of with subsidies. So think about something like 60,000. So most of this 300,000 isn't gonna be tuition related stuff. And so where is that other things coming from that's gonna be in the background? All of that is going to be the residual in kind of this model. So we are going to have, the cost for community college is going to be lower than the cost. The cost of some college, I don't have community, I have some college is going to be lower than a bachelor's degree. The model spits that out that it's going to be that and you know, but we can measure the tuition parts and the tuition really just isn't that big, right?

- This this place an important

- Exactly. Exactly. And so when I, and this is kind of when you get the end, when I start moving tuition, try to figure out of that 30,000, $300,000, let's move it by 60 or some big number, we don't get a lot of action because the model is saying there's still all of these other costs that are un tuition related. So to get my results of why we're not getting the large effect it is really the model wants to spit out that it's just really costly. This is kind of be very similar to the migration literature where people basically find when they're shocks to local, why do people still exist in Detroit? They say the benefit, the incomes in real incomes are higher somewhere else. So they infer there must be these really high mobility mine's gonna be exactly the same. I'm gonna have shocks to local markets, I'm gonna have people going to college. You're not gonna get a lot of people going to college. In response you're gonna say, hey, they're relatively inelastic. The model wants to throw that inelasticity into these cost parameters and that's exactly what we're gonna be getting in in, in when I try to discipline them. That's where the model's gonna wanna load onto all this cost function. Yeah.

- Yeah. I just wanted to float two ideas on, on some possible sources of those costs. One is the, the recently published JPE paper by your, your colleague John List and a number of other co-authors that find using structural analysis for high school that there is significant heterogeneity of productivity of studying. And then that explains why struggling students actually don't study more. And I, I found that very revealing when I was doing some time stuff. I was recently And then the, the second thing is differences in either the cost of credit or their impatience because college gives you this wonderful steep thing whereas not going to college you get more there. So, so those sorts of heterogeneities can help.

- And so I mean to Valerie's point, again some of those are gonna be metaphorically around and how we discipline them is gonna be interesting. One of which we're trying to do not today. I think because we have all this tuition data, I could try to separate out the parts of the costs that are tuition related stuff. That's where the policy wants to be and all the other stuff. And then for the tuition related stuff, then we could do liquidity constraints much, much better in then the sense

- I'm talking about the wage part.

- Oh that,

- That

- In the future they could borrow No,

- No. You know going and being a plumber, you get your wages now but it's gonna be flatter profile than the college.

- Yeah. So in our model that's all gonna be taking the present value of all of that income. So we're not gonna have any of that timing in the static model.

- Yeah.

- And so in the static model that'll, I'm gonna tell them exactly the present value part. So I'm not gonna have anything about the slope. But if you have heavy in the discount factor. Yeah, exactly. Yeah that could be true. Yeah. But that'll come up in our epsilon. So, so again we have, the question is how do I unpack that from other stuff? Which again, I'm gonna wanna show you kind of what I get out, but you can see this is the paper dial. Basically I'm gonna show you how I get these elasticities, elasticities are gonna spit out some big kappas. Then how do we unpack those? Kappas is gonna be kind of the the game, right?

- But this, this story sounds basically like what Jacob Mintzer did in 1965. That tuition isn't relevant, it's the time out of the labor market and the cost. It's all important And that's,

- Yeah, so time outta the labor, but we also have some sense of how big that could be so we know what the average earnings of the, and it still needs something on top of that. But I agree with you Min kind of had some of that, you know, you know Willis and Rosen had something kind of in in that spirit. So I think will, I'm hoping here that by doing it kind of generally doing in kind of digging the selection kind of right, we could kind of then try to get a better sense of what these marginal elasticities might be. And I'm hoping that's kind of be the game that that value added of kind of what I do. Yeah.

- So what individual differences in discount rates or patients

- Ultimately be part of the cost? Like it'll be in my epsilons? Yeah, it'll be in some residual variation that makes it more or less net benefit for you. And so the epsilons are net benefit space, I'm saying the word cost, but it's really net benefit. So if there's heterogeneity and benefit that's not due to your productivity and due to some other preference parameters that will also load into this epsilon dispersion. It won't, the average level will be net out but it will allow, the variation will come in from the epsilon. I'm gonna show you the epsilon pretty dispersed when I show you how I discipline that in in a second. Yeah.

