In our first presentation on the housing situation in Charlottesville, posted almost a year ago now, we noted that FLUM proponents cited the figure that Charlottesville has 71% of its residential land area under R-1 zoning. While we were grateful to see an actual number in the pro-FLUM argument, we wondered what one ought to make of a number presented without any context or comparison. 71% sounds high, but then so does “98.6F body temperature” if you don’t have any other point of reference (it also assumes that the zoning code is enforced inflexibly, which have shown elsewhere to be untrue). At the time, we encountered difficulty finding statistics on the R-1 fraction of cities in America. We did turn up a relevant mapping study performed by a pair of New York Times journalists and a few news stories, and from this constructed a table of R-1 fractions of some other cities. The point was to add some context to the Charlottesville number. We were genuinely curious if 71% was high or low. We reproduce the slide below. The purpose of the slide was to illustrate our high-level finding that R-1 fraction did not tell very much about how dense or urban a jurisdiction could become. We saw several cities that most people would consider more “urban” in form than Cville with higher R-1 fractions (NB: this was a year ago, and since then some of these cities have seen changes to their R-1 schemes due either to local or state legislation, though none as dramatic as what Charlottesville plans for General Residential, to say nothing of Medium-Intensity Residential).

Recently, a reader remonstrated that these comparisons were inappropriate, because the cities cited are physically larger than Cville. While we have elsewhere pointed out the importance of considering “small city” spatial geography effects, the objection did not strike us as particularly salient. These cities are physically larger, but also have much larger populations. But unlike many FLUM supporters, we use numbers in an analytical rather than purely rhetorical way; we subscribe to the Popperian view that knowledge progresses via attempts at falsification. Rather than, like FLUM proponents, throw a tantrum or accuse our interlocutor of bad faith, we tried to take this objection and see if we could make it stick. The gravamen of the objection, as we understand it, is that some of these larger cities may include a suburban “hinterland” that is low-density, and that this explains the high R-1 fraction. We therefore settled on the following analysis. We would look at each city as a collection of its constituent census tracts. If there were truly a low-density hinterland in these larger cities, missing from Charlottesville, we should see a large “left tail” of low-density census tracts in the larger cities, each with lower density than Charlottesville. Below, you can see a density function and empirical cumulative density function of census tracts for Charlottesville and the other cities in the sample. You will see that in fact: 1) there is no such left-tail and 2) with the exception of Charlotte, all the comparison cities have higher densities than Charlottesville across the distribution of census tracts. We thank our interlocutor for pushing us to rule out a potential spatial-geography distortion.

No “left-tail” of hinterland, all but Charlotte clearly more dense than Cville across distribution
No left-tail problem, modes almost all to the right of Cville’s

But while we were doing this analysis, we wondered whether it would actually be that difficult to calculate R-1 fractions for small-to-midsize college towns ourselves. After all, a year of doing the analytical work that a competent CP consultant should have has left us with a much-enhanced capability to gather, collate, and process data. As it turns out, we can do this for many cities. As we said, it is not a statistic we have seen collected elsewhere, so we figured that at the very least, we could add to the available data on the topic of zoning. We started with a limited set of college towns of small to medium size. Most have a population density within the same range as Charlottesville. For each one, we were able to get mapping data on zoning districts. We examined the local zoning code to find districts that are functionally R-1 (allow single-family housing only). For the denominator we used all districts where there was a by-right residential use, whether the district was designated primarily residential or not. This meant we were erring on the side of showing a low R-1 fraction. We find that within this sample of cities, Charlottesville’s R-1 fraction is unremarkable. Some are more heavily R-1, a few are less. But, we found something else interesting. When we went back to the Charlottesville zoning map and applied the same criteria that we used elsewhere (just to check the number we have seen quoted many times), we found that 71% is not an accurate number for apples-to-apples comparison. It excludes from the denominator several districts, including mixed-use districts, where there are several by-right residential uses. To take a real-world example, the Highway (HW) district is not principally residential, but Great Eastern just announced a 350-unit apartment building by-right on an HW-zoned property. When we used as the denominator all zoning districts with a by-right residential use included in the use matrix, we found that Charlottesville’s R-1 fraction on this basis is actually 57%. In the charts below, we show Charlottesville on both bases, but we re-iterate that 57% is the “apples-to-apples” number. And even this is an exaggeration, because NDS has coded in the city database several parks (Greenbrier, Azalea, and Pen Park, e.g) as R-1, and if we remove these from both numerator and denominator the fraction falls to 53%! Nearly every other city that we looked at had a special category for parks and open space, which we excluded.

