Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable. ======================================================================== # Making Room on an Empty Planet: The Spatial Consequences of Depopulation Authors: Tim de Silva, James D. Paron Discussant: None Video: https://www.youtube.com/watch?v=w6ObGDwelyg&t=18638s ## Talk (05:10:38 – 05:40:34) [05:10:38] >> Okay, so welcome back everybody. So just a quick reminder the format is 30 minutes for each presenter 5 minutes without questions and then people are free to jump in and we have 10 minutes of discussion at the end. We have two [05:10:51] papers left on the program. The first is by Tim Dilva and James Poron making room in an empty planet. Um Tim is presenting. Take it away. [05:11:02] >> Great. Well thanks for having us and staying uh as the day is going on. So James will be monitoring the chat and then doing the Q&A. So feel free to write anything in the chat or jump in with questions. [05:11:13] So starting point for this paper is obvious given this audience global fertility rates are low and some estimates put the fertility rate for the world as of today somewhat below replacement and with subrement fertility rates of course populations will [05:11:28] eventually start declining unless something changes and maybe maybe Ron will tell us that something will change. [05:11:33] So Japan's a canonical example of this. It has a TFR of around 1.2. So just to put that into perspective, if nothing else changes, that means Japan's population is going to fall by around half by 2100 and around 90% by 2200. So [05:11:47] that's pretty meaningful. Now there's obviously a ton of work thinking about the effects of declining populations and a lot of that has been focusing on its aggregate consequences. So the work by Chad uh and many others has brought up [05:12:00] many times today. The fact that with less people you have less ideas and that lowers growth. There's also a very long-standing strand of work thinking about fiscal sustainability. You know, we have these pension systems. We have we built them with lots of people. The population starts shrinking. It's going [05:12:15] to be more difficult to service those pension systems. [05:12:18] Now, the question we're interested in in this paper and the next paper is also quite interested in is what are the spatial effects of declining populations? And so, at priority, it's not sort of obvious what to expect here. [05:12:30] So, on the one hand, you may think, well, nothing's going to happen. On the other hand, you may think, well, when there's less people, there's less of us, so there's kind of more benefits to us all being together and reaping the benefits of elomeration. But at the same time, you might think that, well, the benefits of a lomeration depend on the [05:12:45] amount of people that there are. And so, there's not many if there's not very many of us, maybe we should just spread out. Now, this may seem like a question that's kind of like abstract, but I think it's it's important to think about why we would care. So there we kind of see two reasons why we would care about [05:13:00] knowing what what depopulation is going to do to the spatial allocation of people. The first is that a lot of the work in economic geography has highlighted that the spillovers that drive aggregate growth are often quite local. And so if we want to understand those aggregate spillovers and where [05:13:15] they come from, we need to have a sense for you know where people are located. [05:13:18] And then the second one is many governments, Japan being one of them, but there are also governments in um in Scotland as well as in in southern Europe have been introducing specific policies targeted at fighting the kind of spatial consequences of depopulation. [05:13:32] And if we want to evaluate those policies, of course, we need to have a model of what we think is going to happen. So the main argument in this paper is going to be that declines in population levels are going to lead to increased spatial concentration. I'm going to spend a lot of time on the [05:13:47] mechanism, but the the key idea of the mechanism is that housing is a scarce resource that spreads people out. And what declining populations do is they free up uh the amount of housing everywhere, but they really free up [05:14:00] housing disproportionately more in the dense cities where people value it a lot. And so in equilibrium, that's going to generate migration to those denser cities. [05:14:09] Now, just to be clear about what we're doing and what we're not doing, this entire paper is going to be about the effects of changes in the population level. Nothing about the effects of population aging. And so that when the next paper, we're going to get to hear [05:14:22] uh a lot about how aging can kind of be a complimentary force that can drive similar patterns and spatial allocations. [05:14:30] So, let me summarize our results. The first part, which I'll go very briefly over, is is our empirical empirical results. So we're going to show you some evidence both across countries and within countries that when you see declines in population that tends to be [05:14:43] correlated with increases in the concentration of people into denser locations. So Japan's an example of this. The population's been falling uh but the Tokyo's population share and level has been going up. Now where I'm going to spend most of the time in the [05:14:57] talk today is by through talking through a kind of static spatial equilibrium model that gets us a lot of the intuition that we want to highlight in this paper. So we're