Civic Data

Data-oriented thinking about where and how people live.

A better measure of population density

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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.

Perceived Density

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)
NY 19333990 158.4394 15832.51
DC 598414 3803.751 12293.26
HI 1357202 81.60069 6496.256
NJ 8761115 460.3652 5696.584
CA 37145156 92.08261 5589.403
IL 12770832 88.8414 5246.746
MA 6511291 322.7141 4862.258
PR 3992495 444.2985 4537.001
MD 5723643 227.958 4348.399
NV 2694919 9.478293 4255.984
PA 12593779 108.7237 4064.107
US 311725647 34.04841 4024.23
RI 1049107 392.2036 3744.092
TX 25091380 37.09027 3547.602
FL 18743938 135.0074 3329.256
AZ 6376488 21.6755 3298.759
VA 7966975 77.92358 3193.079
CO 5014644 18.68286 3139.779
UT 2760099 12.96994 2893.576
DE 894473 177.3389 2850.064
OR 3821187 15.3714 2845.809
WA 6715366 39.01915 2756.483
CT 3566140 284.4779 2734.935
NE 1818198 9.139048 2362.161
MN 5296048 25.68276 2167.028
WI 5678651 40.49017 2150.686
AK 707240 0.4785273 2075.556
MO 5964397 33.51027 2040.069
NM 2052068 6.532275 2023.881
ND 669100 3.744373 2021.625
OK 3738981 21.05004 2005.878
OH 11484261 108.5711 1995.748
MI 9870560 67.41639 1943.653
LA 4520762 40.41043 1937.115
IN 6447987 69.51789 1898.736
KS 2844137 13.43315 1851.804
ID 1560881 7.292989 1848.406
WY 561035 2.231099 1827.739
IA 3036518 20.99263 1743.859
GA 9669315 64.9225 1682.254
SD 812894 4.140146 1545.785
NH 1312525 56.62046 1458.979
KY 4329388 42.33941 1447.203
TN 6335140 59.33278 1417.803
MT 986152 2.616117 1393.657
WV 1835075 29.48652 1365.568
AR 2911252 21.60401 1237.106
AL 4762649 36.31816 1234.689
SC 4611393 59.24358 1226.788
NC 9522341 75.63584 1215.909
MS 2955790 24.32566 1191.263
VT 624276 26.15562 1086.771
ME 1324000 16.57576 1061.588

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.

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