Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable. ======================================================================== # The Demographic Cliff and the Market for Higher Education: Implications for Public Finance Authors: Dirk Krueger, Alexander Ludwig, Irina Popova Discussant: None Video: https://www.youtube.com/watch?v=w6ObGDwelyg&t=2895s ## Talk (00:48:15 – 01:19:59) [00:48:15] >> Well thank you so much. This is a good discussion. Hopefully you can follow up offline with folks. So we just ate into our our break after the next paper and that's fine. U we that was uh by design to some extent that we have a break that [00:48:29] we can use to catch up. So we'll move to our next paper now on the demographic cliff and the market higher education implications for public finance. So I think we have all three authors here. So who's going to be presenting? Me [00:48:42] >> Arena. Okay great go to it. Thank you. Okay. [00:49:02] Oops. I'm sorry. One second. And again, if um uh the co-authors uh [00:49:33] want to respond to things in the chat, that's all all great too to keep the the conversation going. [00:49:40] >> One more second. Almost there. >> And Ron, you still have your hand up. [00:49:45] Uh, what do we wait? >> Oh, no. [00:49:54] I'm sorry it's taking a bit longer. So, now you should be able to see my slides, right? [00:50:06] >> We can see your bookmarks as well. So, if you just X out the books and and then hopefully you can. [00:50:12] >> Okay. So let me do full screen then. So now you should be able to see the slides, right? [00:50:18] >> Yes. Yes. Perfect. Thanks. >> Okay. Great. [00:50:24] Okay. So uh thanks so much to the organizers for including our paper in the program. It's a great pleasure to be here today and I'm very excited to present this project on the demographic cliff and the market for higher [00:50:37] education implications for public finance. And this is joint work with Durk and Alex who are also both here in this Zoom meeting and I hope they can manage the chat. [00:50:50] So the big question that we address in this project is how population aging and demographic change affect the skill composition of the current young cohorts and more importantly future cohorts that will enter the labor market over the [00:51:03] next decades. relatedly how will the changes affect the macroeconomic aggregates and public finances given the US college market so for today's talk I'll focus on one particular aspect a [00:51:16] narrow question can the response of college education who enrolls which quality and major they choose offset some of the long run fiscal costs of the demographic cliff so let's first look at the demographic [00:51:30] cliff itself so the demographic facts that we analyze here We study the fertility decline that began around 2008. So the well doumented drawing point in the US total fertility rate. [00:51:42] The dashed red line here is the demographic cliff scenario. So this is the actual fertility decline beginning in 2008 projected to persist into the future. The solid blue line is our counterfactual baseline in which the [00:51:55] total fertility rate remains at its pre208 level. Now the right panel shows the corresponding population numbers of 18 year olds. [00:52:05] The two lines begin to diverge in 2026 because the fertility decline around 2008 translates into a decline in the population aged 18 around 2026 which is approximately where we are right now. [00:52:18] Now by 2086, 60 years from now, the population aged 18 is approximately 40% smaller under this demographic cliff scenario compared to the counterfactual baseline. So of course this decline in [00:52:31] the young population also changes the entire age structure of the economy. So the working age population ratio falls from about 78% to 67% along the demographic cliff path. So what this [00:52:45] means for the macroeconomy, this means that labor becomes relatively scarce. [00:52:51] Now let's zoom in on the college market. So the national center for education statistics, the NCES projects that high school graduating classes will shrink by about 5% by 2032 and the Wishi, the Western Interstate Commission for High [00:53:05] Education projects that by 2041 the number of high school graduates will drop by 13%. So we have also seen the first adjustments on the supply side. [00:53:14] Over the past few years, approximately 100 institutions had to shut down. But to be fair, these were mostly relatively lowquality two-year institutions. But this tells us that the sector has already begun to adjust. [00:53:28] But the smaller high school graduating cohorts per se do not tell us how enrollment rates, college quality, and major composition of will respond. [00:53:38] So the way we think about these questions, population agent affects both the returns to college and the resources available to finance it. So on the return side, labor becomes scarcer, which pushes wages up for everyone. But [00:53:52] on top, when capital is more complimentary with skilled labor, wages will rise even more for skilled workers. [00:53:59] On the resource side, as the population ages, wealth gets shifted across generations which can change inheritances