# Russell's Blog

## Travel notes (part 2)

Posted by Russell on December 30, 2008 at 7:48 p.m.
As I mentioned in the previous post, I saw an awful lot of houses. Some of them made me a little jealous, and others made my skin crawl. All of them got me thinking about the housing crisis.

While the housing bubble was in full swing, I had a very strong intuitive reaction to house prices; everywhere I looked, I saw prices that felt two to ten times too high. As it turns out, my intuition was right. Houses that were worth something were vastly overvalued, and there were an awful lot of houses that simply should not have been built at all. The latter was usually due to a combination of uninspired design, remote location, and natural hazards. Again, it turned out that I was right. (I don't claim exclusive clairvoyance here. Lots of people felt the same way.)

There are many things that helped create this situation. The answer the idiot-media has been pushing is that subprime loans flooded the market with money by giving loans to people who didn't qualify. The flood of cash drove up prices, which are now coming down. Leverage is definitely part of the problem, but the subprime aspect is overblown and widely misunderstood.

The fundamental problem is that there simply isn't enough affordable housing. People need homes, and there are good financial reasons why people want to own their homes. If home prices are out of reach, then of course people will abuse leverage whenever it is available. The market simply isn't supplying enough affordable housing.

Why not? The simple answer is the conflict of geography and geometry.

There are two categories of factors that contribute to the value of a home; the home itself, and the resources that can be tapped from the home. The resources available from the house provide options to the homeowner; more options mean better quality of life. More options also mean that a particular house could satisfy the needs of a greater number of potential owners, giving it more resale value. History has proved again and again that the second category is vastly more important than the first. Hence the expression, "location, location, location." This is why airless, vermin-infested closet space in Manhattan sells for millions of dollars while palatial estates in Riverside can be had for less than a tenth as much. It goes without saying that the owner of the airless Manhattan flat has access to more resources, and resources of higher quality, than the owner of the ranch in Riverside. That is the geographical aspect of the problem.

The geometry aspect comes into play when you consider how structures are distributed and how resources are made available in these structures. The Earth provides an approximately two-dimensional plane (actually, modern economic and military history can be viewed as a consequence of the increasing importance of the Earth's spherical geometry, but right now I'm thinking of more local effects -- read, for example, the chapter "Global Midway" in War and Remembrance to get a sense of what I mean). Resources available from a particular location scale like the square of the density of resources within the distance accessible from that point. As the density increases, people will start building upwards (sky scrapers) and downwards (excavation). This introduces a volumetric effect, causing the available options to scale like the cube of the local density of resources. As density continues to increase, it becomes financially viable to build mass transit, which extends the radius of practically available options. This introduces a quartic scaling. As the density increases further, it becomes necessary to seek synergies and greater efficiency to minimize use of space. This introduces a scaling at the fifth power of density.

So, as the density of a settlement increases, geometry militates the use of ever more potent means to reduce the footprint of an available resource, which in turn facilitates greater density. Each new means of increasing density adds an additional linear scaling, so that the ultimate scaling is approximately

${\cal O}(1+n+n^2+n^3+n^4+n^5+\ldots)={\cal O}(e^n)$

Of course, a polynomial of infinite order is the Taylor expansion of the exponential function. So, we can claim that the approximate value of a home scales exponentially with the density of resources in that area. The first three terms are required by simple geometry, and higher terms increasingly represent technological and social responses.

Really, this is the lower bound on the value; the value of a home also depends on how many other people might want it. If people select a home mostly for the choices it makes available to them, and each person has a different collection of choices they want, then there is some kind of combinatorial scaling as well (I'll leave this one as an exercise; you can get several different scalings depending on the assumptions you make).

Meanwhile, the value of the house itself scales linearly with the cost of the stuff you put into building it (labor and materials). However, nicer houses tend to be larger, and thus neighborhoods of big houses tend to be sparse. Thus, if the value of a home is the sum of the value of its location and its embodied value, embodied value will inevitably be overwhelmed by the locational value. This is a classical Malthusian conflict, but in this case the functions represent different things.

So, why the crisis? Well, we have artificially capped the growth of density. Zoning laws forbid the construction of new Manhattans, and require the gradual erosion of existing high-density neighborhoods as their buildings wear out and need to be renovated or replaced.