- There's also this literature by some of the outers you actually mentioned on assortative mating role of college. So how should I think about this? Like a,

- Yeah, negative cost. That was me with Kerwin. So that was the assortative mating. So Kurt and I did the assortative mating by education. Again, this is a single individual, there's no household anywhere. So I have nothing to say.

- How should we think of the disutility and the like not having information or misinformation about,

- Once I show you the last slide is gonna be a bunch of stuff like this. Like basically here's what I got, how could you guys help me kinda figure out how much is these other components like, like education and I, I do think that there is something, as Steve pointed out that maybe Anna alluded to in the dropout margin is very distinct from an associate's degree. The return to an associate's degree in the data people with an associate's degree are higher with three years of college with no associate degree and no bachelor's degree, the dropouts. So there is something, it's not hugely higher. So there that margin and that margin may allow us to kind of figure out, you know, something about information or learning or or things of that nature.

- Yeah. 50 to Valerie. So you have driven value.

- Yeah.

- But some occupation because you went to college will allow you to switch between careers and occupations. Is that going to be how, how?

- I don't have any of that in the model. So there's a static model. You're choosing your education and your occupation in the 25 to 30 5-year-old range. And then you're with that forever so far there's none of that. Lemme just kinda show you the wage function and then I'll tell you how I'm gonna try to estimate these, these elasticities in the, in the last half hour of the talk. So, so your wages are gonna be, you know, applicative. So we're gonna be linear in logs of four components. The one, the occupation you choose is gonna have a productivity beta that's gonna directly affect your wage. So if lawyering gets more productive, the average return to lawyering conditional on your skills is gonna go up. Okay. And then there's gonna be sorting in response to that nice and easy. You're gonna choose an occupation and that's gonna depend upon your comparative advantage. So if some of us are really good in lawyering, we're gonna get a higher wage than some of us who are mediocre in lawyering. Conditional on both of us choosing lawyering, it's gonna depend upon our, you know, total human capital, which is gonna be our absolute advantage alpha. And our investment in those skills, like Ken and I were talking about earlier, the average investment in, in, in those skills that's gonna be raised to the return of those skills in that occupation, the gamma. And so the gamma are gonna determine how much the skills are rewarded that could differ across occupations and within education groups within an ag across education groups within an occupation. So you could basically have manufacturing just as a return reward college as much as doctors. Okay? That means their gamma three of doctors are gonna be higher than the gamma three of manufacturing. Although, and I'm gonna show you in a little while, you know, manufacturing might offer higher returns to some skill relative to another occupation. So all of these are gonna be allowed to be flexibly moving around in the data. And again, those are gonna be the exogenous drivers in the model. I'm gonna try to infer them and then I'm gonna shock 'em. And then I'm also going to have some aggregate, you know, productivity shifter around there to hit the level of wages. I'm going to allow that to vary by education group in theory, even though I'm gonna pin it down when I calibrate just to be the same across all education groups. Why? Because all of that's just gonna load onto the other parameters in the model. But sometimes we might say what happens if there's a general decline to college workers demand? And I wanted to have something in the model that allows me to, to kind of shock that. But right now this last parameter is just to pin down the aggregate wages in the economy. That's all it's do. It's a normalization. Yeah.

- Eric, when I think about large scale policy intervention effect on the supply and negative impact on wages, are they captured here or

- Yes, this will be a hundred percent. I took out my slides on sorting in the average wage. So exactly because all of the selection is gonna move the supply side is gonna move the average wage in the occupation. And if people start going more or less to college, I think as we've been talking about before, you need to be compensated for that as well. And so all of that average wage is going be endogenous to that. I took out for time all of my slides showing you those average wages and how it moves with both the primitives and the sorting going forward. But you're a hundred percent right lu

- You, you do add it up that more people going to lawyering lowers the wage of lawyer.

- Yes, a hundred percent the whole, because of a whole selection effect. 'cause you're bringing in less marginal lawyers as you go through and that's the whole game of the paper. I, but you wouldn't

- Wanna do that on a static basis because you know, I produced one generation of lawyers, well there's 50 years of lawyers already in there.