per person. And eventually how those agentdriven changes in returns [00:54:12] and financing translate into education decisions and eventually macroag aggregates and public finances is likely shaped by how the college market itself adjusts. So what happens to quality, major composition and tuition which are [00:54:25] all indogenous objects and this is exactly what we do in this paper. [00:54:31] So we study how demographic change shapes college education and how that in turn affects the macroeconomy and public finances. So let me now explain our approach and what is new about it. [00:54:44] So our main contribution so the uh new thing about what we do is that we bring an indogenous college supply side with a distribution of college quality and majors intra macro model with indogenous [00:54:58] human capital general equilibrium government budget and an agent population. So demographics here are exogenous to our model. We feed in exogenous population projections. Now key aspects of our analysis first [00:55:11] college supply is endogenous. So profit maximizing colleges compete for students and the resulting distribution of college quality majors and tuition is an equilibrium object. Now on the demand [00:55:24] side, households make endogenous decisions about whether to enroll in college, which college quality to choose and which major to study. Next, importantly, there is wages are also indogenous, meaning that there is a [00:55:37] two-way interaction between the college market and the labor market. Well, saying it broader, there's a two-way interaction between the college market and the macroeconomy. [00:55:47] So now using this framework, we conduct a number of thought experiments, but for this presentation, I'll focus on our main thought experiment, which is the demographic cliff itself. So the demographic cliff that I just introduced two slides ago, we analyze the full [00:56:02] transition path rather than comparing only steady states. [00:56:07] So now here's the outline for the rest of the presentation. First the model, then very quickly calibration in the US college market in the baseline year 2026. Then the demographic transition, then a discussion of the importance of [00:56:20] the specific structure of the US college market for our results and then a brief discussion of mechanisms and then I conclude. [00:56:29] So if there are no questions then I'll jump in jump into the model directly. [00:56:34] All right. So let's start with the college supply side. Each college here is a bundle of quality Q and major P. Following a large literature, we model colleges as clubs, meaning that student ability directly [00:56:49] affects college quality production. Uh colleges operate a constant returns to scale technology under free entry and perfect competition. So here the college quality here is the college quality [00:57:01] production function. So quality Q is produced using two inputs instructional spending per student I and the average ability of enrolled students E bar. [00:57:12] Colleges have two sources of revenue per student. The first is tuition uh the function T here. It can depend on the students ability E and family resources financial resources B and tuition is an equilibrium object. The second revenue [00:57:27] source is the public subsidy v theta which is set proportional to gross tuition and the subsidy rate is a policy parameter. The revenue function V combines both both sources. So for given [00:57:41] quality Q and major P, it gives the revenue generated by admitting a student of ability E from the resource types that yield the highest revenue. On the cost side for colleges there is also a fixed resource cost that is major [00:57:55] specific. So the capa P here is the fixed resource cost that is different between STEM and non- STEM majors. The objective of a college has to deliver a given quality Q at and major at the smallest possible [00:58:10] cost. Colleges choose spending and spending I and ability composition ADA. [00:58:16] So ability composition of their student body. So ADA is the share of liability students to be precise. Uh and with free entry and perfect competition, tuition then adjust in equilibrium so that colleges earn zero profits. [00:58:29] Right? So now uh on the other side of the market are households. They differ in ability high or low and initial resources B. Each household chooses a [00:58:41] college quality Q and a major P with quality zero denoting no college. The market clearing condition requires or the college market clearing condition requires that for each ability type the mass of students choosing a given [00:58:56] college bundle QP has to equal to the mass that sache college actually enrolls. And with free entry this pins down the ability composition of students at each college type QP. So eventually [00:59:09] ADA the share of high ability students at each college QP is an equilibrium object as well. [00:59:20] So uh within each ability group, colleges admit the students who generate the most revenue. Now a useful theoretical result that we prove for our setting explicitly is that any equilibrium allocation can be supported [00:59:33] by a simple tuition schedule