Urban Econ Thought Experiments

Have you seen the latest Metro fantasy map? I love fantasy maps. This one sparked a brief Twitter dialogue that offers the opportunity for a little urban econ thought experiment. Ready? Yglesias tweeted:

This Metro fantasy map could be totally realistic if we repealed the Height Act:

Josh Barro replied:

@ if the height act were repealed, why would you need such expansive heavy rail coverage in the suburbs?


@ a key reason to reduce height restrictions is to reduce commute distance and reduce demand for transportation in all modes

True, right? But that’s only part of the story. So let’s think this through. A repeal of the height limit would mean the elimination of an artificial restriction on supply, and given real estate cost behavior in the District it seems likely that it would lead to new construction, that is, an increase in supply. An increase in supply would lead to falling prices. (In practice, these steps would all take place more or less together, and you wouldn’t actually observe a drop in prices, unless a lot of new supply came online at once.) Falling prices would lead to increased demand, which is to say that people and firms would occupy the new space. Most of the demand would come from other metropolitan areas, but some would come from elsewhere in the Washington metro area, and as space was left vacant in other neighborhoods prices there would fall until all space was occupied. The result would be a similar vacancy rate to that prevailing prior to repeal, but with many more people and businesses in the District. And that’s where Josh leaves matters.

But that’s not the final equilibrium. In the new state, the core is much denser than it was before. Higher density means higher productivity, which means rising wages in the core. Rising wages in the core will increase demand for any location with access to the core. If a job in downtown Washington pays more than before, then housing in Falls Church is more valuable than before, because it’s relatively easy to commute to downtown from Falls Church.

Rising demand will mean migration into all parts of the metro area. This migration will lead to new construction where local rules permit. And ultimately new inward migration will continue until housing and congestion costs cancel out the wage increases. Of course, as people move in, density will continue to rise, pushing up wages, so this process will continue for a while. Ultimately, the Washington metro area will be more populous throughout its full extent, and it will be larger in area — bigger richer cities sprawl more than smaller poor ones. But the weighted average density of the metro area will be significantly higher than before, productivity and wages will be higher than before, and a larger share of American population and GDP will be sited in Washington.

The final distribution of population within the Washington metro area will depend on the infrastructure and policy reaction to new growth. Metro expansion in suburbs will increase the carrying capacity of the suburbs; more people will be able to move to the burbs before congestion costs rise to cancel out wage increases. New highway construction would also increase suburb carrying capacity, but not by as much, and the resulting suburbs would be less dense. But the extent to which rising wages continues to feed back to new population growth, new density, and further wage increases will be constrained by policy.

But there you have it. This full thought experiment also explain why the argument that the height limit boosts neighborhoods along the downtown periphery is wrong. That argument stops at the end of the first round of analysis, before the impact of density on wages and total metropolitan demand is taken into account. NoMa would be a far more vibrant and in-demand neighborhood in a world without the height limit, as common sense would suggest. It’s hard to imagine Brooklyn being a cooler place if Manhattan’s tall buildings were cut off at the knees.


  1. Mixner says:

    Your thought experiment is not consistent with observed behavior because you do not consider the negative consequences of higher density. Higher density means more congestion, more crowding, more noise, more pollution, less privacy, and in general a decline in the quality of life. That’s why people have been moving out of dense cities and into low-density suburbs for more than half a century. And why people who continue to live in the cities pass laws that restrict increases in density, such as the building height restrictions in DC. There is also probably a strong aesthetic motive for that particular law. Adding tall buildings to DC would erode the city’s unique architectural character that results from lots of classically-styled, low-rise government buildings, monuments, memorials and public spaces. So it’s not surprising that people strongly resist lifting the height restriction.

  2. Mixner says:

    Higher density means higher productivity,

    But it is very unclear whether, why and to what extent higher density CAUSES higher productivity. The association itself seems to be very weak. Your first link suggests that a 100% increase in density leads to only a 6% increase in productivity. Glaeser found that a 50% increase in density is associated with only a 4% increase in productivity. I’m not sure why we should consider these numbers a desirable tradeoff. Moreover, Glaeser estimates that about a third of the increase in productivity is the result of selection effects rather than causation. That is, more skilled people choose to live in more dense areas.

    Another problem is that the measures of productivity used in this research (income, wages, GDP per capita) do not take into account differences in the cost of living or in hours of work between different cities and metropolitan areas. If you live in New York, you need to need to make a lot more money to maintain a given standard of living than you would if you lived in Houston, because the cost of living is so much higher in New York. So although New Yorkers may be more productive than Houstonians, measured by income or wages or per capita GDP, New Yorkers may (and I think probably are) worse off than Houstonians because the higher cost of living in New York eats up their higher incomes. And they may only have those higher incomes in the first place because they do more hours of work.

  3. If Glaeser is right that skilled people choose to live in denser areas, density sounds great to me. Seems that the only long-term way that U.S. cities, at least, will find attractive niches globally will be by making it so awesome to live in a U.S. city that people move there just to do so.

    That said, I think Mixner has very strong points about the costs of density and the difficulty of measuring actual productivity. S/he doesn’t even include the regulatory burdens sometimes used to achieve density.

  4. Ben Ross says:

    Land values reflect status-seeking as much as money-seeking. (Look at the enormous fight that was waged to keep new retail development out of Friendship Heights – no one thought Tiffany’s and Cartier would bring lower property values.)

    Urban development patterns can’t be understood by microeconomics alone. It’s as much a sociology problem as an economics problem.

  5. BeyondDC says:

    It’s only hard to imagine Brooklyn being a less cool place if Manhattan’s tall buildings were cut off at the knees, if we assume that just means New York has less stuff overall. On the other hand, it’s very easy to imaging Brooklyn being cooler if New York as a whole had the same total amount of stuff, but more of it were in Brooklyn rather than Manhattan.