going to use that model to make two points. The first is to illustrate the conditions under which [05:15:11] we can get the level of the population to affect where people live. And that's when we say scale dependence, what we basically mean is when the level of the population affects where people live. [05:15:22] And so the condition that we're going to need is either that housing supply elasticities or housing expenditure shares vary across locations. [05:15:30] Now the second result we're going to get out of the model is we're going to be able to say well given the empirical variation in these objects which a very large literature and kind of urban and spatial has been devoted to measuring we're going to be able to say uh given the empirical variation in those objects [05:15:45] which way should things go and what our model says is if it's the case that denser regions have higher expenditure shares on housing or lower supply elasticities that means that declines in the population are going to lead to increased concentration consistent with [05:15:58] the data. The third thing we'll do is try to quantify this force and dynamic model. We do that in Japan because that's a country where there's actually been a decline in the population that we can evaluate out of sample against the model. We're going to find that the movements in the population shares are [05:16:12] quite large. We're also going to find that wages are going to fall everywhere. [05:16:16] But despite the fact that wages fall everywhere in our model as the population falls, our model actually predicts that GDP per capita is going to go up. And that's because the reallocation of people to the denser, more productive places is going to be enough to overcome the aggregate decline [05:16:30] in the population. The final thing we'll do which I have to go briefly over in the interest of time is think about policy. We basically have two main policy results through the lens of the model. The first is that a social planner who maximizes the welfare of [05:16:44] individuals wants to send transfers to Tokyo to encourage migration there. And the second is that in response to the decline in the population, the planner wants to make those transfers even larger. And the core reason is that the planner is trying to encourage migration [05:16:58] to these denser regions because these denser regions have become a lot more attractive given the relative reduction and scarcity of housing. That's at the core of our mechanism. [05:17:08] Okay. So let me talk about the empirical evidence uh briefly. So we're going to see a lot more on this in the next paper, but what I'm showing you in this graph is um some evidence from Japan. So on the left I have Japan's population, the total population in blue and its [05:17:22] growth rate in red. And you can see it starts declining, you know, somewhere in the mid200s right around right around 2010. [05:17:28] On the right, what I'm plotting is on the x-axis the initial population density of regions in Japan. In Japan, we're using the definition of regions that are known as prefixes. And on the y-axis, I'm then plotting the change in [05:17:41] the population share of those prefixures between two points in time. And on the graph on the right, it's 1980 to 1990. [05:17:48] And you can see that region highlighted on the graph on the left. And so what you see is there's not much of a relationship here. And there's not there's also not a relationship if you roll this forward into the 1990s. But starting in the 2000s, you start to see a positive relationship where prefixures [05:18:03] that are denser start to see increases in their population shares. And that happens right at the time that the aggregate population starts declining. [05:18:12] Now, this is just a pan. You can also look across countries. So what I'm showing you here is a graph where on the x-axis I have the change in the population between 2000 and 2020 where we're comput where we're taking that from aggregate data. And on the y-axis [05:18:27] I'm then computing what is the change in the fraction of people who live in the densest regions within each country. And we're using some grid uh data from GHSL to do that where we basically see at the 1 km squared spell level how many people [05:18:41] are living there. And so what we see is that countries that grew faster tend to see reductions in their high density share, meaning that they're spreading out more, while countries that grew more slowly see less of a reduction in their high density share or even an increase [05:18:55] at the for the countries that were for the countries that were shrinking. [05:18:59] You can run this in a regression format. I'm not going to walk through this table in a ton of detail. There's kind of two columns that I want you to to take away. [05:19:06] The first is the third column, which is what happens when we introduce a country fixed effect. So now we're looking within country. It's kind of like a generalized version of that Japan case study I showed you earlier. And there you see a kind of quantitatively very similar effect. And then the other thing [05:19:20] I want to point attention to is that this effect is kind of uh quite strong and and independent of any effect you would see on the old age dependency ratio. So it looks like at least when you look in the cross of countries, the thing that is correlated with spatial [05:19:34] allocations is the level of the population rather than the dependency ratio. [05:19:40] Okay, so now let me talk about our our static model. Um, we're going to do this in two steps. The first is