New Census data offers insight on a better way to measure the density of U.S. cities.

Economists and urbanists have long argued that density plays a key role in innovation and economic growth. As important as it is, density is a tough thing to measure. Metros come in different shapes as well as sizes: Some have more concentrated populations near the center, others are more continuously sprawling. Yet, density is typically measured rather crudely by simply dividing the total population of a city or metro area by its land area.

A new report [PDF] from the U.S. Census Bureau helps to fill the gap, providing detailed estimates of different types of density for America's metros. This includes new data on "population-weighted density" as well as of density at various distances from the city center. Population-weighted density, which essentially measures the actual concentration of people within a metro, is an important improvement on the standard measure of density. For this reason, I like to think of it as a measure of concentrated density. The Census calculates population-weighted density based on the average densities of the separate census tracts that make up a metro.

The differences in the two density measures are striking. The overall density across all 366 U.S. metro areas is 283 people per square mile. Concentrated or population-weighted density for all metros is over 20 times higher, at 6,321 people per square mile.

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This Census report is not the first to use population-weighted density. A 2001 study by Gary Barnes of the University of Minnesota developed such a measure to examine sprawl and commuting patterns. In 2008, Jordan Rappaport of the Kansas City Fed published an intriguing study in the Journal of Urban Economics (non-gated version here), which looked at the relationship between density (including population-weighted density) and the productivity of regions. Christopher Bradford, who blogs at his Austin Contrarian, has also advocated for using population-weighted density to better understand urban development.

What's particularly useful about the new Census report is that it provides detailed data on population-weighted density for all U.S. metros for both 2000 and 2010 (full data set here [xls]). This took some doing, because metro boundaries change over time. To develop consistent estimates, Census researchers went back and recalculated population-weighted densities for 2000 based on the revised metro boundaries for 2010. This makes it possible to compare the two time periods and examine changes over time.

The map below, from the Census report, charts population-weighted density across U.S. metros.

Map courtesy of U.S. Census Bureau

Concentrated or population-weighted density tracks closely with population size, being highest in metros with more than 5 million people (13,328 people per square mile), compared to 5,550 in metros with 2.5 to 5 million people, 3,489 in metros with 1 million to 2.5 million people, and 1,597 in metros with less than 250,000 people.

The table below compares population-weighted density to the conventional measure of average population density for the five densest metros (on the former). As the report notes:

The population-weighted density approach reveals that the areas with people living at the highest density levels—metro areas with 5,000 or more people per square mile—were clustered mainly in California and along the corridor stretching from Boston to Washington. Other very dense metro areas included Chicago, Honolulu, Laredo, Las Vegas, Miami, Milwaukee, and San Juan. Low-density metro areas, on the other hand—those with fewer than 1,000 people per square mile— were generally clustered in the South.

Four of the top five metro areas were the same according to both measures, although in a different order and with much higher values using the population-weighted measure (New York, San Francisco, Los Angeles, and Honolulu). Each of these four metro areas had a population-weighted density of 11,000 people per square mile or greater.

America's Densest Metros by Population-Weighted Density as Compared to Average Density
Metro Area Population-Weighted Density Average Density
New York-Northern New Jersey-Long Island, NY-NJ-PA 31,251 2,826
San Francisco-Oakland-Fremont, CA 12,145 1,755
Los Angeles-Long Beach-Santa Ana, CA 12,114 2,646
Honolulu, HI 11,548 1,587
Chicago-Joliet-Naperville, IL-IN-WI 8,613 1,315

Table data from U.S. Census Bureau

New York and Los Angeles are good examples of the differences between these two density measures. While they are close in the average density — 2,826 for New York versus 2,646 for L.A. — the New York metro has much higher levels of concentrated or population-weighted density, 31,251 versus 12,114 people per square mile. San Francisco, which has lower average density than L.A. (1,755 people per square mile), tops L.A. on population-weighted density with 12,145 people per square mile.

The charts below (from the report) illustrate this, tracking density, as well as the distribution of population, in the two metros by distance from the city center (measured as the distance from city hall).

New York's population-weighted density is much higher than L.A.'s in close proximity to city hall, roughly 80,000 people per square mile compared to between 20,000 or 30,000 for L.A., but it dips substantially about 15 miles out from the city center, falling beneath that of L.A.

Density has long been seen as a key factor in the ability of cities to innovate and grow, but exactly how it does so remains an open question. Rappaport's study, in fact, suggests that there is not a one-to-one relationship between density and productivity, noting that the "productivity required to sustain above-average population densities considerably exceeds estimates of the increase in productivity caused by such high density." Silicon Valley remains tremendously innovative at medium levels of density. The world's densest cities in Asia and elsewhere can take the form of skyscraper districts which limit interaction and function as kind of vertical sprawl. At the same time, more and more start-ups and innovative high-tech firms are choosing locations in the urban districts of New York, London, San Francisco, Boston, and other cities, as opposed to the traditional industrial and office parks of suburban nerdistans.

These new data on various types of density from the Census will enable us to take a deeper look at the role of different types of density on the innovativeness, productivity and economic growth of cities. Look for more on this here.

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