- So another apology slide and we did this in my paper with Pete and Chang, I should have a cohort structure when I'm doing all of this kind of thing. I am calibrating now to 25 to 34 year olds, assuming they are the only things in the data. There are these interaction effects. And so in the paper, like in my work with Pete and Chang, the allocation of of talent paper and chat, none of them are here. So that could, I could skip one of them. It's the same kind of sorting model. But there we had the coding, we had the, we had the cohort structure where they interact together.

- It can be the demand and supply of young lawyers and there's

- Yeah, yeah, again, we, we, I have no cohort structure. They do, they should interact and I have no cohort structure. Yeah,

- Just assume anything about higher order moments and across different occupations and education categories,

- Those are gonna be informative of the distributions. So I'm gonna show you in a little while how I'm going to use those higher earn moments to help pin down those distributional parameters.

- I honestly asked because I, I think Paul Dere has a paper a few years ago on like insurance value of college basically. So know going to college gives you or compared

- I am going to show I don't have any of those kind of effects. I'm gonna show you though the variance of wages in occupation education groups is going to be informative about the dispersion of the alphas and the fees in, in, in the month. And so I'm gonna use those moments to help me pin down distributional parameters. Lemme just do one last kind of, I think I have two more slides of just kind of theory kind of stuff and then we'll kind of get into how we're gonna do the data in the last half hour. And again, the counterfactuals are gonna take me like five minutes. And so from this you could solve for the optimal, again, everything's just log linear the way I wrote things. You have the utility function, people are going to optimize over their occupation, their human capital investments and their educational choice. Given the functional form you could solve for the optimal amount of human capital investment. Notice. No, I shows up in that. So if Steve and I both become economists and he's more productive than me, we are still spending the same amount on our human capital decision. It only depends on the returns to being, you know, a PhD in economics and our dish utility parameters and that's it. All of the variation between Steve and I'S wages is coming from our idiosyncratic stuff, conditional our human capital investment. And this is just gonna, again, to Ken's point, I just wanted to say the game why we're doing this, this is just gonna allow me to have PhD economists are going to make more than high school chemistry teachers because on average the average person is gonna have to spend more time in human capital investment for a PhD economists. And this is just gonna set the level of wages across occupations. Yes,

- John? So it comes from what things you chose to multiply together and what things Oh yes. Put in the exponents.