going to be a relatively simple model that makes some simplifying assumptions that I think gets most of the intuition that we want [05:19:54] to get out of this model. And then the second step is going to be to generalize it a little bit. And when we generalize it, we're going to actually get an additional mechanism. So I'll highlight that when I get there. [05:20:04] Okay. So let me start with this the simpler model. So we're going to think about households indexed by K choosing where to live and choosing how much to consume of h of housing H and of goods C. So they have a standard objective function. For now we're going to assume [05:20:18] Cobb Douglas utility over the two. They have a taste shock which generates dispersion of people across locations and they have a completely standard budget constraint. They get some income from living in a place and they can use that income to consume goods which are [05:20:30] the numer or to consume housing where P is the price of housing. But you know when you map it to the data it's really the rental rental rate of housing because there's no ownership here. [05:20:40] So how does production work? So we're going to use kind of the most standard setup. Production is going to be constant returns to scale and labor where there's going to be a TFP parameter that depends on the level of the population. And that's going to be something that firms don't internalize when they produce. That's the standard [05:20:55] increasing returns to scale effect that you typically have in these type of economic geography models. Wages are going to be then pinned down by a zero profit condition. They're equal to TFP which is the product of the primitive A which is the difference in productivity [05:21:08] across places multiplied by the elomeration force. [05:21:13] Now housing supply to start is going to be very simple. It's going to be completely reduced form and it's basically going to come be housing is going to be produced by combining two things. Land which is in fixed supply that's L and then structures which for [05:21:27] now we're just going to be produced with the number of people that live in that location. [05:21:32] Now once we have a this reduced form function from housing supply we can write housing market clearing. So housing market clearing basically says that the per capita housing supply which is total housing supply divided by the number of people in a given location has [05:21:45] to be equal to the housing demand per capita uh that households demand as a function of prices. [05:21:52] Okay. So we're going to denote this little h which is the per capita housing supply as uh as per capita housing supply and we're going to use that uh that um notation throughout. [05:22:04] Okay. So in this model it's it's very simple model. There are two forces that puts people to concentrate. The first is that some places are just better and the second is that they're increasing returns to scale. And then there are two forces that spread people out. The first is that housing is in finite supply and [05:22:18] the second is that there are tshocks. Now because of the functional form of the tshocks you get the standard nice expression for equilibrium population shares which says that the share of people living in location I so think [05:22:32] Tokyo is proportional to the utility that individuals get from locating in that region with some elasticity 1 over theta relative to the utility that they could get from living in all of all other region. [05:22:44] So the question we're basically asking in this paper is when does these population shares change if I change the level of the population? That's what we mean by scale dependence. And so in this simple setup we can kind of see very [05:22:57] transparently what's going on. So in particular given with the assumptions we've made namely Cobb Douglas utility and the fact that housing supply is in this reduced form function we can just start plugging stuff in. So that's all I've done here. have imposed hardly market clearing and use the household's [05:23:12] utility function. And then we can also use the expression for the wage which just said that the wage was ai * ni to some power uh sigma and we can then solve directly uh for ni over n as a function of some primitive differences [05:23:26] across places a and then per capita housing supply. So a is a primitive difference across place. So that doesn't depend on the level of the population. [05:23:35] And so what this expression tells you is that in this simple model, the only thing that can generate the population shares moving as the total population moves is if something's going on with housing supply. [05:23:47] So more formally you can take this expression and you can differentiate it and you get this result which says that the change in the population of a particular location I say Tokyo as you change the total population is equal to [05:24:01] a constant divided by theta which governs the T shocks 1 - alpha* sigma that's the increasing returns to scale minus alpha some times some elasticity where this elasticity is how housing [05:24:13] supply changes as you add more people. Now to understand this you can first go to a few special cases. So if you if you thought of a model where housing was only produced with land it was only produced with structures or it was Cobb [05:24:26] Douglas over the two. In all three of those cases this elasticity would be constant and it would be something that would not vary with I. And so then on the right hand side of this expression you would have no terms that vary with I which would