Among college-towns, Cville again unremarkable

Aside from the observation that Charlottesville’s R-1 fraction (even the exaggerated 71% number) is not remarkably high, we also found that there is little apparent explanatory power to the R-1 fraction as regards housing cost outcomes. That ought not be too surprising. 71% R-1 could imply 71% of a city with SFH zoning at 1-acre minimum lot-size; or 71% of a city with SFH zoning at 4000 square-foot minimum lot size (in line with Cville’s R-1S districts). The remaining 29% could be relatively large-lot R-2 or allow for 10 story apartment buildings. So even if one takes the view (which we believe our earlier research rebuts) that zoning is the mostimportant determinant of housing outcomes, R-1 fraction by itself would not have much predictive power. Nor does it predict much about housing form outcomes. The percentage of housing units that take the form of detached single-family homes (what R-1 prescribes) in fact varies a lot less that the percentage of land zoned R-1 and is not closely predicted by it. It doesn’t take much land dedicated to higher-density housing or mixed-use to generate a lot of multifamily housing. Serious constraint on housing form and sharp effects on housing cost outcomes may only manifest at very high R-1 fractions, far higher than we see in our sample and far higher than Charlottesville’s level. And even some extremely high-R-1-fraction jurisdictions have SFH percentages not far above Charlottesville — in our original sample, San Jose was pegged in news articles as having >90% of residential land under R-1; yet the percentage of housing units that are SFH is only 52%.

First, housing and land cost. The table below shows that Charlottesville has had quite low housing price growth over the past 10 years, and is nowhere near the top in terms of current average price, either of housing or land (data from Zillow and AEI’s land cost database, respectively). Between house and land price level and rates of change, Boulder and Bozeman appear to be the roughest markets, but they also have the lowestR-1 fraction. The scatterplots below plot the data from the table in graph form (Cville highlighted in yellow and red).

AEI Land Price is for “Normalized 1/4 acre lot”, CBSA level for all except Blacksburg, Wellesley and Evanston, which are based on zip codes.

On to housing form. The table below shows that R-1 fraction has much more variance than SFH percentage. Clearly, variables beyond R-1 zoning fraction have more power to determine housing form. Burlington, Gainesville and Evanston have the lowest percentage of SFH housing, but span the distribution of the R-1 fraction. Gainesville and Tallahassee, in the same state, have R-1 fractions at opposite ends of the distribution but almost identical SFH percentages. Knoxville, with over 80% of residential land zoned R-1 still has almost half of its housing in non-SFH-detached form. Bozeman, with half the R-1 fraction of Cville, has only a few percentage points lower SFH percentage. The scatterplot below the table shows the absence of a significant relationship in this sample. Only at very extreme R-1 fractions do we see some evidence of higher associated SFH percentage.

You might be able to guess what variable does predict the median home price in this sample. It is the very same variable that predicted home prices in our larger study of several thousand jurisdictions, and the variable that every study shows is the most powerful driver of home prices: median income. In fact, in this sample, median income predicts 86% of the variance in median home prices. No zoning or form variable has any correlation of signifiance when added to the simple median income vs median home price equation. If you want some “scarefacts” that are also real and relevant, check out Charlottesville’s income inequality statistics. The ratio of the 80%ile of households by income to the 20%ile is 6.5 in Charlottesville, as compared to 4.75 for Virginia!

R2 =0.86. Cville is the red dot.

For the cities that provided geographic data allowing mapping to Census tracts, we calculated R-1 fractions by constituent Census tract. We observed that beyond differences in R-1 fraction at the city level, there were also large difference is the dispersion of R-1 fraction by tract. That is, some cities had most of their census tracts’ R-1 fractions clustered right around the city’s overall R-1 fraction. Others had census tracts that spanned the gamut from near zero percent R-1 to nearly 100%. High dispersion would suggest some degree of “use segregation” — that is, areas that are highly R-1 and highly SFH, with other parts of the city with almost no R-1 and highly tilted toward MFH. Such a pattern would be consistent with (though not dispositive of) the use of R-1 zoning to segregate apartment-dwellers from SFH-dwellers. The funny thing is that the city that stands out for having an extremely low degree of dispersion is… Charlottesville. The Census tract at the 25th %ile of R-1 fraction has 56% of residential land under R-1, while the tract at the 75th %ile has 65% under R-1 (using the “corrected” R-1 numbers). R-1 and MFH zones appear more consistently mixed in spatial terms in Charlottesville than almost any other city in our sample.

Another way to look at this phenomenon is to see that some cities have a high percentage of residential land sitting in Census tracts that have extremely high or extremely low R-1 fractions. Charlottesville has very little land so situated.

The same pattern is visible when considering the percentage of residential land sitting in Census tracts with an extreme share (under 25% or over 75%) of residential units in the form of single-family-detached homes. The FLUM just-so story might well be applied to some cities, but not Charlottesville.

To sum up, we maintain the view that a cogent analysis of our city’s housing situation, something we consider as indispensable to good policy-making as it is absent from RHI’s work, requires numbers properly described and contextualized rather than cited contextlessly as rhetorically-motivated “scarefacts”. We have amply shown that the oft-cited “scarefact” of a 71% R-1 fraction in Charlottesville is basically meaningless: a statistic with low correlation to outcomes of interest, and arguably calculated wrong to boot. We believe it is also an interesting and pertinent phenomenon that many cities of a more urban character than Cville have higher R-1 fractions; likewise that some cities with lower R-1 fractions have sharply more expensive housing markets. Context is important. Numbers properly contextualized contribute to knowledge. Numbers taken out of context are a mere rhetorical gambit.