- Yes, yes, exactly. And so the data then I'm going to then try to fit through this model. And if I wrote down a model, different model, okay, I'm gonna get different things. And so then I wanna see how good I do on untargeted moments once I run this model. And so that's what I'm gonna do is my validation that the functional forms aren't crazy and then I'm gonna show you, eh, I'm not doing great, which tells me I might be missing something on some untargeted moments. And that's gonna, I'll show you that explicitly in a few seconds. Last thing I'm gonna say and then I'm done. The slide after this was the luigi's point about the wages and selections, but I took it out out, it's just gonna be a discreet choice model now. And so the individuals are gonna make decisions over the return to going to college, the return to go each thing. They could look at what is the return to different educations within those, then they could solve the returns to each occupation. And then it's just gonna be a discreet choice model. There's gonna be a bunch of stuff that's gonna be independent of the individual's dis individual's primitives, and then all of their epsilons fees and alphas, the things they draw idiosyncratic is gonna move different people into different occupations. Steve, what about the selection that could be interesting to play with them? Functional form, I mean it's really, it's, it's everything. So the next slide is the, the functional forms of the, of the distributions are really gonna drive all of the the things so far. John was making a different point. I made the functional form assumption of the wage productivity and the wage as well. But I'm telling you the functional forms of the distributions, that's two slides from math, that's the whole game. You know, I'm gonna make some assumptions and then I'm going to see how I'm gonna discipline those assumptions. And then I'm gonna ask conditional on those assumptions, how well do I do at matching a bunch of untargeted moments. So this is basically, there's a lot of parameters in this model for each occupation. You have the betas, the gammas, and the CAPAs for the data. I have a lot of data too. I have every occupation, every the college share of workers in that occupation. The wages by education in those occupation. So I have basically six times oh moments in six times zero parameters that I'm going to be thinning out. So I kind of do well on this part. Steve's part is the whole game then is what are these distributional assumptions about these idiosyncratic draws that's really gonna determine how people respond on the margin and away from the margin. But what I'm gonna do now is try to tell you how I'm gonna try to get these parameters, then we'll see whether they're sensible or not. I'm gonna do three things. Part one is kind of the six by times o moments in the six times O parameters. I'm just gonna use data on occupational choice, educational choice in wages from census and American community survey for men 25 to 54. I'm gonna show you how I define occupations. I'm gonna show you what those wages and educational shares kind of look like. So that's gonna be the first part. Once I do that, that does the easy part that backs out the Gammas and the Kappas and the, and the, the, the betas, the occupation premise. Anybody who knows, like Steve does like these models of kind of, you know, McFadden or Eaton Cordem in the trade literature, you could always match any set of moments with those sets of data if you have the distributions. And so the whole game of this really is the distributions are gonna be the key important parts of kind of doing the, the inference. So that's part two and part three, how am I going to get these distributions? And so the first thing, second part is I'm gonna use a whole bunch of data from the NLSY of of conditional co variances of wages and occupational choice by different A FQT. A FQT is a proxy for absolute advantage in my model. And then I'm gonna show how those distributions are gonna move around. And that's gonna give me the distribution of alpha, how dispersed wages are and potentially in a correlation of alpha with occupational choice. And then the last part is, my favorite part is I'm actually gonna go to the real world and I'm gonna shock local demand at a regional level and then see how people change their occupational choices. So Steve was the question of going back to the 1970s and kind of do that. That could be good. I wanna basically just look at, you know, kind of China shock manufacturing shock variation at local levels in the United States and see how many people kind of changed their ion occupation educational choices. And that's gonna tell me on who's on the margin if I could get those in the right units. And so that's kind of being kind of the, the right thing to do.

- The fracking thing would be another interesting thing. Yeah,

- That's another

- Because people bemoan the fact that it reduced college attendance but the question is what it to do for utility.

- Exactly. I mean to be fair, I also used the housing boom in my a AR piece with Kerwin before. And basically again the numbers, this part of the paper, I'm gonna get numbers that look like my stuff. You know, with Kerwin it's gonna look like some fracking stuff. It's gonna look like people did in Spain when they kind of housing boom there. And I'm just going to take those estimates which look like the literature and then just filter it through the lens of my model. And so the stuff I'm gonna give you on this, the delta to science is small and the estimates, it's using those estimates to discipline the model is kind of what the delta to science is in this paper. Yeah.

- The reason why you're doing only one, you know one thing that also curr in your first graph is like a massive price and female graduation. Yes you have like 60 40 now, but there is also quite a lot of sorting by gender across different,