tell you that all of the [05:24:40] population shares in each location aren't changing. or in other words, all of the population levels are going up by equal amounts. And so this is kind of the standard uh standard special cases that are typically used and in economic [05:24:52] geography models. Now to move outside of that and to get some intuition for what goes on once you move out of those special cases, we think a very nice case to work with, which we'll show you is relatively consistent with the data, is one in [05:25:06] which you produce housing using a CES aggregate of structures and land. So let me explain in math why this works first and then explain in words what's going on. So in math you can compute this elasticity. It's the standard CES [05:25:19] object. And if you take that object and you plug it into the expression above, what you're going to find is that if you're in the case where ADA is less than one, which means that structure and land are complements in housing production. That's going to imply that [05:25:33] denser regions have more negative housing supply elasticities. meaning that as you add more people per capita housing supply is going to fall by more. [05:25:42] And if you plug that into that expression, that's going to tell you that concentration is going to rise when the level of the population falls. And so what's the intuition for what's going on? It it's very simple. So if you think about a place like Tokyo or New York City, these are places that are very [05:25:56] dense. These are places that people would want to live in and ideally you would build more housing, but you can't because at some point you're out of land. And that's what having a being in a world where um ADA is less than one where things are complement and housing [05:26:10] production means. And so what the fall in the population does is it increases the amount of land per person that you have everywhere by an equal amount if places are equally sized. But that increase in land leads to a much larger increase in housing supply per capita in [05:26:25] a place like Tokyo or New York City where you're really constrained on on land to begin with in producing housing. [05:26:30] And so this increase in supply or this shift out in the supply curve gets people to move there in equilibrium. [05:26:38] Okay, so that was a story for why um basically what goes on on the housing supply side can drive scale dependence. [05:26:46] We're now going to generalize that result and then show you that there's kind of also another force that happens on the demand side. So I have the same model. I'm just highlighting in gold what's different. So here I'm going to work with a completely general utility function. I'm also going to now allow [05:27:00] labor to be allocated between the two sectors. So, some fraction of people are going to work in goods and then some fraction of people are going to work to build structures. These structures are going to be produced by developers who actually now solve a maximization [05:27:14] problem as opposed to just assuming some reduced form housing supply function. [05:27:19] We're going to assume that the developer's problem um can be characterized by the standard first order condition, which is that the marginal cost of hiring more people or building more structures, which is what you use to produce structures, namely labor, is equal to the marginal benefit, [05:27:32] which is the price of housing times the amount of housing you get built. And so once we do that, we can also uh write down another per capita housing supply function that is now endogenous in the sense that it responds to the price. [05:27:44] So we make a couple of simplifying assumptions here just to make the result a bit more clean. Uh but these aren't crucial. [05:27:51] So in this more general setup, if you do the same kind of math that I showed you before, you get an expression that looks like this, which says that the change in the population as you change the total population is equal to some constant divided by theta minus sigma times the [05:28:04] housing expenditure share times the price response. Now you can write that price response in terms of supply and demand elasticities. you get the standard kind of price theory result which says that the price impact of a demand shock is one over the sum of the [05:28:18] supply and demand elasticities and then there's another term just from the increasing returns to scale. So what do this equation say? Well, if we go back to the case that I showed you before where we assume Cobb Douglas demand and [05:28:31] Cobb Douglas to supply the in that in those cases the all the elasticities are constant and the expenditure share is constant. So you plug those in and you get again this simple formula where nothing depends on I. So you have scale dependence if you alternatively assume [05:28:45] cob Douglas demand which is what we were doing before. Now what this result does is it gives you another way of thinking about the way in which housing supply matters. In particular what you need for concentration to increase when the overall population falls is you need [05:28:59] housing supply elasticities to be lower in denser places. [05:29:04] Now this expression also tells you that there's another mechanism on the demand side which is that even if you have Cobb Douglas housing supply you can still get scale dependence if it's the case that the expenditure share on housing is higher in dense cities. And so what's [05:29:18] going on here? Well basically just like the prior mechanism where the idea was that land went up by