On Intersections

Back in May, Reid Ewing and Robert Cervero released a study called “Travel and the Built Environment” that performed a meta-analysis on various papers addressing the various factors that cause people to drive, walk, and take public transit. Ped Shed has a nice summary:

Of all the built environment measurements, intersection density has the largest effect on walking – more than population density, distance to a store, distance to a transit stop, or jobs within one mile.

And they have a picture:

So Venice has 100 times the intersection density of Irvine, and is much more “walkable”–based on the estimates in the paper, the average city going from the density in Irvine to the density in Venice would experience over 30 times as much walking.  Not bad! So what, exactly is causing this? Much of the discussion that followed–from Ped Shed, Grist, and Kaid Benfield–highlighted the connectivity of the streets that intersection density implies. To get from one major intersection to another in Irvine, you have to follow the major thoroughfares between them. To do the same in LA, there are any number of streets to go up and over to get from one place to another–much greater connectivity. Finally, Venice has a seemingly infinite number of paths to take from any one place to any other. So, greater connectedness leads to greater walkability.

I, for one,  am unconvinced. Certainly there is some point of disconnectedness that prevents walking, and Irvine is there. But looking at that part of LA, it doesn’t seem any more difficult to get around than Venice. Easier, really: the straight blocks  are not nearly as dense, but do continue on the direction they start. Seems like it’s at worst a toss-up as to which would be easier to get around.

Now, amongst urban thinkers, there is a definite focus on streets. I understand: streets are how we get around, and the fact that urban ones in the US are crammed with cars is kind of the defining feature of urban areas. “The street” is a handy image and metaphor–the blog network streetsblog is a good example.

I don’t doubt the empirics–I’m a data-oriented economist! But in order to use data, one must be working with the right model. The implicit model that the connectedness of streets is what matters seems to be based on a comparison between, say, typical urban (LA) and suburban (Irvine) areas. But what about LA and Venice? I think the answer lies not in the streets and their connectedness, but in what lies between: shops! Businesses! Neighbors! Things that people want to do!

So, here is my working model. It depends on a couple assumptions that I think are reasonable. First, in a typical American downtown district, the average shop or restaurant follows the same basic layout. The money-making part of the operation—the sales floor—is in front. Behind this are offices—necessary, but meaningless without the front room. Finally, by the alley behind the building, is a dumpster for trash collection and a parking spot for the owner. The most valuable of these is the front room, and the least valuable is the parking spot. If a business owner could pay differential rental rates for these different areas, they would offer the most for the front and the least for the back, with the office space in the middle somewhere in between. If you look at the differential rental rates between the first floor—that is, prime sales space—and higher floors—that is, subprime sales space but just fine office or loft apartment space—you see a similar pattern. Rents are high on the ground floor, not so much higher up (penthouses notwithstanding!) Downtown businesses are paying for a storefront on a street in a specific location. That’s assumption number one.

Assumption number two is a basic one in economics: the demand curve slopes down. As the price of something goes up, people consume less of it. In this case, I’m looking at rent: if rent goes up, then firms will prefer a smaller location. If your rent goes up to $25 a square foot, and that last section of retail goods only gets you $20 a square foot, then you’ll be better off in a smaller spot where you can drop that section and not pay for the room. Alternatively, you might stay in the same spot, but shrink the office. If you can move a few filing cabinets home and get rid of the conference table but add one more section, you might be able to make up the difference without moving. Either way, the price of space goes up and you will react in a way to make do with less. That’s assumption number two.

Now, imagine a location with square blocks. Let’s say 400 by 400 foot square blocks, just so the math is easy, with an unwalkable alley going one way through the middle for trash pickup and employer parking. So we have a block with 16,000 square feet. This block can be easily chopped into eight rectangles, each 100×200. In each case, the business owner values the front half—the sales floor—at $30 a square foot and the back half—the office and parking spot out back—at $20. On the average, then, they value the space at $25 per square foot. So, the value to the renters of this block as a whole is just $25*16,000sq ft=$4,000,000.

