In Defense Of Downward Sloping Urban Housing Demand Curves

Ye That Fear the Dragon Whose Name is Wonk, Turn Back Now

Nicke Rowe at Worthwhile Canadian Initiative has an interesting post passed along to me by James M. Russell, AKA @BurghDiaspora on Twitter.

The post’s is interesting because Nicke Row starts at the exact point I’ve long argued urbanists should start from. This is no surprise since, like Nick, I’m an economist arriving at urbanism accidentally and, in some cases, quite unwillingly:

TL;DR version: Nick’s post is very thoughtful and interesting, but boils down to, “Anyone not dying to live in NYC is lying to themselves.” He means well and isn’t at all condescending in his post, but this is the logical conclusion.

To start with, Nick acknowledges that cities may arise as a result of some kind of random variation, or indeed as a negative feature. Cities may exist because there are geographic chokepoints, or places where geography uniquely favors certain spots. Now, I’m not a fan of the idea that geography is destiny for cities, and instead tend to think that urban populations arise mostly due to the demands for labor, skills, and capital arising from the specific production functions of specific, historically-contingent industries.

But nonetheless, I’m also a big believer in not ignoring the blindingly obvious: most of America’s biggest cities are not located out in the middle of a featureless plan where it is “easy” to build a city. Most of the world’s biggest cities are not in such environments. Nor are cities located in the most desirable locations; they are located in places where they adequately meet the specific needs of the production functions of specific, historically-contingent industries. There has been some historic commonality across many industries, such as access to transportation for both inputs and access to market.

I think Nick breezes past natural geography too quickly, and it’s easy to see why.

Why is there no major city in eastern Kentucky? The reason is simple: geography does not reward, or in some cases even permit, large clusters of people in Eastern Kentucky. More to the point, there are ample sites for urbanization not to far from these hard-to-urbanize places. So any “demand for urbanization” in eastern Kentucky gets satisfied in Lexington. If we dropped nukes all around the Appalachian fringe, wiping out Lexington, Knoxville, Cincinnati, etc, we might see more urbanization within the region as the relative cost/benefit to urbanizing in the hills would change.

All that is to say, while geography isn’t destiny, it does matter.

But there’s more to geography than static landforms. Rivers were better than roads for most of human history. Then came the railroad and BAM! rivers were an inferior mode of transportation, railroad-friendly sites were better. Rivers even become barriers, as bridges are tricky.

In the 1850s, my home county had nine ferry sites or bridges over the Kentucky River. Today, there are a grand total of three crossings. Rivers were once chok-full of ferries and fords and crossings. But now, only a few major roads or railroad cross. The dominant mode of transportation has changed the meaning of geography.

The land itself can change, too. Dams, flooding, irrigation, swamp drainage, hurricanes, climate change, island formation, vulcanism, canal-digging… all can change the viability of a given urban site. Many have played key roles in U.S. history. Dozens of U.S. cities today would have been unimaginable without the canals, floodwalls, and swamp-drainage programs that recreated the land around them.

Usually those programs didn’t begin to facilitate the cities they grew up around. Usually they began to facilitate agriculture in the area, or transportation across a given area, or electricity generation for somewhere else, etc. The cities usually came later, after the impact of the redefined geography began to become clear.

All that to say, geography not only favors some places over others, but there is such a thing as a “geographic shock.” Nick might prefer to think of it as a “technological” shock, which is fine, but the key takeaway is that which spots are advantageous changes over time. It changes both because dominant industries and production functions change, and because the actual economic meaning of physical space changes as the land, and land-related technology and infrastructure, changes. For a quintessential example, note the extension of the railroad west: rails came first, then came cities.

Why Do We Actually Have Cities?

Factory Dormitories, Duh.

Nick suggests that, aside from the natural lopsidedness of the land, cities exist because of strategic complementarity: because there are benefits to people of living near other people.

