Many have examined the decentralization of population and housing units over time. A common approach has been to use the density gradient from the exponential model as a measure of centralization. I have estimated the parameters for the model for large urban areas since 1950. I wanted to consider how well the density gradient actually performed as a centralization measure (which will be the subject of the next post). But to do so, I needed a separate, good measure of the centralization of housing units.
I reviewed a variety of centralization measures in the literature and was not satisfied with any of them, so I developed my own. I wanted a measure that made maximum use of the data on the distribution of housing units by census tract. And I wanted the measure to be interpretable, to have meaning beyond a larger value indicating housing is more centralized. The measure involves calculating two values: One is the mean distance housing units in the urban area are from the center. The other is the mean distance they would be from the center if housing units were uniformly distributed in the area, densities everywhere the same, no centralization. The ratio of the actual to the uniform distance would, of course, be 1 if housing were uniformly distributed and would decline with decreasing mean distance to the center and greater centralization. The minimum value would be 0 if all housing were located at the center. I wanted a measure of centralization that would increase with greater centralization, so this ratio is subtracted from 1. This measure, which I am calling the centralization ratio, is the proportional reduction in mean distance housing units are located to the center compared with a uniform distribution. So a centralization ratio of 0.25, for example, would mean that the mean distance to the center is a quarter less than for an even distribution.
I calculated the centralization ratio for 59 large urban areas for each census year from 1950 to 2010. The widely expected decentralization did occur, on average, with the mean value dropping from 0.25 to 0.18 over this period. But decentralization was far from universal; 14 areas saw increases.
Levels of centralization varied greatly across the urban areas. The highest and lowest values in 2010, for example, were 0.46 and 0.08. New York, Chicago, and Philadelphia were the areas with the highest levels of centralization, not surprisingly. Tampa-St. Petersburg, El Paso, and Jacksonville were the lowest. Urban areas in the Northeast had the highest mean centralization in 2010, followed by those in the Midwest. Urban areas in the South had the lowest levels of centralization (and would have been even lower if Washington-Baltimore, more like other large urban areas in the Northeast Corridor, had been excluded). The very largest urban areas also tended to have higher levels of centralization.
More detail on this analysis using the centralization ratio is in the paper “The Degree of Centralization in Large Urban Areas in the U.S., 1950–2010,” which can be downloaded here.