that is a linear function of student ability. So each college charges a base tuition TQP and high ability students get a discount DQP. [00:59:46] because student ability is an input into quality production. So in the end, these two objects, the base tuition and the ability discount are the prices that clear the college market. [00:59:59] Now let's turn to the household side of the model. Households enter the life cycle with initial assets B conditional onability. This initial financial resources are locked normally distributed and the total mean is a [01:00:13] function of end of life requests. So this is the intergenerational wealth channel that I'll talk about at the end. [01:00:20] In this college period which is the first period of life, households get direct utility from college attendance. [01:00:26] So this is new zero here. Then they get utility from college quality. So the weight on it is then new one. And for STEM students there is an additional ability dependent utility shifter new too. So in this first period of life the [01:00:40] sequence of decisions is as follows. First uh individuals choose quality Q and major P. Then the dropout shock is realized and this dropout probability PI D uh depends on college quality and [01:00:55] student ability. So depending on the dropout shock realization, households enter the labor market either as dropouts or as graduates. So S equal to CD stands for college dropouts and S equal to CO stands for college [01:01:10] graduates. So college choices QP and then this dropout shock realization together determine the labor market productivity over the life cycle. And the this function gamma J is a deterministic age [01:01:24] productivity profile that depends on college quality Q major P uh and whether students graduated from college or dropped out. From the first working period on households solve a standard [01:01:37] consumption savings life cycle problem given their acquired college qualification. [01:01:45] So now let's walk through how we aggregate and close the model. [01:01:50] So first efficiency units of labor across cohorts aggregated to get three labor inputs. P 0 for non-ol labor uh P1 for college non- STEM labor and P2 for [01:02:04] college STEM labor. So in this aggregation equation 5G stands for the cross-sectional distribution over education types at given age G and NG is [01:02:15] the size of cohort G. On the production side the aggregate production physical capital is not equally substitutable with the three types of labor. So capital is more complimentary with college labor and especially so with [01:02:29] STEM labor. Formally this this means that the substitution elasticity between capital and labor is sector specific. So you can see here that the row parameters are [01:02:40] indexed by P. Finally the government budget uh high education spend. So high education spending which is the capital E here uh it's college subsidies and [01:02:54] financial aid to students as well as other government spending not related to education capital G. Uh so this spending is financed by tax revenues. So revenues [01:03:07] from labor income taxes, consumption taxes and capital income taxes. Then the level of the labor income taxation is the policy parameter that adjust each period to balance the government budget. [01:03:20] So throughout we assume that the non-education related government spending scales one for one with population. [01:03:29] uh and finally social security has a separate budget constraint that is also balanced on per period basis. [01:03:38] Now how we how do we discipline this model? So I don't really have time to talk about calibration. I'll just say that we calibrate the model along the transition. So we calibrate the baseline transition using data moments that are [01:03:51] averages over 2010 to 2019. All right. So then taking this calibrated model, let's first look at the college market in our benchmark year 2026. [01:04:05] So panel A which you see right here shows the equilibrium distribution of college quality Q and majors P where Q0 means no college. So blue bars show non- STEM enrollment and orange bars show [01:04:20] STEM enrollment. We use two Y-axis here. The left axis applies to the gray bar at Q0, the non-enrollment rate, and the right axis applies to the bars at positive Q and shows the share of the [01:04:32] cohort choosing age quality and major. So key observations first about 50% of the cohort doesn't enroll. Among those who do attend, enrollment is quite spread out across the quality levels and [01:04:47] the orange stem bars take a relatively larger share as quality rises. [01:04:52] Now panel B shows the share of high ability students plotted against college quality. The point at Q0 so this dot shows the high ability share among those who don't enroll the non- students. [01:05:04] Among enrolled students the high ability share rises monotonically with quality. [01:05:09] So meaning that there's quite pronounced sorting viability along the quality letter. Finally, >> so just a clarifying question, sorry, but so so you said you didn't talk about calibration, but here we're looking at mostly data or how much of this is [01:05:23] filtered