I've hit on this in the comments to other posts, but one of the nice features of weighted density is that it permits us to compare apples to apples (even though the comparison may be royal gala to red delicious). Standard density is extremely sensitive to geographic boundaries. This is why most debates over density quickly turn into squabbles over the proper geographic unit. CMSA? MSA? Urbanized area? Central city? And then it's just a matter of time before someone brings up City X's moutains or parks or other uninhabitable land that drag down its density.
Because weighted density is determined by the density at which most people live, adding or subtracting land at the margin -- even a lot of land -- does not matter much unless the land contains a large chunk of the population. Weighted density does not depend on precisely how the geographic area is defined.
Example: In 2000, Houston's urbanized area had a population of 3,822,000 and a standard density of 2,951/square mile. Houston's Primary Metropolitan Statistical Area* had nearly four times the land area but only about 355,000 (10%) more people. (The PMSA has a lot of cows.) As a result, Houston's PMSA had a measley 706 persons per square mile, just a little over one person/acre.
The PMSA's weighted density, however, was a more respectable 4,296. That's only 5% off the urbanized area's weighted density of 4,514. Adding a bunch of cow pastures does not change the fact that the vast majority of the PMSA population was bunched at a much higher density.
The same holds for Portland. In 2000, its PMSA had a standard density of just 381/square mile. But the PMSA's weighted density was 3,943/square mile, down just 10% or so from the urbanized area's weighted density of 4,383.
Note that a lot of the vacant land around Houston is vacant simply because no one has gotten around to developing it yet. A lot of the land around Portland is vacant because of policies designed to preserve open space and slow sprawl. This difference is often a flash point for disagreements over geographic boundaries. Weighted density allows us to sidestep these arguments by focusing on the density at which the average person lives.
*A PMSA consists of one or more counties within an MSA that have substantial commuting interchange.
I recently calculated the weighted densities for a number of cities using the Census Bureau's "central place/non-central place" classification. As I explained in that post and the comments, this is actually a coarse measure of weighted density because central places themselves are usually large cities with pockets of wildly varying density.
I took the 32 largest U.S. urbanized areas and added Austin and Honolulu for good measure. I pulled the Census data on each census tract partially or completely contained within each of these urbanized areas. I calculated the standard density (i.e., total population/total land area) for each census tract. I also calculated each census tract's share of the total population of the urbanized area. I then assigned each tract's density a "weight" equal to its share of the total population. I summed the weights to get the weighted density for the urbanized area.
I'm preparing a permanent page with more information on the methodology and limits of this approach. (It's a very good method, though, in my opinion.)
But that technical stuff can wait a few days. Here are the weighted densities, ranked from most dense to least dense:
This approach obviously does a much better job of reflecting our perceptions of a city's density. LA's urbanized area is denser than NY's when using the standard density metric; NY's urbanized area is almost three times denser using weighted density. (LA is still quite dense, though.)
Weighted densities straighten out a lot of other counterintuitive "facts." Austin and Tampa are not really denser than Boston (as the standard density figures suggest), and the sprawling suburbs of Riverside County are not actually denser than Chicago.
Note that Portland's urbanized area is less dense than Houston's. The urbanized area most like Portland's, viewed strictly by their density profiles, is Riverside-San Bernardino.
New York is an outlier at the upper end, while Atlanta is an outlier at the lower end.
The "density gradient index" is a term I made up to dignify what is a pretty simple calculation: weighted density divided by standard density. The index would be an even 1 if a city's population were uniformly distributed across the landscape. The larger the index, the more uneven the distribution. I'll go into this in more detail on the permanent page, but you can get a rough idea of a city's urban form just by looking at the weighted density, standard density and density gradient index.
(There really is something called the "density gradient," but it is a curve rather than a number, and there is no "index" for it, as far as I know.)
Glaser and Kahn even allow us to make an apples-to-apples comparison because they have constructed a composite "median" household for each city to use as their points of reference. For example, they don't use per capita gasoline consumption as their point of comparison. They instead estimate the expected gasoline consumption of a hypothetical $62,000/year household with 2.62 members for each city, using survey data and (I assume) some fancy statistical techniques.
