Thinking About Cities with Paul and Zed, Part 2
In my previous post, I argued that when small cities go into decline, what happens is not so much that their populations shrink dramatically (though they may), but that working-age residents are replaced by retirees. Jobs for the remaining workforce are concentrated in sectors providing goods and services to the elderly, health care being an obvious example.
Now I want to focus on whether this should be seen as equivalent to disappearing entirely in Krugman's framework. I hinted at arguments for this conclusion in my previous post, but unfortunately they are not easy to explain in detail, which is why I've written a separate post. All of the following draws on The Spatial Economy by Masahisa Fujita, Paul Krugman, and Anthony J. Venables.
I'll start with "base-multiplier" analysis. Each location has an export sector providing goods and services to the outside world and a nonexport sector providing goods and services to local residents. You can think of the export sector as the "base," with its size fluctuating based on a wide variety of factors. The nonexport sector, by contrast, is essentially a function of the export sector. It consists of (A) goods and services provided to workers in the export sector, (B) goods and services provided to the workers employed in (A), (C) goods and services provided to the workers employed in (B), and so on. This is why the term "multiplier" is used—the nonexport sector is a series of multiples of the export sector, each one smaller than the one before. (Each step yields a smaller multiple because each worker spends a fraction of her income on imports. So you might have $10 of export income supporting $6 of nonexport income, which in turn supports $3.60 of nonexport income, and so on.)
The thing to recognize here is that while the nonexport sector may be much larger than the export sector in any given location, it is the export sector that determines the ups and downs of the local economy. Changes in the size of the export sector propagate through the local economy and end up being reflected in the size of the nonexport sector, and not vice versa. (An interesting variant on this was proposed by Allan Pred. As a city grows, it may become large enough to support certain activities that require a minimum scale to be profitable. When this happens, imports are replaced by a new part of the nonexport sector, increasing employment and population. So the nonexport sector is not always merely an echo of the export sector, but for our purposes we can view it that way.)
So the problem for small industrial cities is that they are losing their export sectors. This should require them to shrink, but by how much?
Agriculture is the classic export industry that supports non-urban economic activity. The existence of an agricultural workforce means that our economy can never completely urbanize. There will always be small villages serving farmers' needs, and larger villages and towns providing more specialized services. Although Krugman didn't emphasize these villages and towns in his blog post, he clearly thinks they will always exist (unless agriculture is totally automated, I guess), and so he doesn't think small cities will truly disappear. They will simply shrink to a level that can be supported by the local export sector, which at worst would be the local agricultural sector. This implies that the cities will shrink until they are quite small—agriculture is too spread out and employs too few people to support large population centers.
But to take a step back, what is an export sector? I gave the literal definition earlier. But we shouldn't think about it so narrowly. For purposes of base-multiplier analysis, an "export sector" can be any activity that brings money in from the outside. It could be tourism, it could be remittances, whatever. Retirees receive Social Security, Medicare, Medicaid, private pension payments, etc., and of course they also spend down their savings. So they can form the base of a local economy in the same way that an export sector can, but unlike agriculture, they need not be spread thinly over the landscape. In particular, they can cluster in small formerly-industrial cities, where housing is cheap and where they support a nonexport sector specializing in health care and similar sectors.
So consider a fading industrial city. As the traditional export sector (manufacturing, usually) disappears, workers leave to find jobs elsewhere, and housing prices drop. The city likely has a decent health care sector already (in fact, many of the legacy industrial firms provided very generous health insurance and created large, advanced health care industries—this was certainly true of Peoria). So the city becomes a magnet for retirees, who find the cheap housing attractive and the health care services at least adequate. Jobs shift from the export sector (working at a factory) to the nonexport sector (working at a hospital or as a home health worker or whatever). The city stops shrinking, or shrinks very slowly. It still shows up as a relatively large population center, much larger than the agricultural village that it could theoretically become. For the reasons articulated by Pred (see above), these cities may support industries that smaller towns can't, and so their manufacturing sectors will not necessarily disappear entirely.
So where do these cities stand in terms of "disappearing" in Krugman's framework? On one hand, they still have decent-sized populations with spending power, and as noted they may even have small manufacturing sectors serving the local region. To the extent retirees consume a particular good or service, their presence in a city makes it more promising as a location to produce that good or service. If the good can also be exported, then you can imagine a town booming as it becomes the center of a cluster of manufacturing activity focused on that product. This would support Zed's contention that small cities can bounce back after long decline.
But on the other hand, these cities have relatively small workforces and, by assumption, they are far from major urban markets. It is hard to see why anyone would locate a manufacturing business in one of these cities instead of an exurb, which will tend to have a larger workforce and be much closer to a city with a larger absolute number of retirees. It could happen by random chance, of course, but this seems like the kind of highly unlikely occurrence that Krugman's point could accommodate with only minor modifications.
