Land Value Increases with Population

In almost every “run” there is. I’m making this post a) because of its relevance to my recent calls for steep land value taxation which was of (relatively) high interest and b) because Paul Krugman and Noah Smith beg to differ. (How often does a not Very Serious Person get to disagree with Krugtron, after all?)

There are obviously strong theoretical reasons to believe that land prices correlate well with population. Probably the simplest argument is a rising demand on a perfectly inelastic supply. More intricately, David Ricardo argued that an increasing working class would steadily increase the demand for grains increasing rents earned on fertile land, thereby the net present value of all future returns and hence the price.

In America, Henry George – perhaps not coincidentally after a failed attempt at finding gold – angrily argues for land taxation in his Progress and Poverty, not with arguments too far from what the classical economists made or what you might hear today.

Smith thinks it’s all about agglomeration:

In other words, New York City real estate is high-priced because New York City is an agglomeration of economic activity. It is not high-priced because an increasing number of people are being forced to live in New York City. That isn’t even the case! No law makes people cram themselves into NYC (except in that Kurt Russell movie!); you are legally free to move out to North Texas and get a nice ranch. People choose to live in the heart of New York City because of the economic (and social) opportunities offered by proximity to all the other people living there. So they’re willing to pay lots for land.

Krugman piggyback’s on Smith’s point and also notes that the city can always spread out into unused land:

Even if people want to stay in existing metro areas, they can hive off “edge cities” at the, um, edges of these metro areas, so that the relevant population density — the density that makes land in or near urban hubs expensive — might not rise even if the overall population of the metro area goes up.

And we have data! Via Richard Florida, new work by the Census (pdf) calculates “population-weighted density” — a weighted average of density across census tracts, where the tracts are weighted not by land area but by population; this gives a much better idea of how the average person lives.

Together, they make a strong argument that only in the longest of runs (and perhaps not even then) when a city can grow in size no more, is land price truly a reflection of population constraints. The logical conclusion of this eternally long run wouldn’t be far from America – the whole thing! – becoming a city state.

But there are a few important problems with the argument, mostly Krugman’s suggestion that the city can just “hive off”. The city is not a discrete blot as much a diffused core. The agglomeration economies then derive from the ability to commute efficiently to a well-recognized center. Now note, not all cities are monocentric, and polycentric models exist. Most business activity and, hence, economic output happens in the immediate vicinity of these centers. Indeed, variations of density can differ by over an order of magnitude and land prices in the core may be over 30 times that in the “hived” peripheries.

But cities are limited in the extent to which they can expand. A highly-developed rapid transit system with a commuter rail allows for cheap and quick commuting. As a new working paper notes:

This raises the issue of population density. When we compare cities cross- sectionally, at the same time but across different sizes, we tend to find that larger cities are denser. Nevertheless, in the United States and increasingly all over the world, we also find many modern urban forms, and especially many low-density large cities, such as Atlanta or Dallas. Are these lesser cities than the West Village that Jane Jacobs knew, or the walkable towns that Smart Growth planers advocate? The perspective of cities as interaction networks tells us how all these urban forms can co-exist: the spatial extent of the city is determined by the interplay between interactivity and the relative cost of mobility. When it is possible to move fast across space, cities become much more diaphanous and are able to spread out while preserving their connectivity. It is in fact the diffusion of fast transportation technologies, especially now in developing world cities, that is allowing them to spread out spatially, sometimes faster than they grow in terms of population (32). This, of course, creates possible vulnerabilities. For example, if the cost of transportation relative to incomes suddenly rises (e.g. because it is tied to oil prices) then cities may not be able to stay connected, leading potentially to a decrease in their socioeconomic production rates. Ideas for shrinking cities that have lost population apply the same ideas in reverse.

From the same paper (Bettencourt, 2013) we get confirmation of something I suspected earlier. There’s a greater flaw with assuming land prices aren’t causally related with population in the short run, but agglomeration economies. Population causes agglomeration. (This is theoretically and empirically founded). That is, on a log-log scale of population and income, the slope is about 1.13. Or a doubling of population increases total income by 113%. People get disproportionately richer. More money is chasing the same land because more people are chasing the same land.

This means land prices do associate well with population, in fact it’s about a 50% increase in rents for every unit increase in population:

There are two important consequences for general land use considerations. First, the price of land rises faster with population size than incomes. This is the result of per capita increases in both density and economic productivity, so that money spent per unit area and unit time, i.e. land rents, is expected to increase by 50% with every doubling of city population size! It is this rise in the price of land that mediates, indirectly, many of the spontaneous solutions that reduce per capita energy use in larger cities. Cars become expensive to park, and taller buildings become necessary to keep the price of floor space in pace with incomes, thus leading to smaller surface area to volume, reducing heating and cooling costs per person. These effects may also create the conditions for public transportation to be a viable alternative to automobiles, even when the price of time is high. Thus, larger cities may be greener as an unintended consequence of their more intensive land use. Policies that increase the supply of land per capita or reduce transportation costs (such as urban renewal), while addressing other problems, will tend to create cities that are less dense and that require higher rates of energy consumption in buildings and transportation.

Smith argues that agglomeration effects are path dependent, and that theoretically if land use restrictions were implemented there could be a chance that agglomeration would decrease and hence price would fall.

He’s right about most of it, but I take a much simpler view of agglomeration:


In other words, it’s all the population. And by the way, the figures are pretty similar across the world (that’s actually what I’m working on for India). Read the paper if you want to convince yourself this just isn’t coincidence.

Smith talks about technology, but then oversimplifies the idea that there’s always unoccupied land nearby. The farther I have to drive to get to the center, the more I pay for gas and the more wages and leisure I sacrifice in commute. Transportation technology can mitigate this to an extent, after which point a city is largely stationary. Krugman’s point that the average American lives in sparser city today is well-taken, but also simplistic. We have more medium-sized cities than ten years ago. We don’t have more Chicago’s than ten years ago.

It’s kind of like saying “the average person in a medium or rich countries today is poorer than he was ten years ago”. That’s because a bunch of people just entered that “medium” category. But we don’t have a new America or Norway. In fact, it’s noted that initial urbanization happens in what happened to Delhi or Mumbai a few decades ago, but after a point the drive comes from the new and small places that are now classified as “cities”.

In any case, Smith’s point is actually causally linked with population. It always has been, and always will be.

P.S. Also read Bill McBride on why land prices will rise as population.

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