an equal amount across all places but that led to a that went to a much larger increase in housing supply in dense cities. Here what's going on in the demand side is [05:29:33] that housing supply per capita goes up everywhere when the population falls. [05:29:38] But if people are spending more on housing in dense cities by revealed preference they value housing more. And so that increase in housing supply drives migration to those places where housing was valued more. [05:29:49] Okay, that's what I just said. So now I'm going to show you two pieces of empirical evidence on how these housing supply and expenditure shares vary across places. We don't have evidence on this from Japan. All we all we have is in in the US and remember what we need [05:30:03] is elasticities to fall and expenditure shares to rise with density or with population. [05:30:10] So here's the graph of housing supply elasticities with respect to population densities across regions in the US. This is coming from estimates by by Stone co-authors. What we find is that yeah exactly what you need elasticities are [05:30:24] lower in places like New York City relative to rural places. [05:30:28] The evidence for housing expenditure shares is a bit more mixed. So what I'm showing you here is a graph of housing expenditure shares across places as a function of the medium income in that place. This is coming from Finley and Williams. There's some evidence that places that are higher income, which are [05:30:43] typically denser, have higher housing expenditure shares, but it's less strong um than the evidence on the housing supply elasticity variation, which is why we focused on that to begin with. [05:30:54] Okay. So let me in my last 10 minutes spend a few minutes talking about how we quantify the strength of these forces in the context of Japan and then and then what that quantified model says about optimal policy. [05:31:06] So I'm not going to walk you through the quantitative model. You can think of it as the exact same as a static model with a couple of changes. The first is that we now make households choice of where to live a dynamic choice in the sense that they choose where to live subject to migration costs. So now they're going [05:31:21] to be pretty forwardlooking. And we also make it so that households can choose which sector, goods or construction to work in. So now we have labor supply curves for for both sectors. [05:31:32] We're going to assume that households have homothetic PIGL preferences. Um if you don't like or you know haven't heard of these preferences before, that's fine. You can just think instead that just like we have CES on the supply side for housing, you can alternatively think [05:31:46] of CES on the demand side with compliments where the core idea is just that there's some notion of weak links. [05:31:52] And really what we need is just some demand system that gives us that housing expenditure shares are a little bit higher in denser regions. [05:32:00] Housing supply is still going to be CES over land and structures and but now the sub structures are going to be supplied by developers who solve a dynamic problem. And the reason it's dynamic is because you need to take seriously the fact that you can't just go around destroying housing and investment in [05:32:14] building houses is something that's uh that's irreversible. [05:32:19] So we estimate the model um targeting a bunch of moments and kind of doing a standard thing in the spatial literature where you invert the model to match population shares in a particular year. [05:32:29] Here we do this starting in 2000. The one parameter I want to focus on because it's kind of the most important is that elasticity of substitution. We estimate it to be less than than one. And the way we estimate it is by targeting that relationship I showed you which is that the relationship between housing supply [05:32:44] elasticities and population densities is negative. On the right I have an estimate of the productivity across places and you get kind of the standard thing that the way the model m rationalizes very high population shares in some regions is is through [05:32:58] productivity. So we've estimated the model in this initial study state that's 2,00 and then the core quantitative exercise is to feed in a transition um to a new study state at a lower [05:33:11] population level. And so what we do is we take a projection from the IPSS which is a statistical office in Japan. Um we basically smooth the projection a little bit just so it makes our model graphs a little smoother. That's not important. [05:33:24] And then at some point we need to decide where to cut it off. I mean, we could let it run to a population of zero, but I think we think that's maybe a little bit too extreme. So, we chose to cut it off in 2200 when the population level gets to around 10 million. Um, but where [05:33:37] exactly you choose this is not super uh super important. [05:33:42] Okay. So, let me show you the results. So, what I have on the x-axis here are the different prefixes, which is the notion of region in Japan. And on the y- axis, I have the population share. So in blue is the values in the initial study state. By construction, these match the [05:33:57] data exactly in 2000. Then in red is what the model saying the population shared distribution will look like across prefixures in the terminal study state when the population has fallen when the aggregate population has fallen substantially. So what we find is that [05:34:12] there's a huge increase in population shares for these uh regions like Tokyo, Osaka and