- It's on the list to do. In order to do that, I really need a much more realistic labor supply margin because there's also a lot of entry during this period and I don't have that in the model yet. So the reason is only just I don't have that ingredient in the model. So because of that and that's so important for women, I've only focused on the men. Okay, so let me kind of show you kind of the, kind of the data you kind of parts first. So of the set of occupations out there, just the dimensionality to six, okay, you could have done 700, you could have done 300, you could have done 79. I'm gonna reduce the dimensionality to six. And I'm gonna try to do this on a two by three kind of sorting mechanism. The educational intensity of the occupation and whether that occupation conditional on education earns high income or relatively low income. And I'm gonna show you, this is how this is gonna split the data. So what I'm gonna do is for every occupation in the census, whatever in the census category of about 300 occupations, I'm gonna sort them by the educational intensity of the workers. And so how many get a bachelor's share, how many get some in college, how many get a high school degree or less? I'm gonna take education group one as being the occupations where it's at the top third of employee, the top third of the population weight or top 30% of population weighted bodies. I'm gonna take occupation, the bottom occupation group, education group. I labeled my one, two, and three like said education group one should education group three, the bachelor's degree, the high school degree is gonna be the bottom third of those occupations. Basically the ones with the highest, highest high school share and all the rest will be in the middle. And then for each of those occupations, I'm basically just gonna run kind of a a, a regression of log wages on education and take the occupations above the median and below the median and call those high and low income respectively. And it's gonna segment the population into six occupation groups, by definition, high education, high income, high education, low income, et cetera. And so these would be the occupation groups. So occupation one is gonna be your doctors and your lawyers and your CEOs and your engineers and senior business leaders. Steves in there as an economist, et cetera. Occupation two is high education, low income, thank your teachers, okay, social workers, et cetera. Occupation three is mid income, high, mid education, high income. Those are gonna be your, a lot of your science techs, your lab techs, your managers in manufacturing, your managers in construction. The mid education low group is gonna be a lot of your office workers in some professional services. Five and six is gonna be all the manufacturing line. Workers in construction, workers in five and then all of your other, some of the construction workers, your janitors, your mechanics, your taxi drivers, store clerks and cleaners. So there's gonna be six groups that I'm gonna look at. By definition, they segment on education 'cause that's how I segmented them. So you're gonna have group one is gonna be almost all bas. Group three is gonna be almost all no bas. And then then you know, 70% are gonna have high school or less. And then the middle group is gonna be a mix. And so there you're gonna see people kind of overlapping with BA shares, some college shares and even high school shares. Notice the other part of this relatively constant time. So it's not like there's shifts within groups that are really driving things. A lot of the mechanism, again, I don't allow that in the model, but a lot of the mechanism's gonna be across groups. And so that's where our, our, our, our drivers are gonna really pick up. This next part though, I think is most interesting. So now let's put the log income of each of these education groups or occupation groups over time. And you should notice some non monotony. First of all, the lawyers and the doctors and the Steves are always at the highest end of the income distribution. But notice the second group is those with some college who are basically going to be the manufacturing bosses, the police, unionized workers, the scientific techs. They make more than the high college teachers. So when you're asking, when you force everybody to go to college, some people could earn more when they don't go to college given their comparative advantage in sorting. So that's gonna be a mechanism in the model that's going to, when you're forcing people to go to college, there's these occupations out there where you could earn a lot without, without getting a four year bachelor's degree. And the same with the manufacturers. That's the yellow group. You know, that's the lowest education of the groups but yet the line workers in manufacturing make a chunk more than the some college office workers and as well as the bottom, you know, the bottom barbers and such. And so this idea that everybody has to go to college to get an income, there's a lot of people in the data in all periods if they work in those sectors, you could make more than another marginal group that got more college than you.

- Yeah. This is pre-tax and transfer income for the ones who choose to work and not adjusting for hours.

- So this is full-time work, I should be very clear. Yeah, so full-time workers would, yeah, pre-tax is gonna be your whatever you get in the CPS as your labor earnings. So it's not gonna have any of the transfers in there for full-time workers. So I restricted to everybody who's working at least 30 hours a week and worked 52 weeks last year And no benefits. And no benefits. It'll be kind of what you report in your, I think without the benefits. So we put in benefits, these numbers are gonna be potentially moving on. I'm just saying the salary stuff or no, by itself it is pretty large but I should have been more clear on that. Yeah,

- This, this assumes that there is no differential probability of employment across groups, right?

- This is steady state. So if there are, to be fair, you're right 'cause I put full-time workers so any of that, you know, kind of cyclical patterns that would be out of this kind of component. The cyclical patterns I imagine, you know, will also scale in somewhat that ranking. We don't tend to get much displacement in a cyclical sense from the lawyers and doctors. You tend to get it more for the barbers and the sales workers down there as well. So that could could add a little bit more to the spread. Oh, so now what I'm gonna show you is some NLSY data that's gonna help me kind of think about the dispersion of absolute advantage. Now part of what I'm doing here is I'm going to load a lot on A FQT score in the NM LSY as being some measure of an individual's absolute advantage. So for those unfamiliar, the A FQT scores is a standardized test be given to all of the armed forces members. The NLSY asked that of all members, they put it in standardized units in percentile rankings. And so then we have people when in the NSY when they're, I'm gonna call it 14 ish, sometimes 12, sometimes 16. And then we could see their N-L-S-Y-A-F-Q-T and then follow 'em out over time. And then we could ask what occupations they go into when they're old based upon their A FQT score and what is their earnings when they're old based upon their occupation education and A FQT score and these conditional moments of occupational choice and earnings is gonna be useful to the model of pinning down the distribution of alphas.