They report pounds of carbon emitted rather than gallons of gasoline consumed, but since they tell us how much carbon they assume one gallon emits (23.47 pounds), we can easily convert their data into gallons.
Here is the relevant table from their paper:
Here is a chart I compiled from their data depicting relative gasoline consumption:
The thing that struck me when I looked at the numbers was the relatively small difference in gasoline consumption between Houston and most other cities. (Third column.) Glaser and Kahn's hypothetical $62,000/year household uses only 55 more gallons per year in Houston than in D.C. It uses only 135 gallons more gallons per year than the corresponding San Francisco household. The Houston-Chicago gap is only 118 gallons per year.
The gap between Houston and old-line northeastern cities (particularly New York) is larger, but is largely offset by their greater consumption of heating oil. (Remember Hugo Chavez offering free heating oil to Boston's poor?)
This chart makes the point better:
There is no question that steep gas price hikes would hurt Houston (or Dallas or Austin) households. At $3/gallon, the Houston household is already spending 5.4% of its gross income on gasoline. At $4/gallon, it would have to spend 7.2% of gross income on gasoline, assuming no change in gasoline consumption. But the San Francisco household is spending 4.8% of its gross income on gasoline, a figure that would rise to 6.4% with a $1 increase in the price of gasoline. That 0.8% difference is smaller than I expected.
Glaser and Kahn also compare city and suburban gasoline use:
I summarize the corresponding gasoline consumption numbers in columns 5 and 6 of my chart, and compare suburban Houston households with central city residents elsewhere in column 7. No surprise that the gap grows significantly. But it is possible that, given their much higher housing costs, central city residents may be even more susceptible to price variations in commodities like gasoline. Those suburban Houston households pay a lot less per square foot of housing than similarly situated households in LA, San Francisco or DC.
These simple charts don't tell the whole story, of course. Gasoline consumption is not completely inelastic, especially over the long run. One could argue that because residents of central cities have access to better mass transit, it is easier for them to substitute away from gasoline use, making their demand for gasoline more elastic than suburb dwellers. Put simply, city dwellers can cut down on their driving more easily than suburbanites.
That's certainly plausible. However, city dweller's access to better transit is already reflected in their lower gasoline consumption. They've already picked the low-hanging fruit, so to speak. The barrier to additional transit use is often not the difference in monetary cost, but the difference in time and convenience costs.
Of course, there is some price at which drivers will begin to substitute to mass transit wholesale. But the suburban drivers have options, too. A Houston suburbanite who switched to riding the bus or carpooling would save (on average) more gasoline per commute than a central city resident. Likewise, a Houston suburbanite who combined two errands would save (on average) more gasoline per errand.
This is ultimately an empirical question. Like everyone else, I think gas prices are headed up, at least over the next few years. It will be interesting to see the relative adjustments made by Houston drivers and those in the more compact northeastern and western cities.
Relative elasticities aside, the numbers are still interesting, especially the aggregate metropolitan area data. I never would have guessed that a "typical" metropolitan Houston household uses only 5 more gallons per month than its metropolitan D.C. counterpart.
One final point. There is one area where western and northeastern cities wipe the floor with us, the denizens of the hellishly hot places: Electricity. We use fiendish amounts of the stuff. (There's archaeological evidence that Austin was inhabited before the invention of air conditioning, but some scholars dispute its conclusiveness.) If electricity prices shoot up like gas prices, we will suffer a lot more than our friends out west and up north, and there'll be nothing we can do about it.
City Council continues to show that it is serious about opening the core transit corridors to Vertical Mixed Use development by standing up to neighborhoods trying to wriggle out of the VMU bargain.
A couple of recent actions by Council are especially reassuring:
The neighborhoods in the East MLK Combined Planning Area asked to opt out all of their eligible tracts, most of which lie along Manor Road east of Airport Boulevard. They offered the typical pretexts (pp. 8-9) -- e.g., lack of infrastructure (although citing chronically stopped up toilets was probably a first), increased impervious cover, inadequate planning and coordination -- while still managing to invoke New Urbanist guru Andres Duany as cover for their unambiguously anti-Urbanist stand.