Kanagawa. [05:34:18] Now, what drives this heterogeneity in the model? Well, it's all population density. So, what I'm showing you here is on the x-axis, I'm ranking regions based on their initial population density. And then on the y-axis, I'm plotting a change in the population [05:34:32] share across steady states in the model. And what you see is there's very steep upward sloping line. So, the place at the top is Tokyo. It's the densest place. It gains population share. While Hokkaido is at the bottom left, it loses population share. [05:34:45] We can ask how much of this is coming from the supply versus the demand mechanisms that I highlighted. Of course, if you turn them both off, you have Cobb Douglas on both sides, you get nothing because the population shares stay constant. If you instead work with a model where you have CES on the supply [05:35:00] side, so it's all about the supply side force, you get around 65% of the effect. [05:35:05] If you work with a model where everything's on the demand side and there's no supply side force, you get around 40ish% of the effect. [05:35:14] We can also look at what happens to wages. So wages are basically proportional to in logs to uh to population levels. And so you see basically wages fall everywhere but they fall less so in places like Tokyo in our [05:35:28] baseline model while in the model in which you don't have scale dependence they fall by an equal amount everywhere. [05:35:34] Now despite these wages falling everywhere as I mentioned earlier the model actually predicts that GDP per capita goes up. So why is that? Well, to understand it, first focus on the gray bar on the left, which is what would happen in a model which you didn't have [05:35:48] scale dependent. So there when you cut the population because they're increasing returns to scale, GDP per capita goes down because you've lost some elomeration benefits. Now in all of our estimated models that feature some form of scale dependence, GDP per capita goes up and it actually goes up by a [05:36:03] non-trivial amount like 25ish% in our green baseline model. The reason that's happening is because while you have the force that you have in the gray bar, the reduction and the elomeration benefits, you have an alternative force which is that people start reallocating to the [05:36:17] more productive place. Remember that was the core core thing we tried to explain in the data. And that reallocation of people uh to more productive places leads to an increase in GDP per capita because those places are are more productive. [05:36:30] Let me show you a couple graphs from what things look like on the transition. [05:36:34] So here we can look at population shares. You can see that they go up in Tokyo um in the first 20 years uh of the of the transition path. Very similar patterns for house prices. The nice thing is we can compare the graph on the [05:36:47] left to the data. So here I'm showing you what the population shares look like in in changes relative to initial densities in the model on the left. If you make the same plot and the data on the right, what you see is that the qualitative pattern is there, but the model doesn't get everything, but it [05:37:02] gets, you know, kind of a non-trivial fraction around a fourth of the increasing concentration that we saw. [05:37:07] So, we kind of interpret this as saying that there's other mechanisms that are likely important in the data, some of which we're going to hear about um in in the next paper. [05:37:16] We do quite a few extensions. I'll just mention a couple. The first is to introduce spending commitments. [05:37:21] Basically this idea that you kind of have some stock of public goods that you provide and when the population starts falling that kind of increases the tax rates that you need in order to justify uh those level of public goods. And what we find is that this substantially [05:37:35] amplifies our our our main uh force. We also incorporate amenity spillovers. [05:37:41] So if you have negative amenity spillovers, this dampens our result. But if you have positive spillovers, which is something the next paper is going to provide us with evidence of, that's actually going to make the reallocation in our model even stronger. [05:37:54] We also do a little bit of work on indogenous fertility. I'm not going to uh spend any time on that in the interest of time. So in my last minute or so, let me just show you uh kind of the key graphs that come out of this when you do optimal policy. [05:38:07] So the way we do optimal policy is we think about a social planner that solves this problem which is to maximize the average utility across all the agents in the economy by making transfers across places. Now just to simplify we assume [05:38:20] that the transfers take this particular form which is that you tax wages and then you give a lump sum transfer. So it's kind of like a constrained uh constrained planners problem. [05:38:30] When you solve that problem this is what you get. So on the left I have the graph of the transfers as a function of uh the initial density in the region and each region gets a transfer. So what you see is that across all these models regardless of whether or not you have [05:38:44] scale dependence the results are pretty similar and you want to do a little bit of a transfer to Tokyo relative to rural regions in the initial study state. Now when you go to the terminal study state things look quite different across the models. In the model without scale [05:38:57] dependence nothing changes. So the policy doesn't change. But in our models with scale dependence, you