To some extent, he’s right. But he misses out on why cities actually came into existence. Before the industrial revolution, the vast majority of humans resided in rural settings. Where cities did exist, they existed to facilitate high-value services like finance, law, government, religion, education, the military, trade, etc. They also facilitated some craft-shop style manufacturing, but most pre-industrial manufacturing was still rural or semi-rural. Cities existed because there were geographic lumps that facilitated transportation networks, and from which political elites could exercise control, which resulted in bubbles of security and wealth, which enabled the tertiary services.

These cities amounted to maybe 5% of global population, maybe 15% of western European population at most.

When cities really began to grow, it was because (1) agriculture got more productive, leading to diminished rural labor needs and lower returns to peasant-farming, causing many peasants to be evicted, and (2) manufacturing experienced technological gains that vastly boosted the productivity of low-skilled workers relative to high-skilled workers, greatly increasing demand for workers in areas where factory technology existed (read: along major waterways and transportation networks). The specific production processes of Industrialization invented the modern city, not complementarity.

Cities did not come into existence because being near other people was so great, desirable, or inherently productive. Yes, it turned out that people pushed close together did quickly find ways to be more productive, and the huge productivity gains in agriculture and manufacturing did create income growth that was efficiently deployed in cities, but the reason for modern urban clustering was the warehousing of factory labor. It wasn’t network effects. Network effects gave us between 5 and 15% urbanization rates. It was manufacturing and agriculture technology shocks altering the production process faster than transportation technology could keep up, requiring extreme density. This density then propelled new innovation in construction, while all these new productivity shocks boosted income and living standards, creating demand for more and more value-added goods and tertiary services.

Imagine a different hypothetical. Imagine that cars, or some equivalently cheap and effective mode of mass transportation, had been invented simultaneous with industrialization. We never would have gotten urban clusters like we have today. Sure, we would have had some urbanization, but many peasants would have avoided the crime and squalor of the city, commuted in, and used their income in the cheaper hinterlands.

So to be clear, we’ve identified a second reason for cities.

Cities exist due to natural geographic effects related to technology shocks, but also because of the historical order and process of innovation, which created large demands for unskilled labor prior to efficient mass transportation technology.

And to reiterate, that effect is not what Nick means when we talks about complementarity.

The proof of this “reason” for urbanization is obvious: as large-scale factories declined, so did all the cities that grew during the industrial age. People moved out to suburbs and exurbs, or to entirely new cities in the Sunbelt that provided a new set of advantages, some related to geography (like climate, or modern airports, or interstate access). When urbanists talk about expensive housing, they do mean all housing in a metro area on some level, but what they really mean is “true” urban housing: downtown, high density, multifamily or townhouse-style living. Even though the suburbs may be the same metro area, in terms of a meaningful “place,” the suburbs are in fact new cities.

Why Do We Still Have Cities?

Compleme — Oh, Shoot, Fixed Costs, Investments, and Institutions

Imagine that everybody “spawns” into the world as an adult, and gets to pick where to live. Nick’s story of complementarity as a major motive for urban clustering would totally make sense. We’d all choose to live in the place we expect to yield the highest average returns over our lifetime, and so we’d all cluster in a few places, boosting each others’ income.

As it turns out though, that’s not how humanity works. In real life, houses exist before our birth. Generations overlap. Later generations inherit housing from previous generations. Employers face large costs to relocate, both in terms of physical capital and retraining or rehiring workers, or paying for worker relocation.

Plus, the wealth of cities gets dumped into geographically fixed assets. Philanthropy must be identified as a key driver of urban fixity: piles of money are dumped into trusts whose job is to maintain a given amenity or institution for time immemorial. Orchestras, museums, charities, nonprofits, these groups create a kind of permanency in wealthy cities that is difficult to dislodge, though not impossible. Stadiums get filled with teams, arenas serve as concert halls for the region long after local populations decline, the physical and social infrastructure of the city that was built during its heyday continues to be used and inherited by later generations.

Over time, even this decays if the city has no economic staying power in it. But the truth is that an inherited house is often cheaper than a house you have to buy. Finding jobs is easier in your current city than a new city. This isn’t because there’s complementarity to being around any large group of people, but because individuals idiosyncratically benefit from being near familiar networks and groups of people. In areas with large historic populations there are large pools of people who are probabilistically likely to experience ideosyncratic benefits to staying-put. In other words, cities have a natural inheritance gravity that encourages people to stay, even if the raw, average “complementarity” benefit may be vastly larger in some other city.

