Friday, November 16, 2012

Exploring Weighted Density

Chris Bradford has recently run an excellent series of posts featuring the Census Bureau's newly-released data covering population-weighted density.  Chris has been an advocate of this density measure (also referred to as "perceived" density) for much longer, though, and has promoted it as a more useful alternative to both standard density and the somewhat more helpful urbanized area density.

At The Atlantic Cities, Richard Florida picked up on the story, noting its significance of these new figures in exploring the relationship between density and productivity.  The topic has been addressed at least once before: a 2010 report from the Federal Reserve Bank of New York, updated last year, used weighted population density to find that:
  • In general, productivity increases by 2 to 4 percent as weighted density doubles.
  • Productivity increases are correlated with human capital (e.g. skills and education), such that cities with a human capital one standard deviation below the mean have no productivity gains from increased density, while those with high human capital have twice the average gain.
  • The benefits of density are especially pronounced for certain industries, including professional services, arts, entertainment, information and finance.
Along the same lines, I've drawn up a correlation chart showing the population-weighted density for all metropolitan statistical areas as compared to several other factors, including total metro area population, population change during 2000-2010 both in net and as a percentage, urbanized area density, median home values, median personal income (a stand-in for productivity in many studies), and finally income-to-home value ratio (an indicator of relative housing affordability).  Each factor has been compared against every other (raw data is available here).

A few of the things that jumped out at me from the chart:
  • Income is more strongly correlated with weighted density than total population, although not dramatically so. However, median home values were even more strongly correlated with weighted density.  The result is that, for cities of equivalent size, the city with the higher weighted density will generally be less affordable in relative terms, even if incomes are higher (for instance, Sacramento is almost twice as dense as similarly-sized and lower-income Kansas City, but is only two-thirds as affordable).
  • Although high weighted-density metros have generally higher incomes than low-density cities, they grew more slowly than these cities, perhaps indicating the push and pull forces of housing affordability.
  • Nonetheless, relative housing value was negatively correlated with population growth, although not strongly.  This suggests a tension between low housing values being a product of low demand, and the attraction of low housing costs in otherwise prosperous cities that have presumably kept prices low through adequate supply.  Looking at only large cities bears this out (see below).
Here is the same chart showing only MSAs with more than one million inhabitants as of the 2010 Census:

The sign for affordability relative to population gain has flipped, and more affordable markets are here associated with higher population growth. 

Another factor I would have liked to include, had it been available for all MSAs, would have been median transportation cost, since to some extent that would offset the poor affordability of certain high-density cities.

I am skeptical, though, that these figures would make much difference for most cities.  Although recent studies have pointed to the transit savings of living in high density areas well-served by mass transit, most American metro areas remain overwhelmingly car dependent. Moreover, while high housing costs cannot be easily avoided, households have more direct control over transportation spending even in low-density cities. 

Beyond these points, I'll leave the numbers out there to speak for themselves.


  1. Very nice work. You've compressed a bunch of information into two small charts. There's a lot here to mull over.

    The correlation between weighted density and housing affordability is particularly interesting. Two points. First, the fact that residents tend to accept lower real incomes to live in denser places undercuts the common view that rising density is associated with net negative externalities. If this were the case, then residents would demand higher real incomes to offset the rising density.

    Second, the correlation between weighted density and affordability among all MSAs drops pretty significantly (to -.250) when California MSAs are excluded, which could be some evidence that California's particularly stringent land-use controls have real bite.

    1. Thanks Chris. That's a good point about the California numbers -- there are definitely regional trends visible here as to density, income, affordability, etc. California does have some unique impediments to development, but on the other hand it has a unique appeal as well, so it's difficult to tell what portion of the prices is due to supply shortfalls alone. The "Inland Empire" cities are also quite dense, but do not have the same out-of-control affordability issues (e.g. Fresno, Bakersfield and Stockton).

      Great point about weighted density and affordability, also. I can say with a lot of confidence that people will put up with a lot (and some almost anything) to live in NYC.

  2. The relationship between weighted density and affordability is counterintuitive, and I think Chris makes an important observation. In California it's much easier to obtain development approvals for sprawl housing in unincorporated areas and new cities where there are fewer NIMBYs than in denser NIMBY-filled older cities. Hence density represents constraints on supply rather than additional supply. While California is well known for this type of institutionalized NIMBYism, I suspect it plays out in other parts of the country as well, further skewing density's impact on affordability.

  3. The weighted density data are wonderful. Thank you for highlighting this Charlie. They really describe the character of metro areas better than straight density calculations. NY and LA metros may have similar densities, but NYC certainly "feels" more dense that LA as reflected in the weighted density data.

    BTW, I'm not sold on density (however calculated) facilitating productivity. I fear the causation/correlation conundrum. One can read all over the internet how density creates/facilitates productivity. I think it much more likely that productive people choose the "it" place to live (presently dense areas) rather than the density spurring the productivity out of those that live there.

    Weirdoes and unreasonable people innovate. Normal, reasonable people conform. Currently the former live in cities and the later live in CC&R-controlled suburbs, but I don't see that there is anything inherent in this layout. If a trendy, tolerant set takes up in less dense environs, more of the same type will follow (see e.g., Silicon Valley).

    I'm all for dense, walkable cities, but we should be careful not to overstate their benefits. It's easy to fall into the trap of applying the tools at hand to whatever problem confronts us. For planner/architect types it may seem natural to hope increased density or better design can improve productivity. I put much more faith in better education, more tolerance and the rule of law.

    1. You could be right. In Canada, the correlation seems pretty weak, although the data set is also smaller. Among the "big 5" Canadian cities, Calgary is the wealthiest by a good margin, even though it's the least dense (along with Ottawa). It's prosperity is mostly related to Alberta's prosperity as a whole.

      Even putting built form aside though, Canada's big 5 are all quite unique. Montreal is the major francophone city by a huge marging, and Toronto is the major anglophone city by a huge margin. Vancouver is the place to be if you don't like cold winters and the outdoors, which means it's overpriced relative to its economy, and Calgary is the main city benefitting from the oil sands (to a lesser degree, Edmonton is too, but their built form and size are very similar), and finally Ottawa is the national capital.

      If you look at the GDP/capita of these cities relative to those of their province, the denser cities do better, with the exception of Ottawa (which makes sense). I'm not sure how much of that can be explained by people choosing the denser cities though.

  4. Charlie, what was the source of data for median home value and median income? ACS? If so, which one?


    1. Yes, sorry for not including that -- it was the 2011 1-year ACS estimates.

  5. This might be of interest to you all as well.
    "Inter-firm job switching of workers is a much cited but seldom measured source of the productivity advantages of spatial employment density."

    I think we look at residential density a lot, but there are a lot of downtowns that don't have many people living there. It's been growing a lot lately but still really low in a lot of cities. I think intensity would be something even better to measure (workers+residents) because it shows how close people work in a place as well as how close they live. Not sure what it would say but would be interesting to note.