The Bay Area is in the midst of a housing affordability crisis, a problem that both squeezes Bay Area households and has been implicated in depressing economic growth and increasing inequality on a national scale. Studies that have looked into the causes of this crisis have generally concluded that a housing shortage is the primary culprit. In short, the housing stock has not grown fast enough to meet demand. This view is not completely uncontroversial; there are those who oppose substantially increasing the amount of housing in the area. And even among proponents of new housing, there are significant disagreements about the proportion of new housing that should be market rate.

But if we accept that increasing the housing stock in the Bay Area is necessary to resolve the housing crisis, we face the question of where new housing should be added. Focusing on San Francisco in particular, we can get a start at answering this question by taking a look at population density. The map below shows population density in each census district in San Francisco, based upon 2014 5-year estimates from the American Community Survey.

What can population density tell us about where new housing should be added? On the one hand, we might think that high density areas have little room to absorb new residents, meaning that lower density areas should see the most new housing. On the other hand, presumably the denser areas of the city are denser for a reason, such as their proximity to transit, which would make them more desirable areas for new housing.

Unfortunately, population density alone can't tell us much about where it would make sense to add housing. What we need is some measure of how many people "ought" to live in a particular location, which we can then compare to the actual population in that location. One such measure is land value, on the assumption that it makes sense for more people to live in more desirable (and hence more valuable) areas. Land value won't be a perfect measure for our purposes -- land value is only an indirect proxy for factors that we want to consider when adding new housing, such as the ability of infrastructure to support new residents. And highly valuable land can and should be put to uses other than housing.

Despite these shortcomings, land value can still give us a rough indication of how much housing an area ought to contain. In particular, we'll consider the ratio of land value to population (the "LVP ratio"). A location's LVP ratio will be high if it has high land values or low population density (or both). We can think of these as the areas where land is currently being used inefficiently. Alternatively, this is where a disproportionately large amount of land value is being "spent" to house each resident. In contrast, a low LVP ratio indicates an area with either low land values or high population density (or, again, both). Areas with low LVP values are those where land is used most efficiently for housing, i.e. where the least is "spent" for housing each resident. The map below uses land values reported in historical property tax data to tell us the LVP ratio for each census district in San Francisco.

By this metric, which neighborhoods are making the most efficient use of land? Somewhat unsurprisingly, the Tenderloin, Nob Hill, and Chinatown, all among the most densely populated neighborhoods in San Francisco fare well. The Mission, which has been a major flashpoint in recent fights over new housing and gentrification, also has a relatively low LVP ratio. In particular, land is used more efficiently in the Mission than in bordering neighborhoods to the west, such as Noe Valley and the Castro.

In contrast, the region stretching from SOMA through Mission Bay and the Dogpatch appears to be underpopulated given its land value. In light of this, the ongoing development in Mission Bay and the recently revised Central SOMA Plan, both of which would add a good amount of housing to these areas, make a lot of sense. The map also shows the Marina, Cow Hollow, and Pacific Heights to make relatively inefficient uses of land, as do the San Francisco Residence Parks, which include neighborhoods like Sea Cliff and St. Francis Wood. This inefficiencies of this last group of neighborhoods should not be particularly surprising, as they were designed specifically to bring suburban-style land use to San Francisco.

We can also see some areas where the LVP ratio is a bit misleading. For example, much of the Financial District appears underdeveloped going by the LVP ratio alone. Of course, this area isn't underdeveloped in any absolute sense, but rather the land is predominantly dedicated to uses other than housing. This can be seen by looking at the region on the population density map above or by considering the following detail from the San Francisco zoning map; the red area on the map is primarily zoned for C-3-0 (downtown office):

This doesn't mean that the Financial District can't play a role in addressing the housing shortage. Just this week, plans were announced to add a 35-story building including residences above the existing building at the corner of Post and Montgomery Streets. Still, there's probably a relatively low ceiling on how much new housing can be added in this area.

The same sorts of issue arise when we consider the area around Islais Creek, which includes parts of Bayview, Hunters Point, the Dogpatch, and Potrero Hill. In this case, the land is primarily zoned for heavy industrial uses, as part of the Port of San Francisco, and production, distribution, and repair districts. These are the grey and blue regions in the zoning map detail below:

While we're on the topic of zoning, it's worth noting that even small differences in the zoning code show up when we look at the LVP ratio. To illustrate, I'll focus on my own neighborhood, Ingleside. Here's our land value to population map again, only this time zoomed in and centered at the intersection of Ocean Avenue and Ashton Avenue.

There's a fairly clear dividing line in this map that follows Holloway, Ashton, and Ocean Avenues. On the north and west sides are the neighborhoods of Ingleside Heights, Mount Davidson Manor, Balboa Terrace, and Westwood Park. On the south and east sides are Merced Heights and Ingleside. At first glance, the zoning map doesn't give us many clues about what's responsible for this discontinuity:

If we ignore the purplish commercial zones along Ocean Avenue, the rest of the map looks more or less the same. But, in fact, there is an important zoning distinction here. Ingleside and Merced Heights have some lots zoned for RH-2, but are mostly zoned RH-1. These codes allow for two dwellings and one dwelling per lot, respectively. In contrast, Ingleside Terraces, Mount Davidson Manor, Balboa Terrace, and Westwood Park also include some RH-2 zoning, but are mostly zoned RH-1(D). Like RH-1, this code allows only one dwelling per lot, but requires larger lot sizes and detached houses. Thus, Ingleside, zoned RH-1, we see streets like this:

In Ingleside Terraces, zoned RH-1(D), we see something quite different:

Again, looking at the LVP ratio reveals how these perhaps seemingly small differences in zoning lead to rather stark differences in the value of the land used to house each person. This is an important lesson to keep in mind not just for identifying neighborhoods with inefficient uses of land, but also for planning new developments. For example, residents in Westwood Park have put pressure on planning committees to limit the density of the future Balboa Reservoir development to keep the new development in line with the existing, low density character of Westwood Park. But as we've seen, this type of low density development is inefficient and is not something we should want to emulate.

The Bay Area's housing crisis won't be solved without building substantially more housing. Looking at the LVP ratio can help us understand where land could be used more efficiently by adding housing and increasing density. The good news is that some of these areas, such as Mission Bay, are already seeing increases in the housing stock. But others, particularly neighborhoods zoned for suburban types of land use, are not densifying and present significant roadblocks for the efforts to add housing to San Francisco.