The authors looked at housing prices in 452 urban areas across the US, along with measures of a couple dozen factors that can influence housing prices—including urban form, but also education levels, weather, demographics, recent population influx, the size of homes, and employment factors, among others. Controlling for other variables, cities that have a higher share of total housing in their "central areas" (as defined by the US census) tend to have slightly lower median home prices, and fewer very-expensive homes, than cities that are more sprawling and decentralized.
This, of course, runs counter to the intuition—and the much-touted arguments from the anti-smart growth set—that housing is cheaper in spread-out, poorly bounded metro areas.
That said, as careful as this research seems to be, there’s good reason not to read too much into it.
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First off,the share of housing in a city’s "central area" may not do such a good job of capturing what most researchers think of as sprawl: low-density housing, homes and services strictly segregated, and streets designed for cars rather than walking. I don’t doubt that there’s some relation between "centralization" as defined here, and "sprawl" as most researchers think of it. But it’s possible that the correlation is loose—and that some "centralized" cities still have relatively "sprawling" layouts by other metrics.
Second, the real story here is that controlling sprawl seems to have a very minor effect on housing prices: 10 percent increase in the share of homes within a city’s central area leads to an 0.2 percent decrease in median home prices. That’s a pretty small effect—and it’s overwhelmed by other factors that the researchers looked at. Household income has about 40 times as much influence on home prices as does "centralization." Construction costs have about 30 times as much impact. So in the big picture, there’s not much evidence that controlling sprawl makes housing significantly cheaper, or that facilitating sprawl makes it more expensive.
But perhaps that’s the point: the effects of urban form on housing prices are ambiguous, and can depend on lots of factors that are as hard to predict as they are to measure. Which can make it just as hard for smart growth advocates to prove that good planning can lead to more affordable housing, as it is for smart-growth naysayers to prove that the unfettered free market makes housing cheaper.