Most people can get a reasonable guess on where they fall in relation to the “average” complementarity benefit, because the big beneficiaries of urban complementarity tend to be high-value service providers, political elites, and beneficiaries of the above enduring institutions I mentioned. In other words, the benefits of complementarity are neither general nor random, thus even cities with declining industries and little current geographic advantage persist because there are still local markets, pools of residual benefits and institutions, and inherited wealth, as well as probably some amount of entrepreuneurship and generally valuable economic activity. Even dying cities have a few successful firms.

So now we have a third reason cities exist:

Cities exist today because they have existed in the past, and it takes a very long time for population, housing, government, institutions, and physical infrastructure to adjust.

Okay. So we’ve explained (1) why cities initially rose, (2) why they got really big during the industrial period, (3) why even big industrial cities declined, but have never fully died even lacking Pittsburg-style-revival. Now, finally, we can interrogate the idea of complementarity that Nick puts forward.

What Is Urban Complementarity?

Amenities, Jobs, Networks — It’s What You Want It To Be

Urban complementarity is a fuzzy concept. Most experts in the field look at productivity. It’s common to believe that urban density boosts productivity.

This view is at best incomplete, and may be entirely wrong.

The academic literature supporting the theory that there are strong urban network effects boosting productivity is not actually extremely compelling. It’s okay if you want to believe this theory, but just understand that you are believing that urban density boosts economic activity, not knowing it. It’s a commitment of will and faith, not, at this point, something that has been, or maybe even can be, empirically demonstrated. Sadly, they don’t let us arbitrarily increase and decrease the populations of major cities and, as I’ve explained above in less formal terms, we have serious endogeneity problems with urban population and various economic factors that could also relate to productivity. Identifying causality in this question is far from easy.

Luckily, Nick is taking a more defensible, if even less empirically testable, position. He’s not saying cities boost productivity. He’s saying cities boost utility.

The summary version of Nick’s claim is:


People value cities because they get growing amounts of utility the more they’re around dense clusters of other people…


A small adjustment to ease housing supply will actually increase prices.

Let’s look at the if part of this claim first.

Does Everyone Value Cities?


First of all, huge problem: some people hate cities. Hi, my name is Lyman, and I want to burn all your cities to the ground, because I am a cultureless barbarian. I warn you, however, us cultureless hill-people are not so few in number. And certainly all the evidence is that most people actually prefer something suburban-ish versus either “true” urban living or “true” rural living.

So we need to modify Nick’s position. Maybe “people” don’t value cities because they get utility from clustering, but instead “some” people do. We need a model where some people derive positive utility from clustering (due to efficient public services, nearby amenities, walkability, public transit, etc), whereas other people derive negative utility from clustering (due to noise, or crime, or because, hello, those downtown apartments are prestige goods and if everyone has one they’re not worth as much). Then there’s a third group for whom real estate is a pure investment asset, who derive negative utility from anything they expect will reduce prices. But I’m going to ignore this group because I don’t have the intellectual chops to know how to really explore what impact their behavior has, especially if we allow them to have irrational views about the future path of prices.

So right there, we can see the issue. Densifying will actually yield disutility for some, maybe for many, people. Any utility benefit from urban clustering is not universal, and therefore to determine the impact on aggregate demand we need to know the actual demand curves of each heterogenous member of the population.

But appealing to micro-heterogeneity is unfair play, because Nick’s a macroeconomist. So let’s drop this critique and pick up a new one.

Does Clustering Have a Formulaic Result for Utility?


Is all urban clustering likely to yield even remotely similar complementarity?

Answer: no. Different cities, given different culture, history, and laws, will yield different mixes of restaurants, public services, public transit, and job opportunities. Some quite dense areas turn out to be jobless foot deserts with high crime. Others are really nice hi-rises surrounded by restaurants, grocery stores, and well-paying employers. In the aggregate, high-density areas do have somewhat higher nominal incomes (note: not higher local-cost-adjusted incomes), but they don’t have much lower unemployment, if at all.