    Also, here’s the subway map of a city that is both much denser than Washington and has a more strict height limit.

  6. ryan says:

    But that’s not how this works in the real world. Some of the activity would move to Brooklyn, but most of it would move to a different city, where the market could accommodate the level of proximity firms wanted. The jobs wouldn’t move to Brooklyn; they’d move to London or Hong Kong. And New York’s tax revenues, population, and wages would be much lower.

    So to be clear on the Paris example, you’re endorsing a model in which the central city is a tourist Disneyland populated mainly be the very rich, while the poor rot in high-rises far from job centers? Perfect!

  7. BeyondDC says:

    Of course that’s how it works in the real world. If it didn’t, we wouldn’t have places like downtown Bethesda and Arlington and Tysons Corner (which though it is urbanistically a mess certainly has a lot of cool stuff). We don’t need theory, we have on-the-ground fact.

    You could conceivably be right that New York would lose some business, especially since New York is an alpha world financial city that competes globally and specifically relies on a critical mass of proximate industry. But you overstate the case to apply it universally and without consideration for other trade-offs. And certainly there are other trade-offs, even if you don’t like to recognize them because they’re not directly related to cost per square foot.

    As for Paris, you may note that the height-restricted central city is residentially denser than the high-rise suburbs. So to be clear, you’re endorsing lower densities just to obtain some tall buildings. Perfect!

    I’m tired of going round-and-round with you on this, so I won’t keep trolling this comment thread with another reply unless there’s something new to say.

    Suffice to say, you haven’t convinced me despite the facts that I’m about as strong a Smart Growth proponent as you’ll find, that I have a soft spot for skyscraper geekery, and that I’ve purposefully enjoyed living in one of the tallest residential buildings in the region. I should be your bread and butter supporter on this; if you can’t convince somebody like me, you won’t get far with the general populace unless you can bring something more to the table than you have thus far.

  8. ryan says:

    What we have here, BDC, is an analytical problem — you’re fine with sloppy analysis, and I’m not. The observation that there are centers of activity outside downtown Washington isn’t remotely a response to the counterfactual of a height-limited Manhattan — for starters because I acknowledged from the get-go that some activity would shift outward. You also ignore the fact that a substantial subset of high-end, central city office space isn’t in competition with suburban office space; it’s in competition with high-end, central city office space in other cities. One can observe this fact in talking to the people who make location decisions for top firms, or for the developers that invest in high-end real estate. Manhattan worries about losing back-office jobs to New Jersey. It worries about losing its top finance and management jobs to London. This is not just about the financial world. Top management firms, law firms, design firms, and so on have to be in places that can support a certain level of economic activity. The height limit systematically limits the District’s ability to retain those firms, those jobs, and those tax revenues. As a planner, you can pretend that one location is as good as another, or that one kind of economic activity is as good as another, but it’s simply not so. Manhattan is expensive! If Brooklyn were just as good as Manhattan, firms would flee Manhattan for Brooklyn until they cost the same amount. But that’s not what happens. And pointing out that people work in Arlington is nothing like proof that the height limit doesn’t constrain the metro area’s population, employment, output, wages, and tax revenues.

    Your Paris response is also analytically sloppy. The question isn’t whether central Paris is denser than the suburbs. The question is whether a central Paris without a height limit is denser than one with a height limit. Are you actually arguing that if Paris allowed taller buildings in its core that density would fall?

    I think the problem here is that you’re trying to see things through a Smart Growth or skyscraper geekery lens when it’s actually much simpler than all that. You seem to look at people and conclude that they’ll work here or they’ll work there and it doesn’t matter economically whether they’re here or there; it only matters for issues like how they get around. But that’s not what we see in the real world. A person working in Midtown is more productive than that same person working in Brooklyn, who is much more productive than that same person working in Des Moines. And because that person is more productive in one place than another, that affects the demand to be around him in one place compared to another. The demand for office space around our worker will be lower in Des Moines than in Brooklyn, and lower in Brooklyn than in Manhattan. And so, other things equal, the world will be denser when our worker is located in Manhattan than when he locates in Brooklyn or Des Moines. This is increasing returns to scale, and it’s the reason cities hold together in the first place.

    It’s true that this isn’t necessarily an easy concept to explain to folks, and perhaps you’re right that I’ll have to do a better job talking about it with laypeople. But that doesn’t change the fact that in your economic model — a model in which there’s no economic loss to shifting people from downtown Washington to Tysons Corner — there is little reason for firms to locate in downtown Washington at all. This is a real problem for your model, since firms do locate in downtown Washington and pay dearly for the privilege. If you’re asking “cool stuff” to do the work of attracting them, you’re putting an incredibly high implicit value on “cool stuff”.

    And if you don’t understand why your model implies this, then maybe you should spend a little more time reading about the economics of cities, if only to put together more coherent critiques.

  9. Ben Ross says:

    Washington is a different case from New York or Paris simply because it’s much smaller. The alternative to locating on the 16th floor on K Street isn’t Tysons Corner, it’s the ballpark area or NoMa. I seriously doubt that the real returns to density from building K Street higher are much greater than from expanding downtown DC into NoMa.

    At least to my taste, downtown DC has a problem of simply not being big enough in area. One great thing about New York and Paris is that you can walk and walk and still be in the city. When I moved to DC in the 80s, it lacked that completely – the walkable downtown ended at 14th St on the east. It’s getting better, but there’s still room for improvement. There’s a strong case that there are greater returns from expanding downtown DC sideways than from expanding it laterally.