through the model because >> so some of the moments are directly targeted, but what I'm showing you now is not targeted. So these are basically free moments that we use partially for model validation. So what we target [01:05:37] explicitly is the enrollment rate, the dropout rate, average spending on tuition, uh wage premier, so the wage differences between college non-ol workers, wage differences between uh top and bottom college quality tiers and [01:05:51] also wage differences between STEM and non- STEM. But what I'm showing you right now, these are not targeted moments. So this is model. But the how do you want to isn't there like a way to map the data on like quality to act [01:06:04] in your model you have a queue and then in the data isn't there like a way to think about college quality and try to map it >> I mean we could discuss it later it's there's no like clear unambiguous way there are many ways you could think about what quality is in the data so that's also part of the reason we don't [01:06:19] really show you now the data counterpart here but I could show you the data counterpart for tuition and at least the gradient is very close to what we have. [01:06:28] So the dispersion between so the difference between low quality and high quality colleges in terms of tuition. So yeah we looked at the data specifically. [01:06:36] So I have a lot of moments from the iPads the integrated post post gradient education data systems. Yes I mean we can discuss it later but I just don't want out of time. [01:06:47] >> So this is the gross tuition schedule by college quality. Again not targeted as I just said and I show it here separately for low ability students. So that's a black curve and high ability students that the blue curve. So a few quick [01:07:00] observations on this. Tuition rises steeply with quality. High ability students pay less. So they receive an ability discount. And as you should remember by now, this is the theoretical feature of our model. So high ability [01:07:13] students help produce college quality. And that's why colleges optimally charge them less. Empirically this can be interpreted as institutional merit based financial aid. So overall our model captures key qualitative features of the [01:07:27] current US college market disperse college quality clear ability sorting and a steep tuition gradient. So now let me introduce our main thought experiment in greater detail. So this is the same thought experiment I talked about in the [01:07:42] introduction just being more detailed about it now. So as I mentioned we focus on the fertility decline that began around 2008. We considered two demographic scenarios. the baseline showed by the solid blue line in all [01:07:55] three panels and also on the slides to come and the baseline assumes that this fertility decline just didn't happen in the demographic lift scenario shown by the dashed red line. Uh we assume that the post 2008 fertility decline uh [01:08:09] persists into the future. So households learn about this decline in 2010. So they learn about the cliff in 2010 and have perfect foresight thereafter. All the transitions are initialized in 1950 [01:08:22] and the final steady state is set far in the future in 2200. But for exposition, these plots here and on the next slides show only a fragment from 2000 to 2100. [01:08:35] Panel A shows adult population numbers over time just to get a sense of the demographic of the magnitude of the demographic cliff. So you see that by 2086 the adult population is about 20% smaller along the demographic cliff path [01:08:48] compared to the baseline path. Panel B shows the annual population growth rate by 2086. It's approximately zero along the cliff path compared with about 6% per year on the baseline path. And [01:09:00] finally panel C shows the change in age structure. So the working age population ratio falls from to about 67% along the cliff path here by 2086 compared with about 72% along the baseline path again [01:09:15] in 2086. So this gap in the age structure in the working age population ratio between the two scenarios. So the gap between the two lines peaks in the 2080s and that's the reason we choose [01:09:27] 2086 as the focal year for our analysis. So on this transition plots, you'll see two vertical lines marking our horizon. [01:09:35] 2026 is the baseline year and 2086 is our focal year for the analysis. So the analysis focuses on this 60-year horizon from 2026 to 2086. [01:09:45] All right. So let's look now at the college market adjustments in our focal year 2086 under the demographic cliff relative to the baseline. So this panel A shows the percent change in the quality distribution. So the same two [01:10:00] yaxis uh axis as in the baseline 2026 plots with the gray bar at Q0 shrinks meaning that the enrollment rate rises so non-enrollment falls so enrollment [01:10:12] rises among those who enroll the mass shifts toward middle and high quality colleges and slightly more so to STEM. [01:10:20] Now panel B shows the share of high ability students plotted against college quality in the baseline black curve and under the demographic lift scenario. So the blue curve since marginal entrance