All that to say, people don’t want “density,” they actually do want specific amenities. And it turns out, there isn’t much evidence that density will create those benefits.

Plus, an benefit for one person is a cost to another. To one person, living near bars is great. To another, it’s awful. Same for stadiums, brothels, downtown, schools, dog parks, you name it. Even “low crime” is not a universal amenity: drug dealers probably don’t choose to live in low-crime, well-policed areas most of the time.

But again, I’m being unfair. Here I double-whammied on micro-variation, repeating the differences in individual preferences, while also appealing to heterogenous effects of density.

But, maybe this isn’t cheating after all.

Why Don’t We Live In One Giant Megacity?

Because Strong Strategic Complementarity Does Not Exist

Let me pull a quote I find revealing:

Notice anything weird about this? Here’s a list of what I notice:

  1. There are few major cities in the U.S. great plains. Where they do exist, it’s either along the rivers that serve as shipping lanes and electricity providers, or at the mountains below major passes and interstates.
  2. The cities that exist on the Canadian plains are fairly evenly distributed, and I don’t know their geography as well, but if anything I see evidence of weak complementarity: a large number of smaller towns, and where cities do exist, it’s mostly political centers.
  3. If we benefit from living near 200,000 other people, why not 400,000 even moreso? This should be the case, mathematically, if we really have Strong Strategic Complementarity, if we really receive bigger benefits to utility the more people we live around. And if 400k, why not 800k? Why not 2 million? Why not 40 million? Why don’t all Americans live in a city of 300+ million people? OUR UTILITY WOULD BE SO HIGH!
  4. How the heck do you get the wonky idea that geography only mattered when we were floating logs and canoes down rivers. Like, what? How is that your go-to? How about “New York City and Boston received immigrants because they were much shorter trips to Europe and so had cheaper fares and required fewer foregone wages and thus immigrants opted to migrate there and once the packet lines got regular journeys going costs fell even further due to economies of scale so geography made northeastern cities grow explosively while southern cities lagged”? How’s that for a “geography matters” bit? Or how about “the invention of air conditioning made southern summers more bearable and thus retirees concerned about ice and snow moved south to get milder winters”? We do not live in a post-geography world.

And this is why heterogeneity matters: because heterogeneity explains why we don’t cluster infinitely. Because complementarity is not perfectly scalable. Let me count reasons why complementarity isn’t perfectly scalable:

  1. Direct disutility of crowding: some folks don’t like other folks
  2. Prestige disutility of crowding: some folks like to be the only folks that live in The Hip Place
  3. Congestion: whether on the road, the metro, or the pool, it sucks to deal with crowds.
  4. Pollution: trash, chemicals, smog.
  5. Crime: surprise, crime is higher in the city. Most crime is a crime of opportunity. Higher density yields greater opportunity.
  6. Geographic constraints: many cities are bounded by water or mountains, so can’t scale.

Now let me list some reasons why we might expect active non-complementarity:

  1. Other geographies may favor certain industries more (for example, forestry)
  2. Some people may prefer less crowding; this is the mirror image of the disutility of crowding
  3. Zoning aside, rural construction is cheaper, so same-nominal-income can generally yield higher-real-income.
  4. Scenery. Some folks really dig the color green.

I could come up with more.

But this is why advocates of urban density appeal to productivity. Because on the grounds of the structure of individual utility, it turns out that there’s no compelling reason to believe urban areas actually are that great, for the marginal person choosing between urban, suburban, exurban, and rural places. There are heterogenous preferences, with the result that the aggregate demand curve is downward sloping.

To get an upward sloping demand curve, then we need a large population not currently residing in a city that nonetheless believes the city will substantively increase their utility, and we also need their post-migration wages and cost of living to adjust such that any change in utility-from-wages-and-costs is no less negative than the compensating differential of utility.

So if, in fact, the marginal migrant is pretty ambivalent about cities, then we would need a substantial wage-and-cost gain to justify them moving into the city. And this is why urban advocates hawk the density-boosts-productivity line: because it’s the only defensible reason to think we shouldn’t set fire to the cities and start fresh. Okay, not really, obviously that would be an evil thing to do, but the point is, this productivity argument is the only arrow in the urbanist quiver (alongside environmental benefits of density, but that’s a different issue).

