Category Archives: Density

More on population-weighted density

Some time ago I did two posts on population-weighted density, which is the mean of the densities of small areas such as census tracts weighted by their populations. In the first post, About population-weighted density, I described this alternative to traditional, conventional density and discussed some of the issues surrounding the use of this measure. The second post was Population-weighted density and urban sprawl, which argued that both conventional density and population-weighted density were appropriate measures of the extent of urban sprawl, relevant to different consequences associated with sprawl.

Doing these posts got me more interested in population-weighted density and led to my writing a full paper exploring this alternative density measure. In addition to expanding on the topics addressed in those two earlier posts, the paper provides much new information. Two of the highlights are the demonstration of the relationship of population-weighted density to conventional density and the comparison of conventional densities and population-weighted (actually housing-unit-weighted) densities across the 59 large urban areas in my urban patterns research.

In the first post I said that to the extent that people are more heavily concentrated in some tracts with higher densities than in others, those higher density tracts will be given more weight in calculating the population-weighted average. This will cause the population-weighted density to be greater than the simple or conventional density. In the paper, I move beyond this qualitative statement to deriving the mathematical relationship between population-weighted density and conventional density. It is actually quite simple: population-weighted density is equal to conventional density plus the variance in density across the subareas divided by conventional density. To the best of my knowledge, this is the first time this relationship has been demonstrated in this manner.

Looking at conventional and housing-unit-weighted densities for the large urban areas, the distribution of the weighted densities is more highly skewed towards higher values, with New York being an extreme outlier on weighted density. The housing-unit-weighted densities were more strongly related to the size of the urban areas, including size in earlier years, suggesting that the presence of areas of concentrated high densities was established in some urban areas decades ago.

Much more information on can be found in my paper, “On Population-Weighted Density” which can be downloaded here.


Density in Houston without zoning

Houston is well-known for being one of the only cities of any size not to have zoning. So an obvious question is how the urban pattern of Houston might differ from that of other large urban areas. Let’s consider the population density.

The density of the Houston Urbanized Area in 2010 was 2,978 persons per square mile. Dallas-Fort Worth seems to be a reasonable area for comparison. It is another large urban area in Texas, so aside from zoning, one might suspect other factors affecting density might be similar. The density of the Dallas-Fort Worth Urbanized Area in 2010: 2,879 persons per square mile, very close to Houston.

What about other large urban areas? Seattle is about as far away from Houston both in terms of distance and many other characteritics as you can get. The density of the Seattle Urbanized Area in 2010: 3,028 persons per square mile, just a tiny amount larger than Houston. Or how about the Philadelphia and Detroit Urbanized Areas, with densities of 2,746 and 2,793 persons per square mile, slightly below Houston.

If Houston doesn’t differ in terms of density, what about the other measures of the urban pattern that I have been using (see this post? Here are the values for 2010 for the Houston and Dallas-Fort Worth areas as defined for my research (note density is now in housing units per square mile):

Urban area Density Dissimilarity (Variation) Centralization Ratio Moran’s I (Clustering)
Houston 1,066 0.31 0.12 0.41
Dallas-Fort Worth 1,066 0.31 0.17 0.51

Density and variation are identical (and their densities were nearly identical in 1950 as well). Houston is somewhat lower than Dallas-Fort Worth with respect to centralization and clustering. Not sure what to make, if anything, of these small differences. And remember that Dallas-Fort Worth is an area resulting from two separate urban areas growing together, so there’s that difference as well.

My major conclusion is that, despite the absence of zoning, the urban pattern in Houston does not look that different from other large urban areas.

Measuring urban patterns

For my research looking at 59 large urban areas from 1950 to 2010, I developed 4 measures of the urban pattern: housing unit density, the index of dissiilarity for variation in density across census tracts, the centralization ratio, and Moran’s I for clustering. (See this earlier post for more details.) These were used as measures of the urban pattern for each census year.

Over the 60-year period from 1950 to 2010, the mean values of the first 3 measures–density, variation, and centralization–dropped steadily. But as important was what was not revealed by the averages: the urban areas changed in very different ways, with some seeing large gains in the measures while others experienced major losses.

The average values for the measures varied by region of the country. The urban areas in the Northeast mostly had the highest means for both 1950 and 2010, while areas in the South were consistently lowest. But a big shift occurred with the mean densities for the urban areas in the West. In 1950, the average density was just above the South, which was the lowest. But by 2010, the density in the urban areas in the West was the highest among all regions, averaging 40 percent higher than the densities in the Northeast and the Midwest.

I used cluster analysis to develop a typology of the urban areas for 2010 based on their values for these measures, dividing the areas into 6 groups. One group consisted of the very largest urban areas, with the highest densities and the highest mean values on the other three measures as well. These were obviously the most complex urban areas. At the other extreme were the smaller urban areas, mainly in the South, with the lowest densities and among the lowest values for variation, centralization, and clustering.