so the new students who enter the [01:10:35] college market are on average less prepared they have lower ability in the language of our model. So the high ability share falls across the quality distribution as a result relative to the baseline and especially so at the [01:10:47] bottom. And finally, panel C shows the gross tuition responses in 2086 relative to the baseline. So these are percent changes of tuition for lower ability students, black curve, and for high ability students, little curve. So the [01:11:01] adjustment is not a uniform tuition change. [01:11:05] With more lower ability entrance, spending per unit of quality rises, pushing tuition up for everyone. That's one force. But offsetting that, colleges raise the ability discount for high ability students since those become [01:11:19] relatively scarcer and low ability students become relatively abundant. And that pulls tuition down for high ability students. And the net result is that low ability students see gross tuition rise [01:11:30] by about 2% at middle quality schools and high ability students see gross tuition fall by about 1.5% at middle quality schools. Okay. So now let's look [01:11:44] at some of the aggregate variables along the transition path. So factor prices and some of the aggregate macro variables. [01:11:52] So first looking at the factor prices. The left panel shows the annual interest rate. The middle panel shows the college to non-olage ratio and the right panel [01:12:04] shows the STEM college to non-olage ratio. Focusing again on our focal year 2086, the uh the second vertical line on these plots, the interest rate is about [01:12:17] a quarter percentage point lower under the cliff than on the baseline path. [01:12:22] Wages rise for all groups relative to the baseline, but they rise more for college workers than for non-ol workers and even more so for STEM college workers. So this differentiated weight responses follow directly from the [01:12:36] production side assumptions because as I mentioned and I hope you remember the model explicitly capital skill complimentarity and capital stem complimentarity. [01:12:45] So now the next three plots so please pay attention I just swapped these plots. This is a new set of plots. Uh so here we see on the left the college enrollment rate for the young cohort aged 18 to 21 in the middle the labor [01:12:59] income tax rate and on the right GDP per capita. [01:13:03] So enrollment is about 9 percentage points higher in 2086 under the demographic cliff scenario than in the baseline. This the same effect we saw one slide earlier but now shown over the full transition. On the fiscal side, [01:13:18] middle panel, the labor income tax rate by 2086 is about 1.2 percentage points lower than on the baseline path. [01:13:27] And finally, right panel, output per capita is higher along the cliff path by about 2.3% in 2086. So overall given this indogenous college education responses the demographic cliff is [01:13:40] mildly positive in per capita terms and more than self financing from a fiscal perspective. [01:13:48] So far I've shown you the effects of the demographic cliff in our benchmark economy with this differentiated college market with heterogeneous colleges in terms of quality and majors. Now the question is how much do those results [01:14:02] depend on the specific college market structure that we model. [01:14:06] We conduct the following exercise. We replace the differentiated college sector by a representative college that has the mean quality of the benchmark distribution. It offers a single major that averages across the two benchmark [01:14:20] majors and sets tuition using the same price setting mechanism as in the baseline in the benchmark economy. So with this simplified model version, we simulate the same demographic cliff. And as you can see in the in the second row [01:14:34] of this table, relative to the benchmark economy, enrollment still responds, but by about 5 percentage points less than in the benchmark economy, output per capita falls instead of rising and the labor income tax increases instead of [01:14:48] falling. So the sign of the responses flips and the fiscal relief disappears. [01:14:54] And what I just showed you is a relatively stark finding. So the bottom line from that is that how much dem demographic pressure so fiscal pressure from aging education can absorb depends [01:15:08] critically on the structure of the high education market. So let me explain exactly why in the representative college world the intensive margin is absent by construction. So there is no scope for skill upgrading for those who [01:15:22] are already enrolled meaning that there is no quality letter to climb. There is no STEM versus non- STEM choice. [01:15:29] And interestingly the extensive margin is dampened as well with only one representative college entry cost is relatively high for borrowing constrainted marginal students who are near the enrollment margins. So there [01:15:42] are fewer new entrance. So saying it broader, it means that when aging raises the returns to college and also increases intergenerational wealth that is available for college funding in this representative