Can Housing Quotas Affect Demand For Housing?

Economist Nick Rowe at Worthwhile Canadian Initiative  has a provocative piece asking whether housing demand curves might actually slope up. He puts his argument in abstract mathematical terms (again, he’s an economist), but the germ of the idea is that “everybody wants to live near everyone else, wherever that happens to be.” Our decisions about where to live are dependent on what everyone else decides to do. If you move from the countryside to the city, I get more out of moving to the city, too. And vice versa. Our decisions mutually reinforce each other.

Rowe assumes that these decisions not only reinforce each other but are “strong strategic complements,” which means roughly that they generate positive feedback. We can think of it in probabilistic terms: if my probability of moving from the countryside to the city is conditioned on your probability of moving, then our decisions are “strong strategic complements” if a 10% increase in your chance of moving increases my chance of moving by morethan 10% (and vice versa). That’s not a completely arbitrary assumption: if you and I live in the countryside, your decision to move not only makes the city a more desirable place (because it now has more people) but it makes the countryside less desirable (it is now a bit lonelier). That is, when you raise your probability of moving, you not only increase my chances of being stranded, you make the consequences of my being stranded more dire. I adjust my probability by ratcheting it up even more.

This positive feedback will cause people to continue pouring in from the countryside into the city, at least over some range of population. (Overcrowding, congestion and so forth will dampen the feedback at some point.)  Within this population range, increasing the amount of housing further increases the demand for housing. But if the city adopts a housing quota through planning restrictions, the population will stabilize and prices will adjust so the housing market can clear. As long as strong strategic complementarity prevails, relaxing the quota (i.e., building a little more housing) will, counter-intuitively, cause prices to rise. Rowe explains: 

It’s a bit like Say’s Law (“supply creates its own demand”), only even more extreme. If you build delta S more housing, so delta S more people move to the city, even more than delta S more people will want to move to the city at the previous price of housing, so the equilibrium price of housing must rise. If you build 100, 150 will come.

It’s a provocative argument. It turns the Econ 101 arguments upside down. Not surprisingly, it generated a fair amount of annoyed twitter chatter from market urbanists (including me) and sage head-nodding from those who believe new construction begets high home prices.

Rowe’s model is dependent, of course, on this very strong assumption that location decisions are subject to positive feedback. This assumption might hold for places like Lagos or Dhaka, which have experienced accelerating growth over the last couple of decades despite any the lack of large-scale industrialization. If you live in Nigeria or Bangladesh, these cities might be increasingly attractive despite (hypothetically) deteriorating living conditions just because everyone else you know is moving to them. Their growth more or less forces you to move there too. (Or maybe not. Nigeria and Bangladesh are both growing rapidly. Those new residents have to live somewhere.)

But I don’t think the assumption of strong strategic complementarity applies in the United States. There are 35,000 cities, towns and hamlets in the United States of every size. Many small towns are growing and large cities are shrinking (or are growing very slowly), so his assumption clearly does not hold as a general rule. We have cheap, fast-growing cities (Houston, Dallas, Phoenix) and expensive, slow-growing cities (San Francisco, New York). Neither group fits Rowe’s model, which predicts that growth will accelerate even as housing prices rise, and that tamping down growth will hold prices in check.

Ultimately, I don’t think the model holds in the United States because people don’t care that much about total population. Perhaps the best way to put it is this: if your moving to City A really would increase my utility of moving to A, then I’d already be living in larger City B. We mostly care about other criteria when we shop for cities.

But Rowe’s assumptions might be modified to produce a useful model for American cities. Let’s think in terms of neighborhoods rather than cities. If we assume that people care more about some quality of a neighborhood than the gross population of a neighborhood, housing quotas could create positive feedback. For example, if people care about the average income of a neighborhood, then a rise in a neighborhood’s average income will raise the price of housing (because the neighborhood will be more desirable). As prices rise, the neighborhood becomes unaffordable to lower income buyers (because high-income buyers are generally willing to pay more), which in turn ratchets up the average income, and so on. On the other end, as high-income buyers stream into the neighborhood, the average income of the neighborhoods they leave drops, lowering the demand for these neighborhoods. These conditions might cause the high-income to cluster together in a high-priced, high-income neighborhood, and the less well off to cluster together in cheaper, low-income neighborhoods.

Whether there is actually positive feedback of the sort Rowe describes probably depends on the housing supply curve. If housing can be added cheaply and quickly to a neighborhood, the feedback effects might be very weak. A temporary rise in a neighborhood’s average income will make the neighborhood more attractive for everyone — it will entice rich and poor alike to the neighborhood — thereby limiting the long-term rise in neighborhood income.  We can reasonably assume that this will affect what people are willing to spend. After all, what’s the point of spending a lot of money to live in a high average income neighborhood if the high average won’t stick? In this case, loose housing supply dampens the feedback rather than intensifies it.

Housing quotas ensure that a neighborhood’s high-income income “sticks.”  They increase the returns to the high-income from clustering together.

That’s just a thought. I haven’t tried to work it out rigorously. But a few thoughts on what we’d expect to see under this model:

• Merely imposing a quota on one neighborhood could destabilize a city-wide equilibrium and cause the rich to congregate together — even without any change in the city’s total population or the individual income or preferences of its residents.
• Residents of high-income neighborhoods have an incentive to resist any sort of housing that would lower the neighborhood’s high average income. High-income residents might be peculiarly averse to unobtrusive housing (say, dwelling units tucked into a backyard) if the housing is likely to attract low-income residents.
• Residents of high-income neighborhoods will be indifferent to loosening the planning restrictions in low-income neighborhoods. Increasing the supply of housing in a low-income neighborhood will not drop the average income of the high-income neighborhood.
• Historic zoning can be thought of as the ultimate down-zoning: the housing capacity of a neighborhood is limited to whatever happens to be on the ground when the historic zoning is approved. Residents of a moderately prosperous neighborhood have an incentive to agitate for historic zoning (or other down-zoning) in hope of triggering positive feedback effects.
• Rent-controlled renters in high-income neighborhoods have an incentive to oppose new housing that attracts below-average income residents because rent-controlled renters benefit from a neighborhood’s high average income just like everyone else. In fact, they may have a stronger incentive than the typical homeowner since they don’t have to worry about feedback effects pricing them out of the neighborhood.

Of course, my assumption that people shop for neighborhoods based on average income is overly simplistic and might not hold even in a simplistic sense. But I think people do tend to care about a neighborhood’s average income, even if they usually state it in other terms (e.g., average student test scores), and people don’t care much about total neighborhood population.

[Originally published on the blog Club Nimby]