Housing, Productivity, and Nerds


A quick comment about Krugman's last NYT op-ed about housing costs, mobility, and productivity. He starts with several facts that are, I think, uncontroversial at least in a broad sense.

1) On net, people are moving from NY and SF to Atlanta and Houston
2) Housing prices are higher in NY and SF than they are in Atlanta and Houston
3) Wages are higher in NY and SF than they are in Atlanta and Houston

Great. What Krugman concludes is that this represents a loss of productivity. The high wages in NY/SF must capture high productivity in those places compared to Atlanta/Houston, so the movement of people is lowering productivity. If housing prices were not so high in NY/SF, then people would not move, and they would stay in these those high-productivity areas - and perhaps people would even move from Atlanta/Houston back to NY/SF. So making housing more affordable in NY/SF would be a boost to productivity.

This argument is basically the slimmed down version of what Chang-tai Hsieh and Enrico Moretti study in a recent working paper that I saw presented at NBER this summer. Here's the core concept, simplified from my casual reading of the Hsieh/Moretti paper, but hopefully capturing the basic idea. Each city has some productivity level. For the moment, let's assume that productivity is highest in San Fran, and lower everywhere else. If each city had constant returns to scale in production and produced an identical good, then the optimal allocation of labor is for everyone to move to San Francisco, to work in the highest-productivity place. That allocation would maximize output.

Of course, this might not be the optimal allocation for welfare. The geographical space is limited, and furthermore there are lots of restrictions on building in the greater Bay area, so real estate prices would go to something approaching infinity if all of us moved there. For Hsieh and Moretti, and by extension Krugman, this what keeps us from achieving the allocation of labor that maximizes output. The sensitivity of housing prices to population is so high in the Bay area that it isn't worth the higher wages to live there any more. So people leave for Houston and Atlanta. This raises movers welfare, but at the cost of lower overall output because we move farther away from the output-maximizing equilibrium.

[This, of course, is leaving out completely the concept that not everyone might want to live in San Francisco. There is a high danger of running into 49ers fans in San Francisco, which we can all agree is equivalent to getting a root canal. But in the Hsieh/Moretti set-up, people don't have idiosyncratic preferences over cities, and it's actually not crucial to their findings. This is also probably a good spot to mention that I live in Houston, but as you'll see below I'm not going to argue that Houston or Atlanta are demonstrably better places to live than SF or NY. Preferences actually aren't the story here.]

Let's take the Hsieh/Moretti/Krugman setting as given. The implication is that we should act to lower the house price elasticity in SF (e.g. allow skyscrapers in Palo Alto), so that prices are not so sensitive to population, and then people can move from Atlanta and Houston back to SF where they will all be more productive. Output and welfare will rise.

Of course, there is an equivalent solution - move everyone in SF to Houston or Atlanta. The reason SF is the most productive city is not because of some fixed, inherent quality of the location at 37.78 degrees North, 122.41 degrees West. It's certainly not because of it's fantastic summer climate. San Fran is the most productive city because it so happened that a unique collection of nerds coalesced there starting in the 1960's. More nerds were attracted to the bright, shiny things that the original nerds were making, and now I have an iPhone. But here's the thing about nerds - they are easy to move. You can easily strap one to a dolly and wheel them anywhere you want.

If you want to maximize welfare in the Hsieh/Moretti/Krugman model, then you want the cost of housing to be relatively insensitive to city size. This allows all the people to congregate in the most productive city without driving up costs so much that people no longer want to live there. So you can either lower that sensitivity in places like NY or SF, or you can make Houston or Atlanta the most productive city. It's non-obvious which is the right solution. Arguably, it is far easier to incent Bay area nerds to relocate south than it is to convince existing Bay area home-owners (a much larger group) to take a massive capital loss on their houses.

What do we make of the steady shift south, then? Perhaps for right now, it is productivity-lowering for all those people to leave San Fran and NY. But if housing prices remain so fantastically high in those places, then eventually Houston and/or Atlanta will become the high-productivity city, because at some point even the nerds will move. Maybe the right answer is to speed up this movement, not try to reverse it as Krugman suggests.

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