college economy, [01:15:56] there are just fewer potential students who are induced to enroll uh compared to the benchmark. [01:16:03] So regarding those intergenerational wealth transfers, let's focus specifically on the wealth channel. [01:16:09] Under our benchmark redistribution assumption, be the quest redistribution assumption. By 2086, inheritances per capita are about 9% higher on the demographic lift path relative to the [01:16:21] baseline path. So this benchmark request for distribution scheme is calibrated such that the model matches average transfers received by the YAN households in the 2013 ID. So this is the rosters and transfers [01:16:36] supplement to the PSID. Uh in this table uh the middle column the first row so the blue number right now uh you see the GDP per capita increase under the demographic cliff relative to the baseline path in our benchmark model. So [01:16:50] this is this number that you've already seen. This is our headline result. But now I want to use this table to illustrate how the intergenerational wealth channel interacts with the college market structure. So here we [01:17:05] vary the strength of the intergenerational wealth channel. The first column shuts down the wealth channel by holding inheritances per capita fixed at the baseline path level. [01:17:17] The last column in contrast gives all extra requests to the young. And as you can see in our heterogeneous college benchmark economy, shutting down the intergenerational wealth channel makes the output per capita response slightly negative. So effectively it disappears [01:17:31] while giving all extra requests to the yan makes the output per capita response about more than four times larger than our benchmark number. Now if you look at the second row in contrast the same exercise repeated in the representative [01:17:46] college economy. So here by contrast the output per capita response really moves across this different intergenerational wealth for distribution schemes. So the bottom line is that the intergenerational wealth channel interacts strongly with the college [01:18:01] market structure. When you have this adjustment margins, so the quality upgrading margin and a more responsive extensive margin, then this extra resources through the intergenerational wealth channel translate into much [01:18:14] bigger effects. So again, the strength of the the power of the intergenerational wealth channel depends strongly on the structure of the college market and whether this structure allows for this adjustment margins. [01:18:27] All right. Now to conclude and then I hope we can have a bit of a discussion. [01:18:31] I I hope I wasn't rushing too much. So, let me restate the main question with which I started. Can the college choices people make whether to enroll, where to go, and what to study offset the long [01:18:44] run fiscal cost of aging? Our answer is yes. Given the US college market, smaller cohorts become more educated. [01:18:52] Enrollment rises by about 9 percentage points over 60 years, and there's quality upgrading and a slight shift towards STEM education. output per capita rises by over 2% while the labor income tax falls by a bit more than one [01:19:06] percentage point. Uh so overall again to repeat the demographic cliff ends up being mildly positive on a per capita basis and more than self financing from a fiscal perspective. The mechanism here is that agent boosts both the returns to [01:19:20] college education and the resources available for education financing. If you replace the differentiated college market with just one representative college, the enrollment response would be much smaller, output per capita would [01:19:33] fall and fiscal relief would disappear. So the structure of the college market really matters for the education response to population aging. And the direct implication of this which we think is also interesting is that in a cross-country context that would mean [01:19:48] that countries with different high education systems may experience very different effects of population aging on the skill composition of their workforce. So let me stop here and I'm looking forward to questions. ## Q&A (01:19:59 – 01:26:12) [01:19:59] >> Thank you so much Arena. It's fascinating and thank you for staying right in in time and thank you Durk for answering some of the questions in the the chat uh in real time. Are there we have a few minutes for open discussion. [01:20:14] Uh Ron, you'll probably be absorbing Durk's response, but are there any other questions meantime that folks want to jump in with? Yeah, Adrian. [01:20:23] >> Yeah, thanks. So, this is super interesting. So, I guess two quick questions. So, one is uh I know counterfactuals are hard, but you were starting kind of a while back and like you said, the US education kind of [01:20:36] higher education landscape's already been shifting. So can you is there like kind of some indirect test of your mechanism like what colleges are are shrinking or closing versus what colleges are expanding along the [01:20:51] education or along the quality margin um and uh and also the responses of tuition right so is there kind of some indirect test of like