Some fun facts: New Jersey (at 460 people per square kilometer) is the densest state in the United States. Connecticut (at 285/km^2) has more than double the population density of the state of New York (158/km^2).
Obviously, while New York State contains New York City, the densest city in America, it also has miles of empty hinterland upstate, while Connecticut has relatively low-density suburbs covering a large fraction of the state. Crude population density is relevant if, say, we plan to split the state up evenly and give everybody a plot to farm, but it doesn’t really capture the difference between New York and Connecticut.
A more relevant way to calculate the population density of a place is to ask “How far apart are the typical neighbors in this state?” Or similarly, “What is the density perceived by the average resident?” I was inspired to calculate perceived density by this Austin Contrarian blog post, and so I’ll quote his explanation:
An extreme but simple example: Suppose Metropolis consists of a central core of 100,000 residents on 10 square miles, and a suburb of 10,000 on 100 square miles. Its standard density is 1,000 persons per square mile.
But this is a meaningless number. Most of the residents of Metropolis live in a very dense environment. The roughly 90% who live in the core are packed in at 10,000 per square mile, while just 10% live at the rural density of 100 per square mile. By giving the core’s density a weight of 90%, we get an adjusted density of 9,100 persons per square mile, a much better description of the density perceived by the average resident.
One key difference between my calculation and his is that I use census block-level data. This calculation becomes more accurate the more granular your data is. Also, I use 2010 Census data.
(Also AC notes in another post that the idea of perceived density has been floating around at least since work by Gary Barnes in 2001. And apparently the Census Bureau has started calculating perceived density too! I guess this post would have been more groundbreaking a few years ago…)
Anyway, without further ado… the data:
|State||Population||Bulk density (km^-2)||Weighted density (km^-2)|
A few things of note:
- New Yorkers are actually pretty urban, as expected. The state’s perceived density of 15,832/km^2 is actually far higher than the bulk density of just the New York City metro area, which Wikipedia quotes as 720/km^2.
- New Jersey loses its top spot but is still relatively urban.
- Alaska, with by far the lowest bulk population density of any state, actually moves to the middle of the pack in perceived density.
- Perceived densities in general fall in a much narrower range than bulk densities.
A Cute Application
One contributing factor to my interest in cities are the books of Jane Jacobs, particularly The Death and Life of Great American Cities and The Economy of Cities. In the latter, Jane Jacobs convincingly argues that cities and the interactions they spawn are the main engines of economic development through history. The idea of interaction and social learning in cities is one important component of agglomeration economies.
I won’t rehash the book here (though you should definitely read it!), but I thought it would be fun to compare the population density of states to their level of economic development, as lazily measured here by GDP/capita. The log-log graph below compares how the two measures of population density correlate to economic development. (Here I include only the 50 US states.)
The trendlines are a simple linear regression on the (logged) data. Weighted density is much more closely correlated with economic strength than the cruder bulk population density. (If I remove the two largest outliers from each dataset — AK and WY for the bulk density, NH and NY for weighted density — the R^2 values increase to 0.21 and 0.47 respectively.)
As always, correlation does not imply causation, but it’s at least consistent with the idea that cities are the main drivers of economic development. It would be pretty easy to do a similar comparison of density and GDP/capita at the scale of metropolitan areas — probably a more direct test. Of course, from the point of view of causality, both are limited by unseen correlations. One could imagine, for example, that the relationship might be weakened by in-migration to economically strong regions resulting in decreasing GDP/capita (ceteris paribus).
A note on data: I grabbed block-level census data by state here, and processed the data in Python. (Edit: as of Dec. ’12, that link seems to be dead; the same data can apparently be accessed here.) I ignored all census blocks with given areas of less than 30,000 square feet (the defined minimum size of a census block according to this Census pdf). A total of 634,800 were disenfranchised by this procedure, corresponding to no more than 0.9% of the population in any state (West Virginia), and typically more like 0.2%.
Some of the weirdest Census blocks turned out to be prisons. This corrections facility in Mississippi claimed to have 2946 “residents” in a census block of 480 square meters, which frankly doesn’t make any sense looking at the map. This prison by itself actually changes the weighted density of MS by a factor of 5! (No other states showed levels of variability anywhere near this.) Another was a housing project in Irvington, NJ, where 1040 people live in 785 square meters. These figures are at least believable but were eliminated due to the non-conforming Census block area for consistency. These examples give some reason to be concerned about other data errors but I think the results above pass the smell test.
The GDP/capita data was grabbed from Wikipedia.