- I have a clarification. Yeah. So do I have to think about these scores as affecting my cost of going to college as well

- Or so that would be fantastic. So I'm gonna have no correlation in that right

- Now. Right now you don't have

- It but, but again, the correlation between comparative advantage and correlation of cost, I think the model's gonna need it. I'm gonna show you where I'm gonna fail in a couple seconds of doing this and it looks like I'm failing in a way that's gonna need some of these correlations. Right?

- Well you just said where does comparative advantage come in? I would've thought that was the occupational choice in the royal model.

- Okay, it it. So I'm gonna have to discipline that variation in comparative advantage. So all of this is, I'm, I'm being very sloppy in my language. Adrian will get mad at me. All of this is gonna be jointly identified through the lens of the model. So no one moment is identifying any one thing. So I'm writing it in using a language that this moment pins down this. So the comparative advantage, the absolute advantage and the costs are all going to be jointly matching these moments. I'm trying to intuitively say this might be helpful on this dimension, but to Rick's point, all of these will be inferred individually. So when I show you this picture, which is basically in the analyst Y, this is data, what is the occupation share of different occupational group sorting of different A FQT groups relative to the average. So everything should be looking relative to the average here. So a number like 20 is 20% judge points more likely than the average occupation. And you can see high A FQT people, that's gonna be a FQT group four are much more likely to be doctors and lawyers and economists and much less likely to be gardeners and you know, shopkeepers and, and you know the low, the low education group and there's a little bit of modernity, not huge. The red and blue doesn't mean significant or not. So all of these could have information I just highlighted the top and the bottom just to draw your attention to. And conversely, if you're in the lowest A FQT group, you're very likely less likely to be a a lawyer or a doctor or Steve. So again, these moments are gonna be useful again, jointly determined. Now the comparative advantages in there as well. But all of these things are going to be kind of interacting together. And then I could just ask the wages when they're 30 ish of people in different A FQT quartiles and different education bins. And you could see as you're highly educated in a high A FQT group, you tend to get an average, your wages are like 80% higher than if you were in the low A FQT group and the low education group. So this spread of wages is gonna be a little bit useful on the spreads of these, again, in my mind A FQT. But all of these things interacting together.

- Yes. What about just having different utilities for different occupations?

- Is that in the, that's not because if like if you go back on, that'll be in the Kappas as well. So the average CAPAs is gonna be anything that makes an occupation much higher, more desirable on every, I'm using the Kappas as costs. Yeah, but it'll be, it should be like net costs relative to those other things there as well. And so the cost would actually, I'm gonna get a number like 300,000 and if it's actually more utility, the cost could even be higher than that. If, if some of this is, is actually utility based as well.

- Okay,

- Let me do one last thing and then I'll kind of show you some counterfactuals. I'll show you where the model fails and then I'll show you some counterfactuals. The last thing I'm gonna do is kind of use this regional variation in local demand shocks to try to pin down how at the local level people respond to these local demand shocks in terms of your education attainment. Like Valerie said, there's lots of literature on this, myself included. Then I'm gonna turn those estimates into model units and then I'm gonna try to use those mo those estimates to help discipline the other parts of dispersion in the model. And those, for those unfamiliar, I'm just gonna use a traditional shift share instrument. You could call it a bar instrument, which basically is gonna be, each region is going to have some industry mix. In some pre period, we'll call it 2000, there's gonna be some national demand changes for those industries like manufacturing declines naturally nationally that's going to hit Detroit more than it's gonna hit Orlando. Orlando produces Disney World, Detroit produces manufacturing. So when national manufacturing goes down, it's gonna have disproportionate effects on the residents of of Detroit relative to Orlando. So this is exactly what I did in my housing instrument paper. We got nearly identical instruments. David Otter has done something, the version of this with a China shock, other people have done it with fracking. I'm just gonna use all the industry kind of shifts together as as my shock. And then what you're gonna see is patterns like others have gotten in the data, which is going to be for this first pan, I'm gonna ask what happens to non-college wages. The more negative shock you get in this case, the negativeness of your shock is on the X axis. What happens to your log wages of non-college workers on the right panel, the left panel y axis. And it's gonna basically say places that had big negative shocks had the wages of low skilled workers fall and the wages of some college workers fall as well going through this estimate. Then for the average size of the shock, the average size of this negative shock was about four percentage points. The elasticity was about 1.4. It's basically saying the average shock was getting you about 5.3% decline in wages. Why is that important? I'm gonna tell 'em to scale the shock in my model, I'm gonna pick a shock in the betas that is gonna give me a 5.3% decline in wages and then I'm gonna ask what happened to education in the data and then I'm gonna choose the parameters. Those dispersions of comparative advantages cost in our model to match these moments. Which is basically when you had a negative shock, the share of people going to some college on average went up by about two percentage points for the average size stock, the share of people going to a bachelor's degree zero. So what happens is you're gonna say from these local shocks concentrated disproportionately to the low end of the distribution, you're gonna have very little effect on bachelor's but a non-trivial non-zero effect on some college. And so our model's gonna say that's gonna be a little bit more elastic on the non-college margin than it is on the bachelor's margin.

