Figure 1 adds a couple of patterns to the figures I used in the previous post.As discussed in that post, until the turn of the century, home prices in every city looked like the red dots or the gray dots. The larger the city was, and the more it attracted productive workers, the more it would move along that trajectory, up and to the right. Some cities, like New York City, that provide the sort of amenities that can come from density, moved even further up that trajectory - the agglomeration hill - and also tended to be a bit more expensive, especially for households with low incomes, who especially value the inferior amenities created by density.The red dots are from the before times. The Rosen-Roback times. The spatial equilibrium times. Households moved to the places they favored. Nominal spending on housing trended with incomes, both over time and cross-sectionally.By 2005, the Closed Access cities (New York, Los Angeles, Boston, San Francisco, and San Diego) looked like the blue dots. A cap on housing growth raised home prices in a way that was entirely uncorrelated with incomes (or, as I track it in the Erdmann Housing Tracker, price/income was negatively correlated with income). That created mass economic outmigration. And the cities those migrants fled to ended up looking like the orange dots. Demand booms tend to affect home prices across a market similarly, and prices rise in the same proportion.By this century, multi-family and infill housing was so over-regulated throughout the country, the only way cities were staying near the old patterns was with exurban, single-family construction. That meant that no new cities could transition from red to gray. And, it meant that, when the mortgage crackdown was imposed in 2008, as a misplaced reaction to the blue and orange cities, it blocked the only form of housing that could still be constructed at a sustainable scale. And, so every city started moving toward those blue dots. Today, cities like Phoenix, Tampa, and Las Vegas are somewhere close to the yellow dots. Other cities fall somewhere between the yellow dots and the red dots, depending on how much growth pressure there is and how binding their land use regulations are.Where a shortage creates a housing musical chairs game, prices rise across a market uniformly, rather than proportionately. It’s a monopolistic scarcity premium. And, when it becomes binding enough and strong enough, it forces households to choose regional displacement, or in a minority of cases, homelessness.The scale and distinctiveness of these patterns is so peculiar and discernable, that once you see them, it is clear that the things that make housing today different than it was in the 20th century should dominate your understanding and discussion of it. Most of the challenge for me to communicate this is that peer reviewed economics literature doesn’t appear to include any knowledge of these peculiar patterns. As I discussed in the previous post, I think this actually leads economists to mis-specify their models until their models cram the round pegs of the blue, orange, and yellow cities into square gray and red holes.In that San Francisco Fed paper that I keep harping on, they have a stunning couple of sentences:Howard and Liebersohn (2021) show that the effect of income growth on their newly constructed rent index from 2000-2018 is independent of the measured housing supply elasticity, which they attribute to a high migration elasticity. Similarly, Aura and Davidoff (2008) and Anenberg and Kung (2020) use quantitative calibrated models to argue that relaxing local housing supply constraints is unlikely to significantly affect local house prices due to strong migration responses.A “high migration elasticity” is econ speak for “people easily pick up and move when costs change a little bit.” The blue dotted metro areas seem to highly refute that claim. To be clear, local moves are easier. The migration elasticity from dots changing positions as cities evolve is high. Ironically, as I discussed in the previous post, the local land use regulation that causes all these problems is largely in place to stop the sort of building that creates local migration that is easier. But, after 4 million households have been displaced from a city entirely, the 4,000,001st household is the household that has been holding out with poverty incomes after rent expenses because under the housing shortage households self-select over time according to how low their migration elasticity is.I’ll try my hand at some econo-speak. Those models are broken because migration elasticity is endogenous to supply conditions. That breaks one of the important assumptions of Rosen-Roback.In one way or another, all these economists twist the blue cities into gray cities, and calibrate their models to conditions that were reasonable when cities were gray or red. One common way they do that when households struggle to keep hold of a home in their preferred city, driving up local prices, and then finally move away when they have to give up, raising the average income of households that remain, the researchers misinterpret those rising incomes and rising home prices as a sign that the city is really popular among households with high incomes. They misinterpret the pattern to mean that high demand from newcomers is the source of the pattern, so that new building won’t lower rents and prices much. It will just attract more demand because of “high migration elasticity”. It’s kind of crazy when you see it in the wild. They systematically misidentify cities with high gross and net outmigration as cities with high in-migration. But, it’s easy to say the in-migration is only low because of the high prices, and that makes the round pegs fit like a glove. It’s kind of madly poetic, really. By construction, the level of in-migration those models claim would keep prices from declining if more homes were permitted is always out of sample. There can be no actual measurable rate of in-migration to calibrate to for the supposedly high-agglomeration markets, because there aren’t any examples of cities with very high in-migration being expensive.A city goes from gray to blue for one reason and one reason only - “migration elasticity” becomes agonizingly low as regional displacement accumulates.The abstract of the Anenberg and Kung paper ends with, “The reason for this result appears to be that rental rates are more closely determined by the level of amenities in a neighborhood--as in a Rosen-Roback spatial equilibrium framework--than by the supply of housing.” Certainly, at any point in time, cross-sectionally, the level of amenities in a neighborhood determine where the dot is relative to the other dots in its market. The main distinguishing feature of the most expensive cities is that a measurable, uniform lot premium applies to every home in the region, and the premium is very high in cities with high levels of gross domestic outmigration because families pay exorbitant sums to avoid migrating.To give an indication of real world numbers, Figure 2 shows income and home prices in Atlanta from 2002 to today. These are nominal measures on a log scale. The dotted line is the equivalent of the red dots in Figure 1. Atlanta had been climbing that line, just like every city does, since the beginning of Atlanta. It was basically on that line, climbing it, in 2002, 2005, and 2019. There was a brief detour in 2011. I didn’t represent that on Figure 1, but that is what the mortgage crackdown did to cities like Atlanta.Since the consequence of that was to hobble the construction industry so badly, we are still fighting supply constraints to get back to a sustainable level of construction. And, so Atlanta moved back up to the agglomeration hill and right past it, up toward the blue dots in Figure 1.Economists think Los Angeles and New York City have just been climbing the agglomeration hill faster than Atlanta has, and that if they build more, they will just climb it faster. Figure 3 shows incomes and prices for Los Angeles. The mortgage crackdown did the same thing to Los Angeles that it did to Atlanta and every other city (moving it from green to yellow in Figure 3), but the scarcity premium was already high enough in Los Angeles that it didn’t push lot values into negative territory, and that’s why construction recovered more quickly in Los Angeles.More homes in Los Angeles will pull it back down to the agglomeration hill (a line roughly extending from the red dots), and the average local income will decline because that will stop the annual outflow of Los Angeles’ poorest residents.Or, maybe I’m wrong, and we should assume that something that never happened in the history of any of these cities will now happen if Los Angeles, New York City, Boston, and San Francisco start permitting homes like Austin does. Austin, by the way, does have a measurable history of high in-migration to calibrate models to. But, sadly, Austin lacks the specialness of the Closed Access cities. It doesn’t have that Je ne sais quoi.1 It behaves as all cities in the history of cities have behaved, and climbs the agglomeration hill as it grows.1: We can’t know, after all, that something that never happened couldn’t have happened. Since it did happen in Austin, we have the burden of knowing that Austin isn’t so special.Original Post