Now I want to focus on whether this should be seen as equivalent to disappearing entirely in Krugman's framework. I hinted at arguments for this conclusion in my previous post, but unfortunately they are not easy to explain in detail, which is why I've written a separate post. All of the following draws on The Spatial Economy by Masahisa Fujita, Paul Krugman, and Anthony J. Venables.
I'll start with "base-multiplier" analysis. Each location has an export sector providing goods and services to the outside world and a nonexport sector providing goods and services to local residents. You can think of the export sector as the "base," with its size fluctuating based on a wide variety of factors. The nonexport sector, by contrast, is essentially a function of the export sector. It consists of (A) goods and services provided to workers in the export sector, (B) goods and services provided to the workers employed in (A), (C) goods and services provided to the workers employed in (B), and so on. This is why the term "multiplier" is used—the nonexport sector is a series of multiples of the export sector, each one smaller than the one before. (Each step yields a smaller multiple because each worker spends a fraction of her income on imports. So you might have $10 of export income supporting $6 of nonexport income, which in turn supports $3.60 of nonexport income, and so on.)
The thing to recognize here is that while the nonexport sector may be much larger than the export sector in any given location, it is the export sector that determines the ups and downs of the local economy. Changes in the size of the export sector propagate through the local economy and end up being reflected in the size of the nonexport sector, and not vice versa. (An interesting variant on this was proposed by Allan Pred. As a city grows, it may become large enough to support certain activities that require a minimum scale to be profitable. When this happens, imports are replaced by a new part of the nonexport sector, increasing employment and population. So the nonexport sector is not always merely an echo of the export sector, but for our purposes we can view it that way.)
So the problem for small industrial cities is that they are losing their export sectors. This should require them to shrink, but by how much?
Agriculture is the classic export industry that supports non-urban economic activity. The existence of an agricultural workforce means that our economy can never completely urbanize. There will always be small villages serving farmers' needs, and larger villages and towns providing more specialized services. Although Krugman didn't emphasize these villages and towns in his blog post, he clearly thinks they will always exist (unless agriculture is totally automated, I guess), and so he doesn't think small cities will truly disappear. They will simply shrink to a level that can be supported by the local export sector, which at worst would be the local agricultural sector. This implies that the cities will shrink until they are quite small—agriculture is too spread out and employs too few people to support large population centers.
But to take a step back, what is an export sector? I gave the literal definition earlier. But we shouldn't think about it so narrowly. For purposes of base-multiplier analysis, an "export sector" can be any activity that brings money in from the outside. It could be tourism, it could be remittances, whatever. Retirees receive Social Security, Medicare, Medicaid, private pension payments, etc., and of course they also spend down their savings. So they can form the base of a local economy in the same way that an export sector can, but unlike agriculture, they need not be spread thinly over the landscape. In particular, they can cluster in small formerly-industrial cities, where housing is cheap and where they support a nonexport sector specializing in health care and similar sectors.
So consider a fading industrial city. As the traditional export sector (manufacturing, usually) disappears, workers leave to find jobs elsewhere, and housing prices drop. The city likely has a decent health care sector already (in fact, many of the legacy industrial firms provided very generous health insurance and created large, advanced health care industries—this was certainly true of Peoria). So the city becomes a magnet for retirees, who find the cheap housing attractive and the health care services at least adequate. Jobs shift from the export sector (working at a factory) to the nonexport sector (working at a hospital or as a home health worker or whatever). The city stops shrinking, or shrinks very slowly. It still shows up as a relatively large population center, much larger than the agricultural village that it could theoretically become. For the reasons articulated by Pred (see above), these cities may support industries that smaller towns can't, and so their manufacturing sectors will not necessarily disappear entirely.
So where do these cities stand in terms of "disappearing" in Krugman's framework? On one hand, they still have decent-sized populations with spending power, and as noted they may even have small manufacturing sectors serving the local region. To the extent retirees consume a particular good or service, their presence in a city makes it more promising as a location to produce that good or service. If the good can also be exported, then you can imagine a town booming as it becomes the center of a cluster of manufacturing activity focused on that product. This would support Zed's contention that small cities can bounce back after long decline.
But on the other hand, these cities have relatively small workforces and, by assumption, they are far from major urban markets. It is hard to see why anyone would locate a manufacturing business in one of these cities instead of an exurb, which will tend to have a larger workforce and be much closer to a city with a larger absolute number of retirees. It could happen by random chance, of course, but this seems like the kind of highly unlikely occurrence that Krugman's point could accommodate with only minor modifications.
posted by James | 4:15 PM
4 Comments:
As a disclaimer I don't have strong views on the actual empirical question. I'm just trying to make sure that I understand the simplified models and their implications.