find that you want to transfer even more to Tokyo uh than you were doing so in the initial study state. And these transfers are kind of quite large. The the optimal [05:39:12] kind of tax rate that you're using to to do the transfers more than doubles uh in these models with scale dependence. [05:39:19] So what's going on? Um well basically the planner has some usual externalities that it's trading off. it has a redistribution motive versus an elomeration motive. Those quantitatively don't turn out to be that important. [05:39:32] What's very important in our dynamic model is basically the fact that what happens with scale dependence is you have a place like Tokyo that was a very good place, but you couldn't get a b you couldn't the planner couldn't have a bunch of people live there because it would push housing prices up so much. [05:39:46] And so what the fall in the population is doing is it's allowing the planner to get more people into Tokyo because Tokyo is now less constrained by housing supply or housing is kind of less scarce there. [05:39:58] What's sort of interesting about this is that this direction of the transfer is actually the opposite of what many existing policies do. We don't want to say that like the direction that that our model uh that our model is spitting out is the right one. We just want to say that it's interesting that when you [05:40:12] write down a model like this which incorporates lots of forces, this is what you get out. So you basically need other forces if you want to justify what people are doing. Okay. So I'm out of time. Um I'll just conclude there. The main me uh message of the paper is that [05:40:26] depopulation leads to more concentration and we have more work to do to understand the policy implications. ## Q&A (05:40:34 – 05:50:30) [05:40:34] >> Great. Uh thanks so much Tim. You're right on time actually. So um thank you and we'll open up the floor for questions. There's been a few questions in the chat actually that James has been [05:40:45] fielding already. Um Ron had an another question about the MPL in agriculture. [05:40:53] Maybe you do you want to uh since >> Yeah, James, I'm happy to let you do the >> say that out loud and then we'll have you Hey. Yeah. [05:41:04] Sorry. You're you're muted, Ron. You're muted, Ron. Yeah. [05:41:12] I was going to say my comments are a little bit off topic. They're on sort of rural area conditions fight back and uh and Jim says uh yes, you're I mean the [05:41:26] the scale effects on amenities and uh schools and so on and so forth that you you've already now you say you have done that as an extension. Now I'm wondering about increasing marginal product of [05:41:39] labor on land in agriculture with more land. And maybe that's no longer relevant in the modern era of agricultural production. I have no idea. [05:41:48] But these aren't things that go to the heart of your argument. It's just getting late in the day and hard to focus, I'm afraid. [05:41:55] Well, I'm happy to give a a quick answer anyways, which is in in all of the baseline model that Tim showed, no, we don't have any uh kind of like differentiation between the returns to scale in one sector versus the other. [05:42:07] Um, we do do another extension uh in which we uh allow basically certain regions to specialize in agriculture uh which has lower returns because it's using land as a fixed factor uh and we assume it doesn't have you know very high elomeration which kind of makes [05:42:22] sense. It's a very low low density activity. Um as opposed to urban land which does like manufacturing and services and does have the increasing returns and is not land intensive. Uh and that you know to to give you the short answer it it amplifies uh what we're doing. [05:42:37] >> Thanks. >> Great. Yui has a question. [05:42:43] >> Yeah. Uh it's very interesting. So I have one question about the mechanism and uh I had a chance to think about this uh for the revision of a paper. I'm not sure whether you guys are the [05:42:56] referee but anyways the um the um I think there are two things going on uh one is uh as you're emphasizing the heterogeneous housing elast let's talk about the supply side uh for now one is [05:43:11] the heterogeneity of the supply elasticity which I completely agree but I think there's another thing going on which is that as the um the you know the land becomes relatively more abandoned [05:43:24] uh and the under the complement assumption uh of housing production the relative that sorry that the share share of the expenditure for the housing construction uh sector to land is going [05:43:38] to go down. So it's it looks like um in the aggregate uh the economy relies less and less on uh on the on land and land is that dispersion force right like that land is the reason why there there's you [05:43:53] know people may not live uh all everyone doesn't live in Tokyo so I think I I my understanding is that these are two different forces and it's happening you know precisely because of your [05:44:08] specifications I I'm not like criticizing that feature, but I'm wondering like whether you have a sense of which one is more important. Um, and uh, so maybe some kind of is useful. So, [05:44:21] so I'm actually not sure I I see the difference because if you think about what's going to happen in a a world with CES supply and compliments, you can think of that, we don't we we didn't talk about this explicitly, but you could think of there being an associated [05:44:34] price and expenditure share on land or a share of value on land uh and a price and share of value in structures. uh and