this mechanism in the data um and then the other one is actually connected to the first paper like [01:21:04] thinking about how the migration policy interacts with this and you know in particular like what colleges you know uh or like just generally immigration policy uh for students. [01:21:18] So regarding the first question, I mean it's relatively hard to do some validation exercises concerning the contemporaneous responses. Um so we could look into the past maybe uh to try [01:21:31] to see how earlier uh fertility fluctuations were correlated or associated with changes in college tuition and uh major composition, quality composition. No, I think for the for the current experiment, it's it's [01:21:45] very hard to do uh direct validation and regarding immigration that's also in our agenda in fact. So that's potentially one additional exercise that we want to implement. think about changes to STEM immigration and how then [01:22:00] u this changes in the STEM workforce would interact with the college market and also potentially thinking about foreign students because colleges rely strongly on foreign students um in terms of tuition revenue. Yes. So that's on [01:22:14] our agenda. Yeah. Yeah, but about the first question, we would need to think more about it and maybe when we could find uh maybe for specific uh college like local college markets, maybe for some states, we could find data that we [01:22:28] could use for validation, but at the federal level, so nationwide data, I think it's it's hard, but I don't know if maybe my co-authors want to say something on that. [01:22:39] >> So so so a quick a quick remark. So in 2026 since the demographic cliff just starts you wouldn't see very much but if you push it forward what the model has predictions about is in what quality [01:22:52] segments would you see the largest contractions and in what segment of the college market would you see the largest expansions. So first of all the demographic if you're going to miss a bunch of students right I mean I guess the number of uh high school students in [01:23:07] that 2086 year uh is is much lower. So universities will uh have fewer students uh but because of skill upgrading especially the middle and uh higher end of the quality distribution is going to [01:23:22] be less affected than the low end of the distribution because of constant returns to scale. We cannot make statements about whether this expansion or reduction is fewer colleges or the same number of colleges with fewer students. [01:23:36] That that is indeterminant in the model. For that you would need some good notion of fixed costs or the likes. So we cannot make statements about you know Stanford shutting down or Pennis shutting down. But what we could make statement what we can make statements [01:23:50] about is whether um colleges in the quality level of Ben and Stanford whether they are shrinking or expanding and you know because of the demographic cliff all college uh ranks have reduced [01:24:05] students because you're missing a ton of students uh but those at the middle at the high end of the distribution are less affected than those at the low end. [01:24:13] But but but I guess my question was I think inspired by your first slide which showed actually the decline in fertility relative to what you would have predicted like say as of 2008 or something right and I mean or or let's [01:24:27] say you go to 2000 right and so now you can say you can say well what colleges have actually like how has the distribution of uh co of of enrollment shifted along the college quality kind [01:24:41] of benchmark. just to see if the the responses you're seeing in your model are like in line with what's happening to the education market right now >> again the cliff didn't yet start materializing in aggregate terms so I think [01:24:56] >> the cliff not but I guess there have been demographic shifts in the past and the model in every period because we start the transition in 1950 every period the model has predictions about the cross-sectional distribution of people going to college we could compare [01:25:10] we could compare that so this this is not a question about the demographic cliff per se, but in the past there were demographic changes. The model has predictions about them and we started the transition in 1950. So we we we could compare two numbers uh that we can [01:25:24] actually already observe that that's a fair point. That was not the focus of the counterfactual but that's some something in terms of model validation we we could look at. We we didn't so far but we could >> yeah we could look at the historical data and do sort of validation based on the past [01:25:39] >> but also maybe one point to mention that our model is inherently about the long run. So um this constant returns to scale assumptions that we make they apply mostly to long run adjustments. So we need to look like at the long time [01:25:54] horizon. >> Well fantastic. Thank you all and it's great use of the the chat to continue the discussion. So why don't we take a five minute break? If anyone wants to [01:26:08] continue to discuss during the the fivem minute break that's that's fantastic.