Now, imagine that the city takes this same 400 ft by 400 ft block and turns it into four blocks, each 200 by 200, with extra streets running down the middle. Now, 4*200*200=16,000—the area hasn’t changed. But now, if the area is divided into the same 100×200 rental units, then each unit has street access on three sides, instead of the one (or two, for corner units) before! So, how does this change their behavior? At this point, there is no “back half” for offices—the sensible store owner would want easy access from all outside streets. The office will clearly get smaller—let’s say that the owner moves the office home, for simplicity’s sake. Thus all 100×200 square feet are taken up by “front half” sales floor areas. The landlord knows this too, and charges accordingly: rent goes up to $30 a square foot. But, because the space is now being used entirely as sales floor, renters agree to pay it. So we have the exact same 16,000 square feet of space, but the new roads going through have caused the value to increase: $30×16,000=$4,800,000, an increase of $800,000!

Furthermore, my demand curve assumption enters the situation: as the rent goes up, firms demand less space. Landlords can respond by subdividing the spaces, so that there are no longer two 100×200 units per square block, but four 100×100 units. So, on the same amount of land, we go from eight 100×200 to 16 100×100 businesses.

Which neighborhood sounds more walkable? I certainly would posit the second, with 16 smaller businesses. There’s more room for variety, and the higher rents will encourage innovation in design. The area is also likely to create more jobs, leading to more demand for all the businesses—spurring further development. More expensive land prices push towards higher density, and higher density allows for a greater diversity of products. There are cyclical effects pushing towards more and more walkability over time. Furthermore, there is evidence that a greater density of entrepreneurship is a key ingredient in promoting living standards, paying even greater dividends.

And finally, the switch from 400 foot blocks (and a lower land valuation) to 200 foot blocks (and a higher valuation) has one more effect: we’ve more than doubled our count of intersections, from four to nine. Now, perhaps I was too harsh on streets: it is what’s between them that matters, but my assumption that businesses value storefronts implies that businesses value streets—presumably because that’s where the people are! But just like my last post—which provided a framework for thinking about recessions beyond the cyclical mess implied by “the economy”—simply stating that “connectivity” is key is not enough. To understand the relationship between intersections and walking, we must understand the causal chain of interactions that arises from an increase in the density of intersections. This is the thing that attracts me to economics: the discipline that formal economic models require can pay high dividends in terms of understanding. Having the wrong model, on the other hand, impedes understanding and leads to disastrous policies.

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3 thoughts on “On Intersections

  1. Overall, I liked your idea though it was bit number heavy for what I like to read to be honest. I think your 16 shops exemplifies the different cultures of each of the original examples’ general places: the US and Europe. Luckily and charmingly for Europe, all those tiny, twisting, turning roads that sprang up over the years and years of villages and towns and cities being around pays off. Venice is “walkable” because it’s found to be charming , quieter, and driving isn’t so easy. And, having a plethora of accessible, interesting, local shops all over the place helps. In the US, many streets were developed over a much shorter period of time, and, especially as you move West, with the automobile in mind (or railroad cars). The US also had tons of space. And once they killed all the American Indians, there was even more! “Why cram everything so close? Let’s spread out. And in the future we’ll be able to drive there in our air conditioned Expedition.”

  2. While you are right that Europe’s population density (and walkability and thus charm) owes to the fact that the population was already something like 550 million people in 1950 (which was sort of the dawn of suburbanization in its modern car-based form), I hesitate to say “luckily”–not because I think you’re wrong, but because of the potential for fatalism it endengers. While European density was something of an accident of history, this sort of density doesn’t have to be an accident of history. The US population has more than doubled in the last sixty years, and is liable to increase by another 120-150 million in the next sixty. We added 60 million people in the last 25 years. If we do that again, that will be the equivalent of adding 7 New York cities to the country. Furthermore, it seems likely that the southward trend in migration will reverse, at least to some extent: increased temperatures will probably push people farther north. What this means is an enormous opportunity for shaping the built environment of the future–and hence the livability of our cities. Because, as you suggest, there is some path-dependence in city “type”, this opportunity is tremendous–particularly in light of the many side-effects that come from density (or the lack thereof), both environmentally and economically.

    Fodder for another post..

  3. I agree. I mean “luckily” in that much of that population growth has added to charm. But, I like that bit about the opportunity the growth affords us very much. Conservatives don’t seem to be buying into birth control any more than they used to, overtly anyways. But, more to the point, seizing the opportunity will be difficult given the tendencies of white suburban US. Too many people in the US 1) seem to not like to live to too many people different than themselves and 2) not be too crowded (car culture, rural culture, resistant to change, etc.). Those factors may be very hard to overcome.

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