- But it's possible that these are people that drop out that try to go college.

- It could be exactly, exactly. So what I should be very clear, it is some college in the definition that Anna put out before could be associate's degrees or trying and dropping out in the model. It'll have that in the wages of these people average. And so now I'm just going to do exactly what I said and put it in model units. I'm gonna shock the demand for low-skilled workers in our model 'cause that's where these co shocks were concentrated such that it gives a 5% decline in wages. Like the data says for an average shock, I'm then going to choose in a calibration sense the dispersion of my parameters so that it matches those moments such that we get about a two percentage point decline in non coll some college or 2% increase, percentage point increase in some college and no effect on S. Yes. Five minutes. Perfect. That's the thing. So now that's what I'm gonna do. So that's gonna pin down in a GMM sense kind of the model. I'm gonna show you three things and then I'll show you the counterfactuals to end and those will be relatively quick. This is just what comes out of the model in terms of these dispersions, the log normal of alpha of being 0.3, it says it's about a 30% dis dis standard deviation dispersion on absolute advantage. That's what the model's saying. Comparative advantage of five in a fresher sense it's gonna be our comparative advantage. Isn't that great? That's kind of a relatively small amount of comparative advantage and the costs are very dispersed. So a comparative advantage, the CO for shape parameter of one means hugely dispersed kind of costs and the cost dispersions are going to be much more for the bachelor's costs could be utility in all of those other things relative to the sum college. And that's what the model's throwing at what is the average size of the CAPAs that come out of the model. It's gonna come out at a number like 1.4 or 1.5 somewhere in there. You're saying Eric, what does that mean? Well in the model I could turn those into dollars units. And so just taking those in models units, 'cause you know the CAPAs are in log earning kind of space. A CAPA just to hit the line of about 1.4 comes out to being something like 30 $300,000 in model units when I turn it into wages. That's why I say this is huge. Well

- Is your model not just saying, well there's these huge wages if you go to college, they didn't go to college so they must have seen huge costs or are you

- Yeah they're they don't conditional on their skills. Yes. And so the model is then saying, there says two things. It says the returns to being a lawyer is really high given the dispersions of people's skills. We see a lot of lawyers but not everybody's being a lawyer. So it tells me somehow that there's gotta be cost to going to lawyer lawyers or the comparative advantage or absolute advantage is really bad at being lawyers. The fact that there is some people on the margin making adjustments tells me it can't. The net benefits have to be, you know, where some people move be at least on the, some college margin and then the wage distribution tells me something on average about how the disperse these costs are. And so putting it all together is yes. And so that's kind of what it is the model wants to shoot at. And so the average costs though are really kind of coming from these elasticity parameters, not the level. So let me just do again, I have three minutes, I'm just gonna show you, this is where I fail. So as an audit samples test, I try to pick people into A FQT bins and just say how much average schooling do you get? Right? Left hand side is the data. It's steep by model. Much more muted. And so I think again we get some, you know, you get something but I think the correlations will be very helpful on this margin.