More information on findings using these urban pattern measures can be found in my paper, “Measures of Urban Patterns in Large Urban Areas in the U.S., 1950–2010” which can be downloaded here.

Developing urban pattern measures

No single measure such as density can capture the complexity of urban patterns, including the distribution of housing units. For my research looking at 59 large urban areas from 1950 to 2010, I wanted to develop multiple measures of urban patterns to better characterize these areas.

Since around the turn of the century a significant amount of work has been undertaken to identify many variables to quantify urban patterns, mostly to assess levels of urban sprawl. I have raised questions about these multiple dimensions of sprawl efforts before on this blog (here and here).  I am not claiming now to be measuring sprawl, but these efforts provided many possible measures to consider. Too many, as some studies included literally dozens of variables with meanings and differences difficult to discern.

My objective was to identify a small set concepts that captured the most important aspects of urban patterns. I then selected a single variable for each concept that I felt was both among the best measures and, to the extent possible, was easy to understand and interpret.

The overall density of housing units in the urban area is the first, obvious measure.

The extent to which densities varied across census tracts came next. This is measured using the index of dissimilarity. This is a measure of the proportion of housing units that would have to be moved to other census tracts to produce a uniform distribution with equal densities in all tracts.

The centralization of housing units in the urban area, the extent to which more housing units were closer to the center, is an important aspect of the urban pattern. For this, I developed a measure I am calling the centralization ratio, which looks at the mean distance housing units are located from the center and is the proportional reduction of distance compared with the mean distance to the center if housing units were uniformly distributed.

Finally, while centralization is one form of clustering, multiple clusters of higher density housing units can exist at various locations in an urban area. This clustering is measured using Moran’s I, a measure of spatial autocorrelation. This is essentially a correlation coefficient between tract densities and the densities of the adjacent tracts.

More information on these measures, their rationale, and an empirical assessment can be found in my paper, “Developing Multiple Measures of Urban Patterns,” which can be downloaded here.

Nearly everything involves tradeoffs

Those who advocate for urban futures typically describe an ideal urban environment that will be superior to current urban areas. I think they are missing two important facts in doing so. One is that people are different and have different preferences. An urban environment that best meets the needs of one person will fail to be ideal for someone else. The second thing that is seldom addressed is that in making choices about the urban environment (and many other things), nearly every choice involves making tradeoffs among competing objectives. I’ll give a few examples of the latter.

The most commonly considered tradeoff, at least among urban economists, is that between accessibility to the center and space that is the foundation of the standard monocentric model. People can reduce transportation costs by choosing a residence closer to the center or they can have more space for the residence by living farther away. But the tradeoff with space involves not only costs of commuting to the center. There is a tradeoff between having a walkable neighborhood with multiple destinations within walking distance and space for the residence as well. This must be the case because higher residential densities can support higher densities of commercial and other activities. In lower-density areas, commercial activities will be more widely spaced to achive sufficient markets.

In the design of street patterns for residential areas, a tradeoff exists between connectivity and restricting through traffic. High street connectivity supports walkability (though there are other ways of achieving this as well) while restricting through traffic with cul du sacs and curving streets may increase safety, especially for smaller children. I discussed this in an earlier blog post.

Another transportation tradeoff involves the use of streets. Space for lanes used for motor vehicle traffic can be converted for dedicated transit use or bicycle lanes. This achieves very laudable objectives. But it also can slow automobile travel and increase congestion. Political conflict associated with making such tradeoffs can be very real. Los Angeles had reduced the number of traffic lanes in one section of the city to increase safety, including by the addition of bike lanes. This produced an outcry among both motorists and businesses in the area, led to lawsuits, and ultimately to a restoration of the traffic lanes.

Limiting the physical expansion of an urban area to reduce sprawl can achieve worthwhile objectives. But given the laws of supply and demand, reducing the supply of developable land may lead to higher housing prices. This might be ameliorated by other regulatory policies, but those too will involve yet more tradeoffs.

60 years of exurban growth

In an earlier post I described the tremendous variation in the sizes of exurban areas surrounding large urban areas in 2010, looking at both their land areas and numbers of housing units. In a subsequent post I looked at variation across census regions and factors associated with this. I have extended the analysis, looking at exurban areas from 1950 to 2010. The variation in size among the exurban areas was very large at every census year. For example, in 1950, the smallest area in terms of land area had only 5 square miles; the largest had near 2,000 square miles. The minimum number of housing units was under 700, the maximum was over 400,000.

The exurban areas exploded in size over this period. The mean land area across the 59 areas grew from 233 square miles in 1950 to over 1,700 square miles in 2010. Mean housing units jumped from just under 40,000 to nearly 240,000. The sizes of the exurban areas were closely related to the sizes of their urban areas throughout the period. But the exurban areas grew more rapidly in size than the urban areas.