Props to Council. At its February 28 meeting, it voted 7-0 to retain VMU zoning on all of the tracts, and approved parking reductions and additional ground floor uses to boot. (This was 1st reading only; 2nd and 3rd readings are on the March 20 agenda.)
Bryker Woods was not nearly as intransigent as the East MLK neighborhoods. It agreed to leave most of its tracts in the VMU district, but asked to exclude seven tracts (mainly over worries about parking, from what I saw of the Planning Commission hearing.) Council voted (6-0) to zone five of the seven tracts VMU anyway, and deferred the other two to its March 20 meeting.
Council has decided that it is not a rubber stamp.
Not every neighborhood is an East MLK. Some neighborhoods have embraced VMU unreservedly. Not only did North Loop not ask to exclude any of its VMU-eligible properties, it asked to opt in several other tracts. Some neighborhoods, at least, recognize that VMU developments will enhance their neighborhoods even as they provide additional room for multi-family development.
Every once in a while -- invariably in a debate over sprawl -- someone will toss out the "fact" that the Los Angeles metropolitan area is denser than the New York metropolitan area.
It's true. At least, it's true if one uses the standard definition of density as gross population divided by gross land area. According to 2000 U.S. census data, the Los Angeles "urbanized area" has a density of 7,068 persons per square mile. The New York urbanized area has 5,309 persons per square mile. Ergo, Los Angeles is denser than New York.
But common sense tells us that this coarse statistic is misleading. Ryan Avent puts it well:
Los Angeles is hemmed in by its geography, so it can’t just keep spreading at ever lower densities out into the wilderness. As such, its density profile is like a plateau–not all that tall at anyone point, but with a respectable average height, because the long tails are excised. New York, by contrast, is like a mountain. It has an enormous peak containing most of the mass, but the flattening sides of the mountain continue on for miles.
In other words, the fact that the last million or so people in the New York metro area occupy an incredibly large area while the last million or so Angelenos are in moderate density suburbs packed against the very edge of the basin, skews the relative density figures, making them pretty uninformative.
A more meaningful metric is "weighted" density or "average perceived density." Carve the metropolitan area into distinct regions (census tracts, for example), compute the density of each, and then assign each a weight based on its percentage of the total population. This discounts large, sparsely populated census tracts, and gives extra weight to densely populated tracts.
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.
I show the weighted densities for some U.S. cities below the jump.
Economists Ed Glaeser and Matthew Kahn have written a new paper estimating the differences in carbon emissions across different metropolitan areas.
Using a hypothetial household with 2.62 members and $62,000 in average yearly earnings, they attempt to calculate how much carbon dioxide this household would emit in a given metropolitan area. They estimate household emissions from driving, public transportation, home heating and electricity (which includes air conditioning), and they factor in the relative cleanness of the region's electricity supply.
Their findings are not all that surpising:
"Per capita emissions generally are lowest in Western metropolitan areas and highest in Southern ones. Metropolitan areas in the Northeast and Midwest fall in between these two extremes."
"All told, if the social cost of one ton of carbon dioxide emissions is $43, then the annual environmental damage associated with an additional home in greater Houston is more than $500 greater than the damage for a new home in greater San Francisco."
Car-dependence obviously plays a large role, but often not as large as electricity consumption: The typical Houston MA household emits 3,000 more pounds of CO2 per year from driving than does the typical San Francisco household. But the typical Houston household emits 23,000 more pounds per year than the SF household due to extra electricity use. As we all know, air conditioning is expensive.
Their tentative conclusion is that perhaps we should make it easier for households to move from Texas to California, rather than vice versa:
This work is far too preliminary to be a sound basis for particular policies. However, it does emphasize the contradictions of current American land-use policies. Local land-use restrictions cannot stop development in the nation as a whole. They simply have the ability to move development from one area to another. Our current land-use restrictions tend to stop development in those areas, like California, that are environmentally friendly and to encourage it in areas, like Texas, where households produce more carbon dioxide. Within metropolitan areas, land use restrictions often push development out towards the urban fringe where energy use is highest. Our results do suggest that it makes sense to look for policies that would encourage building in more enviornmentally friendly cities and discourage it in areas that have the greatest carbon dioxide emissions.