Some furter zoning analyses for Madison

A follow-up post on zoning and density in Madison and how it compares to other cities in the US.

I got some good feedback after posting my article on Madison’s zoning restrictions on Facebook and Reddit, prompting some additional analyses.

Why do you look only at residentially zoned land?

Several people pointed out that comparing the zoning districts that only allow detached single-family homes (SFR) to all residential zoning districts may be misleading. In many cities the densest parts are not in residential zoning districts but in downtown areas zoned for mixed use. I think that’s a fair point, but it was the original NYT article that chose only residential areas as the comparator, and I wanted to make Madison comparable to the other cities in the NYT analysis.

Nonetheless, I quickly ran the analysis comparing SFR to any district except “special districts.” These includes parks, conservancies, agricultural land, airports, or the UW-Campus—in other words districts that are highly unlikely to ever have residential use.

#detached single-family only
res_sfr <- data %>%
  filter(ZONING_CODE %in% sfr_zones) %>%
  summarize(sum(ShapeSTArea))
# only special district area
other_area <- data %>%
  filter(ZONING_CODE %in% other) %>%
  summarise(sum(ShapeSTArea))
total <- data %>% summarize(sum(ShapeSTArea))
res_sfr/(total-other_area)

  sum(ShapeSTArea)
1        0.4873358

The result? 49% of all land that reasonably could have residential units on it allows only single-family attached housing. Since there is no point of comparison to other cities, it’s hard to interpret that number.

Is there a correlation between the percentage of SFR zoning and overall density?

It’s a good question: Does the metric the NYT used actually have an association with overall density of a city? (Note that even if there is a correlation, this absolutely doesn’t mean there is a causal connection! There are many, many factors that impact a city’s overall density.)

There are few data points to work with. I retrieved density information for all cities in the NYT article and Madison from Wikipedia:

City	Density (pop./sq.mi.)	Single-family (%)
New York	27751	15
Washington	11367	36
Seattle	8642	81
Los Angeles	8483	75
Minneapolis	7821	70
San Jose (CA)	5776	94
Portland (OR)	4504	77
Arlington (TX)	3810	89
Madison	3233	75
Sandy Springs (GA)	2707	85
Charlotte (NC)	2400	84

Let’s see what the overall correlation is:

# A tibble: 1 x 1
  `cor(density, sfr)`
                <dbl>
1              -0.885

Hm, -0.89. That’s a very, very high correlation. But it’s always good to look at your data points in a scatterplot to see what’s actually going on:

Okay, New York is clearly way out there. Let’s exclude NYC and do the correlation again:

 dens_zon %>% 
   spread(Measure, Value) %>%
   filter(City != "New York") %>%
   summarize(cor(density, sfr))

# A tibble: 1 x 1
  `cor(density, sfr)`
                <dbl>
1              -0.693

That gets us a correlation of -0.69. Much lower, but still pretty high. Is DC also an outlier?

 dens_zon %>% 
   spread(Measure, Value) %>%
   filter(City != "New York" & City != "Washington") %>%
   summarize(cor(density, sfr))

# A tibble: 1 x 1
  `cor(density, sfr)`
                <dbl>
1              -0.366

This lower the correlation to -0.37. That is, there is a small negative association between how dense a city is and how much of its residential land is zoned exclusively for detached single-family homes. But more data is needed to confirm this.