We can argue whether cities boost productivity. I think they generally don’t. Other people think they do. It’s very hard to test.

But I’ll say this: we know that areas with more rapid housing supply expansion do in fact experience less of an increase in housing costs. This in turn, to me, suggests that the price effect of gains in aggregate demand due to rising willingness-to-pay are less than than the price effect of gains in housing supply.

And if we can pretty well bet that increasing density probably has little direct aggregate effect on demand, since it may attract some but will repel others, then we must grant that the effect on productivity of increasing density is smaller than the effect on price. Any gains to aggregate demand driven by increases in productivity (if there are any at all) due to higher density are more than offset by the supply increase necessary to facilitate that increase in density.

In sum, if, like me, you think that density has little effect on productivity, then the only interpretation of Nick’s post is that he is modeling the average human being as someone who loooooves hi-rise apartments, not because that’s where their job is, but because they just like dense living for its own sake. I think the average human being as preferences that more closely match how the average human being actually lives.

Some Final Notes

Nick said to take his post with a truckload of salt; so to be clear, I think he’s making a valuable contribution here. It is worthwhile to consider this issues. Unfortunately, I think he’s a bit ambiguous in what it is he actually thinks is happening. His cell phone analogy is not very apt, because cell phones are actually a technology for connection. The benefit of a network is clear. It is not clear exactly what benefit Nick thinks arises from density. Jobs? Productivity? Shorter commute? What is it? Without a better sense of what exactly Nick thinks is the benefit of density that people might prefer, it’s hard to read his argument clearly.

Nick also seems confused about if he’s making a small or large change in housing policy. He says it’s a small change, but he represents a “low quota” and a “high quota.” That sounds like a large change. It also looks like a large change: visually, he increased supply by 50% or so. So I’m not sure how to read his graph.

Nick’s summation of his claim, “If you build 100, 150 will come” is wonderfully clear, and makes wonderfully clear why he’s wrong. Urban housing still has vacancy. Areas that increase supply more actually do have lower rents. And the idea that 150 people will show up just because you built them houses is ridiculous. I live in a prime neighborhood with low crime 100 yards from a major metro stop, with ample available parking too, 10 minutes walk from 2 separate restaurant/bar districts, 5 minutes from a major sports stadium. The new apartment complex by my house has been open for 4 years. They still have a giant billboard advertising vacancies, and looking online reveals they still have about a fifth to a quarter of their apartments unfilled. They built 100, and 150 did not come. 80 did.

Where Nick does make a valuable contribution is in suggesting that there are reasons to be skeptical that incremental changes in land use law will achieve meaningful price drops. They won’t. Incremental changes will produce incremental results that will be swamped by economic factors. Big changes, like, say, filling the National Mall with high-rises, are not going to happen either. So Nick is right to raise the alarm that urbanists promising big things may want to back off. Zoning’s effects are slow, technical, and require large changes to get large results.

Nick notes his model won’t work for the whole country, but misses that, if what people want is “complementarity,” then you must model multiple cities with divergent price, supply, and demand situations all simultaneously. Migrants can select between multiple cities, and do so at substantial rates.

Finally, I hope Nick keeps writing intelligently about “urban” issues. It’s a fascinating topic, and I really think more economists should study it. Unfortunately, Nick may need to take off the macroeconomist hat and start thinking micro-heterogeneity.

Check out my Podcast about the history of American migration.

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I’m a graduate of the George Washington University’s Elliott School with an MA in International Trade and Investment Policy, and an economist at USDA’s Foreign Agricultural Service. I like to learn about migration, the cotton industry, airplanes, trade policy, space, Africa, and faith. I’m married to a kickass Kentucky woman named Ruth.

My posts are not endorsed by and do not in any way represent the opinions of the United States government or any branch, department, agency, or division of it. My writing represents exclusively my own opinions. I did not receive any financial support or remuneration from any party for this research. More’s the pity.