Weighted densities of the big four Texas MSAs

Standard population density is a useless statistic for metropolitan statistical areas* (MSAs) because MSAs are defined by political boundaries (county lines) and consist mostly of vacant land. But weighted density is still meaningful when applied to MSAs. Weighted density tells you something about the density at which the typical resident lives. More precisely, weighted density is the average density of the census tracts within the the metropolitan area, weighted by population — e.g., a census tract with 10,000 residents counts twice as much as a census tract with 5,000 residents. Alternatively, an MSA’s weighted density is the expected density of the census tract inhabited by a randomly-chosen resident.

As I’ve explained before, weighted density does a better job than standard density (gross population divided by gross land area) of capturing our intuitive sense of density. It is counter-intuitive to say that the Los Angeles urbanized area is more dense than New York City’s urbanized  area since the defining feature of the NYC urbanized area is the extreme urban density at its core. And, if you take the point of view of a person chosen at random from each of those urbanized areas, it’s untrue: a person selected at random from the NYC urbanized area is likely to live in a much denser census tract than a person selected at random from the LA urbanized area.

We can calculate weighted densities for metropolitan areas as well as urbanized areas. Weighted densities are inevitably lower for metropolitan areas because they contain not only one or more urbanized areas but also a bunch of rural, low-density census tracts. The weighted average has to account for the chance that a person chosen at random lives in one of these rural tracts. But because most people in a metropolitan area live in the urbanized areas at the core, metropolitan weighted density is largely driven by the density of the urbanized area at the core, as this chart illustrates.

In 2000, roughly 80% of the Dallas, Houston and San Antonio MSA population lived within the urbanized area in the core of the MSA. In 2000, 0nly 72% of Austin’s MSA population lived within the Austin urbanized area. Consequently, a random resident in the Austin MSA was more likely to live in a rural/small town census tract, which partly accounts for the lower weighted density  of the Austin MSA. (Austin’s urbanized area held almost 80% of the MSA population in 2010.)

All four of the big Texas MSAs experienced rapid growth between 2000 and 2010. Note that the Austin MSA 2010 is slightly bigger than the San Antonio MSA in 2000.

Because none of the four MSA boundaries changed between 2000 and 2010, the standard population densities of the four MSA increased by the same percentages, which is one reason standard population density is such a worthless stat for MSAs.

The Dallas, Houston and San Antonio MSAs all experienced similar growth rates between 2000 and 2010. (The Austin MSA grew a bit faster.) And I assumed, before calculating their weighted densities, that they all experienced the same pattern of growth. But, after calculating their weighted densities, I don’t think that’s true. The Houston MSA experienced a sharp decline (-9.4%) in weighted density between 2000 and 2010. Dallas experienced a small decline (-3.77%) while Austin was basically unchanged and San Antonio saw a small increase.

The change in weighted density does not tell you anything directly about where growth is occurring or its form. But it does give you this information indirectly. We know that the central-city density tracts are the densest. A sharp decline in weighted density like we see for Houston tells us that, proportionally, a larger percentage of the population in the Houston MSA is now living in lower-density census tracts. While Houston experienced infill development in the aughts, a much larger share of the development necessarily occurred on the suburban and exurban fringes. San Antonio, which saw a slight increase in weighted density, either had proportionately more infill development, or its suburban/exurban development occurred at higher densities. Either way, it’s hard to argue that San Antonio and Houston experienced the same pattern of development when their densities moved in opposite directions.

This surprised me. I expected Houston’s weighted density to at least hold steady given all the infill development. But this is why we rely on numbers rather than our visceral impressions. The Census Bureau is scheduled to release the urban/rural data for census tracts this month, which will allow me to calculate weighted densities for urbanized areas. It will be interesting to see whether the changes in urbanized area densities mirror the changes in MSA densities.

 *A MSA consists of a core urban area plus any adjacent counties that have a high degree of social and economic integration with the urban core, as defined by commuting patterns.