I then looked at the sizes of the exurban areas relative to their urban areas, the ratios of exurban to urban land areas and housing units. In 1950, the mean ratios were far higher for exurban areas in the Northeast compared with the other three census regions. But by 2010, the relative sizes of exurban areas in the South had grown rapidly and the mean ratios had virtually caught up with the Northeast. The relative size of exurban areas in the West remained very low. Exurban areas in the Midwest ended up in the middle. As I found for 2010, the relative sizes of exurban areas having arid climates were significantly smaller than for other exurban areas throughout the period.

More information on the the growth and evolution of exurban areas from 1950 to 2010 can be found in my paper, “Exurban Areas Around Large Urban Areas in the U.S., 1950–2010,” which can be downloaded here.

This is not your father’s (or mother’s) suburb

I currently am living in Southern California, about 35 miles east of downtown Los Angeles. I frequently drive further east into the adjoining city of Rancho Cucamonga for shopping or other activities (recently, jury duty!). A normal person would take the freeway or the main east-west commercial artery, the old Route 66. But being interested in urban patterns, I occassionally will drive on other through streets that run mainly through residential areas. I had certainly seen numbers of apartment complexes, but on one of these explorations I was especially struck by the continuous line of apartments. Not exactly stereotypical suburbia.

First, a little background on Rancho Cucamonga. This is a very new city, largely developed since the 1970s. When I lived in Southern California in the mid–1970s, when driving through this area on the freeway, one passed through miles of vineyards. This was the last undeveloped gap between Los Angeles and San Bernardino to be filled in, as you can see on these maps for 1970 and 2010 of census tracts which I classified as urban for my research:

Urban census tracts in the Los Angeles area in 1970 (Rancho Cucamonga outlined in red).

Urban census tracts in the Los Angeles area in 1970 (Rancho Cucamonga outlined in red).

Urban census tracts in the Los Angeles area in 2010 (Rancho Cucamonga outlined in red).

Urban census tracts in the Los Angeles area in 2010 (Rancho Cucamonga outlined in red).

The popuation of the city of Rancho Cucamonga was 55,000 at the 1980 census and 177,000 according to the 2016 census estimate. No earlier populations are reported as the city was only incorporated in 1977!

Suburban residential development is generally associated with large expanses of single-family housing units on medium- to large-size lots. Some suburbs do have some apartments, but the general impression is that single-family housing dominates. In Rancho Cucamonga in 2015, only 62 percent of the housing units are detached single-family houses. So nearly 40 percent of the housing does not fit the suburban stereotype.

The overall population density for the city in 2016 was 4,430 persons per square mile, certainly more than many suburbs. But even this is misleadingly low. The city still has significant amounts of vacant land and has large areas developed with industrial uses, mainly for warehouse and distribution activities. (The broader area has developed as a huge distribution center, handling many of the millions of containers that come through the ports of Los Angeles and Long Beach.)

A better picture of the level of residential densities can be seen by looking at densities in individual census tracts, some of which will naturally be more residential and more completely developed than others. My research (using 2000 tract boundaries) has 9 census tracts within or predominantly within the City of Rancho Cucamonga. For several reasons, I have chosen to focus on housing units and housing unit densities rather than population densities for my research. The two census tracts with the highest housing unit densities in 2010 have densities of 3,330 and 2,835 units per square mile. Since population densities are more commonly used and are thus more familiar, these can be estimated by using the national average of 2.34 persons per housing unit. This gives estimated population densities for these tracts of 7,791 and 6,634 persons per square mile. The denser of the two tracts has a population density far greater than the overall density of the densest Urbanized Area in the U.S., Los Angeles. Both are denser than the New York Urbanized Area.

There is, of course, no standard criterion specifying what are “suburban” densities as opposed to “urban” densities. I believe that for a variety of reasons, no urbanists want to go there, as there would be no consensus. But an interesting article on the FiveThirtyEight website tried to get at this, reporting on work by the real estate website Trulia that surveyed people asking whether where they lived was urban, suburban, or rural. They also asked for ZIP codes and compared the responses to characteristics of the ZIP codes. The study found, perhaps not surprisingly, that the best predictor of how people described where they lived was the population density of the ZIP code. And the dividing line between suburban and urban was 2,213 households per square mile (or by my estimation of population density, 5,178 persons per square mile). Using that criterion, the two densest tracts in Rancho Cucamonga could easily be considered urban as opposed to suburban, and two more, with over 1,900 units per square mile, come close. (I need to acknowledge that their use of ZIP codes could have produced a lower value than if tracts could have been used.)

The bottom line is that this very recent development in Rancho Cucamonga does not look like the traditional idea of suburbia with single-family homes on spacious lots.