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Tuesday, July 19, 2005

If There Was a Housing Bubble In Wichita, Would Anybody Notice?


It's often said that while there may be a housing bubble in some areas, especially big cities on the coasts, there isn't a nationwide bubble. But what if there's a nationwide bubble in land prices, a bubble that's being masked because land just isn't a very big of house prices in many places?

One of many recent statements of the idea that the house price boom is confined to a few areas comes from Greenspan-in-waiting Ben Bernanke, who recently argued,
While speculative behavior appears to be surfacing in some local markets, strong economic fundamentals are contributing importantly to the housing boom.
Econbrowser James Hamilton chimes in:
I would argue that the huge differences across communities in the rate of housing appreciation are much more of an embarrassment for Bernanke's critics than they are for him. Those challenging Bernanke's interpretation are forced to suggest that there are hundreds of separate little bubblets, expanding in different communities at curiously different rates.
One simple point that hasn't received enough attention is that standard statistics on house prices actually measure a combined package that includes both land and the structures built on them. And we'd only expect a bubble in land prices, not in the price of structures.

The price of structures will be constrained by the cost of construction. The price of houses themselves (absent the land) can never rise much over the cost of building a new one. On the other hand, it's pretty hard to make more land, so as long as the demand is there, the price can go sky-high. In the language of econ 101, the supply of structures is quite elastic, while the supply of land is very inelastic.

It may seem a little odd to think of land and houses being sold separately. But if we imagine a city with abundant land, it's pretty easy to see that we can't have much of a boom in house prices. If house prices start to rise, people will just build new homes instead of buying existing ones, and prices will fall back down.

In high-priced areas, land is a bigger portion of house prices, probably a much bigger portion. In Wichita, land may be only 10% of the price of a house (of the house-land package, that is), while in New York City, 90% of the value of a house or apartment may be in the land. If land prices doubled nationwide, people in Wichita would hardly notice: the price of a house would only go up by 10%. But in New York, house prices would go up 90%.

At a casual glance, this is exactly what's been happening, with booming prices in places that already were high-priced to begin with. We can test this a little more rigorously by estimating a regression. The regression tests whether there is a relationship between rents in the initial year and later house price growth. The idea is that cities with high rents are cities where land prices will be a high fraction of the house price package.

Specifically, I regressed the percent change in house prices from the first quarter of 2000 to the first quarter of 2005 (measured by Freddie Mac) on the natural log of median rent in 2000 (from Census 2000), for the 163 metro areas tracked by Freddie Mac. The graph below plots the data. The regression equation is


(House Price Growth) = -5.74 + 0.97 ln(Median Rent), N=163 Metro Areas

(-8.43) (9.18)
The t-statistics in parenthesis indicate that the effect of initial rent on later house price growth is highly significant. The t-stat of 9.18 is way above the cutoff of 2 that's usually taken to indicate statistical significance. The correlation between the two variables is 0.59, fairly high. So the regression shows that the boom in house prices has been much stronger in areas where rents were high initially. I also tried this regression with initial house prices (also from the census) instead of rents, and got similar but slightly weaker, results (t=7.6).

Now the regression doesn't prove that there's a bubble, that the house price boom has been driven by speculation rather than favorable fundamentals like low interest rates. But it does provide an answer to Hamilton's "embarrassment ... of hundreds of separate little bubblets." It suggests that something is happening nationally, not just in certain cities.

Is there a nationwide bubble in land prices, that's being masked by the fact that we only measure the combined price of land and structures? I'm not sure, but it is consistent with the data.

[hat tip to Bostic, Longhofer, Painter, and Redfearn, whose recent paper emphasizing the importance of land prices inspired this post]

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