- You, you're just saying that there's so much variation there should be more smart people down in the ones that

- Exactly. Exactly. And our model isn't given what the data is, so something's pulling them away from going to that. And so I think some of the correlation between the primitives in the model like the, you know the high alphas have lower costs, you know that was Paula's story I think could be doing that. I wanna show you in the model, we could also do those RD kind of studies people on the margin. We have all of these margins in our paper of you know, people on the border of going to lawyering bachelor's degree versus you know, teacher bachelor degree versus teacher some college. And so we have all these people on the margin and we could just take people and turn 'em over to the other side of the margin just by kind of moving them to the other side of the bar. And you could see in our paper we get something like a 7% enga average income gain by just taking the average person and moving them over the bar. Which is kind of what, you know, Jack gets in his paper but the utility in our model is zero. They're marginal. They would've made the choice if there was a gain. And so in this kind of thing we could be having a model consistent with these marginal effects but you know, but still have no utility gain. This is John's point. Early on in our model we get income effects without utility effects for the marginal people. Okay, last thing we do six counterfactuals given the model all by changing CAPA and we do it in a variety of different ways. I'm gonna show you the results of them pretty quickly. They're all roughly the same. What we're gonna do is we're gonna move tuition by about $20,000 for bachelor's. That's about 5,000 a year. We give anybody who wants to go, we're making bachelor's degree free. We're giving everybody $5,000 a year to go. And if you go to associates, we're gonna give you 5,000 a year, but it's, I'm gonna say two years on average. So we only give you 10,000. We're gonna lower the CAPAs for bachelor's by 20,000, lower the CAPAs for some college by 10,000. Then I'm just gonna lower the CAPAs for some college by 10,000 or the first two years of college by 10,000, which is some college. Or you could go to a bachelor's. I could do that only for STEM occupation. Suppose we just wanna stem subsidize occupation one, I could only do that for highly talented alpha people give scholarships in a way that only target the top of the alpha distribution. Or I could target the top of the alpha distribution who also have the top of the Epsilon distribution. Maybe those are the people with the most idiosyncratic costs, maybe they're liquidity constraints. And so for each one of these six exercises, I'm gonna show you a picture like this. I'll flip through 'em quick and then I conclude, which is basically just what happens to the bachelor. Share some college wages and utility. I'm gonna focus on the first two, what happens to the bachelor share and what happens to the utility. That first column just tells me the average of the data of how many people are going to college. And by giving everybody $20,000 to go to a bachelor's degree and $10,000 to go to associate's degree, I move the bachelor's share by three and 0.4 percentage points at the bottom and 1.2 percentage points at the top. All the utility gains in the last column go to the top. 'cause they were already going to college anyways. So most of them are just getting this infra marginal transfer from this free college. And if we put this in dollars per bachelor's degree space, we're basically spending $400,000 of policy for every bachelor's degree to make a $5,000 going through. And so don't have to look at the next numbers. I promise I'll conclude this. Just look at the bottom line of how many dollars per student. Suppose I only give $10,000 to the first two years of college, make associate's degrees free. That's about a half a million dollars per bachelor's degree that would cost.

- But Erica, so one question I have is that your correlation here is gonna matter, right? Oh, tremendously. Yes. Suppose that I give money to everyone but only the one that are really talented.

- Yeah, but that, that is something that's right now that's kind of what I'm doing. It'll even get worse. Okay. When I put the correlation in. 'cause those really talented people who will already be going, but that's col occupation five. I'm just, let's give those, I give $20,000 only to the high alpha people.

- Okay,

- That's more than a half a million dollars per bachelor's degree. And the last one is, suppose I give it to the high alpha but only also the high Epsilon quartile as well, assuming that there's some friction there. And that one, it's only $300,000 per bachelor's degree. All of these have large negative ROIs. Now again, it's a structural model. I've gotta take care of my calibration a little bit more, but it does kind of tell me that my playground is kind of something useful I think of to try to think about these marginal and for marginal responses to policy. I know I have a lot more to do on the correlations trying to separate that last part, future work, the monetary costs from the other types of costs, like to look at liquidity constraints. And then as Steve's point, what these other costs are really tells me whether there's a role for policy or not. Maybe providing information better, maybe you know, these other kind of maybe investing more in like a heckman sense and getting people's alphas up before they go into the college decision or kind of the right policies as opposed to trying to make college free for all when there's all these info marginal people. Okay.