That said this particular version of the "multiplier" idea seems to me over-specific. The base intuition is that there'll be an *increase* but I don't think it's mandated to be linear. So for instance it could be a "squaring" or a cube instead of a multiplier. Say that industry brings N people to a town; the model you quote says the other people are qN, where q is some fixed N-independent number. Another possibility is that the multiplier is nonlinear, so N initial workers lead to qN^2 people in the city. And so on. Once you allow for this it is not hard to write down models in which, even after the initial industry vanishes, the population saturates to a stable constant value rather than zero. I.e., instead of being out of equilibrium, the model might have multiple equilibria, only one of which is N = 0.
In the model in Krugman's post the town goes to zero in the sense of ceasing to be a potential Schelling point. This doesn't happen in your version. I'm not convinced that retirement communities cannot subsequently become "hubs" or are somehow very unlikely to -- especially not when so much of the economy is healthcare.
Agreed that it's theoretically possible for a retirement-oriented city to become the center of a new manufacturing (or whatever) cluster. But I'm not sure I follow your point about whether the nonexport sector is a linear function of the export sector. So long as it is monotonically upward as a function of the export sector, it seems as though the point holds.
Bear in mind also that although the population might remain high, the workforce would be expected to shrink, especially the young, educated workforce. My claim is that employers would much rather locate where labor markets are thick and talented than where they are thin and relatively unskilled.
So the real point is that what you've got is a large service economy with maybe a small amount of manufacturing-like activity sticking around for Pred reasons. For instance, I believe there is a Wonder Bread bakery in Peoria, which a really small town probably couldn't support. But I do not anticipate that Wonder Bread is going to form the basis for a new manufacturing cluster.
Health care is complicated. There are two things you could be thinking of. One is that a city like Peoria could provide specialized medical services that draw patients from around the world. I don't see this happening, but you could always point to a place like Rochester, MN (home of the Mayo Clinic) or even the Cleveland Clinic. I guess that's possible, but we're talking about VERY few "winners" in that kind of race, and those providers have to compete with big-city hospitals for patients and medical talent. Anyway, though, I'm happy to concede that Rochester, MN has a good chance of remaining a small city centered around health care and technology. But Rochester didn't back into that after losing a manufacturing base, it has been a medical center for over a century. I'm not nearly as optimistic about transforming other small cities into destination health care providers.
The other thing we could be talking about is some kind of manufacturing activity centered around health care. Here I am even less optimistic. Of course you can't rule it out, but it seems that it would take some highly unlikely confluence of circumstances to be sustainable. It would have to be immune from outsourcing, which I think means transportation costs would have to be high. (Maybe test tube organs for transplant?) On the other hand, if transportation costs are high, why would you locate the activity out in the middle of nowhere (particularly somewhere with shitty winters, which make air transport unreliable) instead of near a population center? This, by the way, is what I suspect Krugman means when he says there's no economic justification for small, remote cities, although I suppose we can agree to disagree about that.
I think you're too fixated on manufacturing clusters for fancy exportable goods. But maybe the biggest new job driver is something like Amazon warehouses, or some other dystopic low-end stuff. There was recently an NYT piece about San Bernardino-Riverside noting that they had a ton of job growth but it was all in dismal jobs. This seems a possible future for currently low-income and depressing small towns (they could become low-income and depressing large towns). A thing people sometimes say is that at the moment jobs are being hollowed out in the middle of the income range and growing at both ends; this is one place where that trend could go.
A lot of small cities are in the south and do not have particularly shitty weather. (Well *I* think hot summers and mild winters are shitty but that's a minority opinion.)
I think there are ways to get zero industry equilibria. Suppose the attractiveness of a place to a new person is (a + b N), where a is some extrinsic thing (like an industry) and N is population. Say the marginal new person is a waiter or something. Then beyond a certain level the thing driving new people into the city is the fact that it's above a certain size. (In this model everyone goes to the biggest city, but the key thing is that if a new, more attractive city springs up, the old city is still a good local minimum with a big barrier to crossing.) Now you can complicate this further by saying that if the population gets too big the commutes get nasty and so forth. This might be a further nonlinearity that favors multiple clumps of some optimal N. And so on.
Well again, the discussion centers around small cities far from urban centers. That doesn't seem like an ideal place to put something like an Amazon warehouse. In fact it doesn't seem like an ideal place to put anything, which I continue to believe was Krugman's original point. If we're talking about exurbs, it's a whole different story. I don't think Krugman would deny that exurbs have growth potential.
More later.
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