The previous post addressed housing unit densities and their change for 59 large urban areas from 1950 to 2010. This post continues by addressing several factors associated with levels of density and density change in the urban areas.
I started by looking at what might be related to housing unit densities in 1950 and 2010. Three factors were considered: First, the size of the urban area. In larger urban areas I would expect greater competition for locations closer to the center, raising land prices and increasing densities. Second, the size of the urban area at an earlier period–how much housing had been developed earlier and was older. This idea I had here was that housing built long ago, especially before the widespread use of the automobile, would be more dense. And since housing is relatively permanent, that would contribute to higher densities later on. Finally, if physical barriers such as mountains or wetlands limited the expansion of the urban area, densities might be greater.
Looking at densities in 1950, I used the number of housing units in the urban area in 1950, the 1910 population of the urban area as a percentage of the 1950 population for age of the housing, and an indicator for the presence of nearby mountains or wetlands (a judgement call on my part). The size of the area and the presence of more older housing were both significant; physical barriers were not.
For 2010, I repeated this but had the issue of what to use for the age of housing–population in 1910 as a percentage of current population or population in 1970, forty years before, as was the case for 1950. I initially tried each one. The size of the urban area was again highly significant and now physical barriers were as well. (Being significant now as opposed to not being significant in 1950 may make sense as the urban areas have expanded and are now encountering the barriers.)
The curious results came with the age of housing, earlier population as a percentage of current population. Using 1910 population, there was no association. Apparently too many changes had occurred over the century for this to continue to affect densities. Using 1970 population as a percent of 2010 population produced a very weak but statistically significant effect. However, I could think of no good reason why 1970 should be important and why housing built before that time should have an effect. So I tried population in other years as a percent of current population. To my surprise, the strongest relationship was for the population in 2000. That’s hardly a measure of the presence of old housing. But it is a measure of the amount of new, recently built housing. The more recent, new development, the lower the density. My guess as to what is happening is this: With new development, the urban area expands with some of that development taking place on rural land at the periphery. But initial development in those areas is scattered and random, leaving, at least for a period of time, vacant land. These newly developed areas meet the minimum urban density threshold and become part of the urban area. The vacant land contributes to lower overall densities. With more recent development, larger areas of this new development are added to the urban area, resulting in lower densities.
Looking at the change in densities from 1950 to 2010, three factors were considered and all were clearly associated with density change. Greater densities in 1950 at the start were associated with larger declines in density. Given the magnitudes of some density declines over the period, this almost had to be the case, as those declines could only have been possible in areas that started out with higher densities. The growth of the area, the change in the number of housing units from 1950 to 2010, was positively related to density. Increasing demand and therefore greater increase in the size of an urban area should have this effect. And finally, the presence of mountains or wetlands as physical barriers to urban expansion was clearly associated with greater increases in densities.
These were very simple, basic models predicting density and density change with 3 variables. But it was surprising how well they performed in accounting for the variation in density and density change. Each of the models predicting density in either 1950 or 2010 had R² values between 0.6 and 0.7. And the model predicting density change had a whopping R² of 0.86.
More detail on this analysis and the overall examination of densities and change is in the paper “Density of Large Urban Areas in the U.S., 1950–2010,” which can be downloaded here.