and what what exactly what you said is going to happen as a result of the CES assumption which is uh that the land [05:44:48] share value is going to fall once land becomes uh much more abundant. Um so I would kind of view that as just as as maybe another helpful way of thinking about it. But but if you if you disagree and you think there's like that's a different story then [05:45:02] >> no no I I as I said I I completely agree both of them are generated because of your CS um but I think these are kind of like different channels and I I don't know [05:45:16] whether like you know but it's it's um one is more about the cross-sectional patterns of elasticity and the second is more like you know time series trend of the land [05:45:30] share over time and I think these are kind of different things and I don't know how to separate them I I mean as you said like you have a very passimmonious specification that generates both which is I think an [05:45:42] interesting feature and um yeah but it's it's it's a little bit of a comment because again like I I thought it's kind of interesting that the same specation generates both predictions And I have a question about the optimal [05:45:59] policy. I I I didn't it went too quickly and I didn't follow but the so you are emphasizing the moving cost that but the moving cost is uh is is is technological cost that is incurred by private agents [05:46:14] and social planners. So what do you mean by it's the reason uh why optimal policy depends on that? [05:46:22] >> Yeah. So first what we mean by sorry Tim did you want to say >> no no no go ahead I was just going to go back. Yeah. Okay. I was just going to say what we what we mean by it's the reason is uh it is the difference in prediction between the static model and [05:46:36] the dynamic model. So it's that's just pointing out that it's making a big difference in determining the direction of optimal policy. The the the channel like the the economics of how it works is um in a in a model without the moving [05:46:50] costs. So basically the static model that we wrote out um uh people are going to equate expected like conditional on their shocks average utility across all regions because they can freely move between the regions. But once you introduce the moving cost you you [05:47:04] actually introduce a differential in the average utility in one location versus the other and and in this particular model average utility in Tokyo is higher than in the rural areas. And it's the moving cost that prevents people from arbitrageing that difference. And so [05:47:18] what the planner is wanting to do with respect to this particular channel is to basically pay people to be willing to pay the moving cost in order to move to Tokyo. [05:47:41] >> Thanks. I'll I'll check the paper to think of it. [05:47:46] Will >> I'm just curious about the thinking about the the case of Tokyo and then trying to generalize from there. When I you know talk to people anecdotally [05:47:59] about Tokyo, they think about the large capital stock that was invested in to create a huge city. Uh and as you go from a country of 130 million down to you know 80 something million you have [05:48:12] this huge stock which is depreciating slowly but the the people talk about this large value to moving to the city because of this uh existing stock of of [05:48:27] capital from all these decades of prior investments that you know people can benefit from. I mean is this you know quantitatively important to think about or is this you know somehow you're you're thinking about it in the model uh already you know separate from the the [05:48:41] land and the housing stock. >> Yes. So I think this relates to some of the discussion we had in the chat over uh and and also the extension that Tim mentioned about the what we called spending commitments. Uh and the idea [05:48:55] there is basically that um over time as you increase the the kind of tax base of a dense region, you can afford to kind of increase the quantity of amenities, the public goods that are being provided. But once you go along this [05:49:09] transition of declining population and therefore uh um declining tax base, there may be some adjustment costs associated uh with continuing to finance them. You can't just immediately shut down your fire department and your [05:49:22] schools and everything. And our point with respect to like whether that's quantitatively important spatially is that that that that we show in the model that's disproportionately going to hit um the rural areas um relative to Tokyo. [05:49:34] So people because they're moving to Tokyo, it's going to be easier to maintain the existing stock of of amenities. It's going to be less painful. Now it's still painful for everywhere because everywhere is losing people and everywhere is having to maintain this this slowly depreciating [05:49:48] stock. But it's it's you're much better off being in Tokyo with respect to this uh this part of life. [05:49:56] The only small thing I'd add there is just yeah so the the other thing and this goes to what you said about the stock of capital and depreciation. Um it's very important in the model that's why we wrote the dynamic one to account for the depreciation of structures [05:50:10] because that's actually substantially quantitatively slows down the transition relative to just thinking about a world in which you could freely adjust the amount of structures. So we are kind of taking into account in when we qualibrate the model that there's a huge [05:50:24] stock of structures and it's may depreciate slowly differentially across places.