This is the story we tell each other about how this happened; the automobile gave people greater mobility, allowing them to live in the suburbs and countryside while they still work in the city. So, there was a great exodus from city centers to suburbia. This narrative has things exactly backwards. Density at the city periphery was legally capped and aggressively driven down, which forced people into the suburbs to seek affordable houses, making automobiles necessary to access resources that were previously available on foot. The first story is a marketing pitch, the second is recorded history.

In the early post-war period, opinion surveys consistently showed that the top transportation issue on the minds of Americans was the improvement of streetcar service, and the top housing issue was the rapid inflation of rent and other prices in city centers after the wartime price controls were lifted. People did not particularly want cars and suburban bungalows; they simply made a rational choice in the face of exploding rent and decaying public transportation. Even so, suburbia remained relatively unattractive for most people until Brown vs. Board of Education in 1954, and picked up steam in the early 1960s when racial tensions transformed the suburban exodus from an economic issue into a racial one. See, for example, the abandonment of Detroit, or white flight from Los Angeles to Orange County. That is the story of suburbia.

There is one more geometric factor to consider regarding the value of a house. The cheapest possible thing to add to a house is square footage. The "core" of the house -- the appliances, utilities, cabinetwork and main structural elements -- represent the bulk of the cost of home construction. Big houses are worth less, on a per-area basis, than small ones.

For the last 50 years, we've been building increasingly sparse neighborhoods of increasingly big houses. In real terms, the cost of ownership has gone up dramatically (heating, cooling, lighting, transportation, maintenance, taxes), while the real value of our houses and neighborhoods has decreased. Both of these scalings are exponential in nature; a modest increase in square footage translates into an exponential reduction in value per square foot.

In 1950, the average American home was 983 square feet. In 2004, it was 2349 square feet. In the neighborhoods most impacted by the building frenzy from 2004 to 2007, it almost doubled again, to around 4000 square feet for new construction. We're talking about a quadrupling of home sizes in 50 years!

Bigger homes require more land, and so density of resources available from these places must scale inversely with the square of home size -- and by the reverse of the argument above, decreasing density introduces higher order scalings whose sum produces an negative exponential effect. So, as homes increase in size, their value will exponentially approach the cost of the raw materials that went into them, until at some point the value falls beneath the associated costs, and owning one becomes a net liability.

The benefits and costs of owning a particular home are tied to labor market conditions, commodity prices, nearby development, and many other things. Thus, the narrower the margin between the benefits and the costs, the more likely the normal fluctuations of the economy will land you with a net liability. Adding leverage into the mix just makes the margins even narrower.

There is the nub of the issue. "Affordable" doesn't mean low price; it means getting a lot of value for a given cost (I am using the terms 'value' and 'cost' in a concrete sense, so you may substitute 'enjoyment' and 'effort' if you like). It means having a comfortable margin between the benefits of home ownership and its associated costs. It means a margin that is wide enough to absorb the risks we face in the event that they become realities. It means that you can still pay your bills if gas prices go up, or if you get a new job, or whatever. This lack of affordable housing doesn't just hurt poor people, it hurts all home buyers. We have a huge glut of houses that have virtually no value in them it all, except maybe as firewood, and almost no available houses with a decent number of readily available resources.

This isn't a situation we can bounce back from through financial mumbo-jumbo. The problem is intrinsic to our built infrastructure. The solution requires physical changes to our landscape. It will take a long time. Much hay has been made about the culpability of Wall Street in this crisis, usually portraying "Main Street" as the innocent victim. This is bullshit. Main Street is just as culpable, and maybe more so. Solving this crisis will require re-writing building codes and zoning laws, not just baking regulations. The crisis will ease up when we have enough compact, high-quality homes in good neighborhoods. By "enough," I mean we have to keep building them until the prices for these places puts them within reach of households at or below the median income.

It really doesn't help that our cultural prejudices insist on equating square footage with value; it is a false economy. Square footage is the high-fructose corn syrup of our financial system; cheap to produce, tragically unhealthy, and no matter how much you have, it never satisfies.

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