GIGO from the San Francisco Fed

I recently highlighted a really interesting new paper that provides some interesting insights about housing in spite of the blind spots about the current market among economists.

In this post, I will be discussing a new letter from the San Francisco Fed that doesn’t fare so well.

The abstract:

Understanding housing demand dynamics through two indicators, income growth and population growth, provides important insights into housing affordability. Research shows that average U.S. income growth is strongly related to rising house prices but is essentially unrelated to changes in the supply of housing units across metropolitan areas. Instead, greater population growth translates into greater housing supply growth, with housing supply generally outpacing population, even in expensive markets. Thus, differences in affordability across areas may reflect differences in the growth and type of housing demand rather than different housing supply constraints.

This appears to be an extension of an earlier paper that some of the authors were involved with, which I have written about previously. (Others also reacted to that paper, including Salim Furth and Michael Wiebe. The authors responded to them.)

Here, they write:

Places where economic growth translates into strong demand for highly skilled workers, such as San Francisco, will tend to have more growth in house prices and less growth in housing supply relative to places where there is very little income growth but significant growth in middle- or low-income jobs, like Houston. Critically, these growth dynamics are independent of housing supply constraints and so are more likely to reflect deeper trends in the underlying drivers of economic growth.

Their explanation? Are you ready?

As income grows, there may be little effect on the demand for housing supply. If we control for population growth, there is essentially no relationship between the two.

What might be causing this lack of connection? One important possibility is that housing demand can vary with income levels. In areas with lower average income, households tend to be relatively large, with many individuals sharing a housing unit to reduce costs. As income rises, some growth translates into demand for additional housing units to reduce crowding. Thus, as a society becomes relatively wealthy, household size declines and housing unit demand increases. But once households are relatively small—as they are on average in the United States—then additional income increases may not translate as much into demand for additional housing supply. Instead, many households may prefer renovating, relocating to a more attractive location, or otherwise increasing their demand for housing quality.

As the saying goes, [citation needed].

As I wrote in the previous post, “Since the entire economics academy is ignorant of the most important thing to happen to US housing this century, they fill in the 80% of the story they haven’t discovered with true and barely relevant causes.” The paragraph above might be at the scale of Cal Ripken’s consecutive games played record for filling in the gap of ignored variables with truish(?) irrelevancies.

You might ask, if families with low but growing incomes have strong housing unit demand, then why do families in Texas express that demand by moving into more homes in Texas while families in California express that demand by moving into more homes in Texas?

The authors write a lot of words and they use a lot of equations, but if I can work my way through the haze of all of it, I think what it comes down to is that they are saying the migration is the thing that equilibrates the markets. I don’t know how that is any different than saying inelastic supply conditions in California force families to move to other places.

I think it’s because they are using spatial equilibrium models, which are one of those true but unimportant variables that economists are using to confuse themselves about this. As far as I can tell, they are saying that affordability and amenities are just two of various factors people look at when choosing housing and location, and when rich newcomers move to San Francisco, the poor families move away because they value the affordability of Texas more than the amenities that the rich newcomers bring to San Francisco. No muss, no fuss. Like shopping for potatoes. Displacement is just another ho-hum expression of preferences.

It’s empirically wrong, as I will discuss below. But, I think that’s the rhetorical two-step going on here.

Supply Elasticity Really Isn’t Different in Different Cities

As I discussed on the previous post on the earlier paper, there are a lot of issues here. One problem is that the mortgage crackdown really did remove much of the cross-sectional differences in housing elasticity among cities. Before 2008, the Closed Access cities had clamped down on growth across the region, both single- and multi-family. But, multi-family construction has been thoroughly limited throughout the country, so before 2008, other cities had a band-aid on the problem, and the missing multi-family homes were replaced with entry-level single-family homes in the exurbs.

So, I am not surprised that from 2000 to 2020, they don’t find much variation in supply elasticity across metropolitan areas. Figure 1 shows regional trends in multi-family and single-family construction from 1988 to 2024. There is little variation in multi-family construction across time or cross-sectionally. Multi-family construction is universally inelastic in 21st century American cities. So, they are correct to find that differences in supply elasticity in multi-family construction don’t explain recent price differences across cities. Marginal multi-family supply price elasticity is zero almost everywhere. There are millions of parcels across the country where multi-unit construction could pencil if it was legal. Those parcels are upzoned through arbitrary political discussions mostly unrelated to price and cost. In fact, a common complaint at municipal feces-throwing events is that parcels shouldn’t be upzoned, because the developers will profit from the upzoning and charge high rents. When NIMBYs call YIMBYs developer shills, the NIMBYs are saying that upzoning would lead to a lot of profitable construction, and that supply is currently perfectly inelastic because of zoning. And they intend for it to stay that way. Supply would naturally be elastic and they insist on keeping it inelastic because the value that upzoning would unlock for residents is so high that some commercial institutions would profit by unlocking it.

When single-family construction collapsed in 2008, multi-family completions hardly budged anywhere. Where demand crosses multi-family supply curves today, they are routinely vertical across the country.

Figure 1

After 2007, the mortgage crackdown also collapsed single-family supply. The Federal Reserve has banking oversight responsibilities. In a different world, economists at the Federal Reserve Bank of San Francisco would notice that it was something important to control for, or at least discuss in a letter about housing supply during a time when mortgage originations collapsed. Not in our world.

In any case, the Northeast is dominated by inelastic cities. Single-family construction in all 4 regions fell to Northeast levels for a few years after 2008. The Midwest is still there. The West has moved only slightly higher. For most of the period covered by this paper, single-family construction even in the South was well below the construction rate of the 1991 recession.

Furthermore, by the time single-family construction started to recover from Northeast levels in other regions, the national construction sector had been so thoroughly beaten down that it was supply-constrained at a national level. It was not in a position where starts could suddenly jump by hundreds of thousands of units to meet demand. As I told Shane Phillips, for the past decade, we have been a country producing 2 million potential households per year but with only the capacity to produce 1 million homes.

So, for the past decade, market forces have distributed the capacity to build in proportion to demand. The more demand drove up rents in a city, the more local builders were willing to bid up the price of inputs to direct new construction to that city. So, for the past decade, measured supply elasticity really has been relatively similar across the country. Differences in quantity of construction have been generally associated with regional demand differences.

Figure 2 shows the relationship between construction rates and rent inflation among 80 metro areas since 2015. There is none.

Figure 2

If we treat average rent in 2015 as a sort of legacy of previous supply elasticities, Figure 3 shows how the housing market had been working for a couple of decades before the 2010s. Most cities were similarly affordable and they grew according to demand. That was a world where spatial equilibrium was true and relevant. Families moved aspirationally. And, in those cities, when they moved, supply responded. Supply conditions are kind of either/or. Supply elasticity is either very high or basically zero. Vertical or flat.

Figure 3

But, there were a handful of cities - the Closed Access cities - where supply was inelastic. Spatial equilibrium was a true model in general, but not a reliable way to describe motivations about spending on housing in the Closed Access cities. Those cities are expensive because families are paying ransom rents for idiosyncratic endowments - paying because displacement would be very painful for them.

Both today, in all markets, and in earlier periods outside the Closed Access cities, rent inflation was not strongly correlated with construction activity. In earlier periods that was because most cities had elastic supply conditions. Today it’s because every city has similarly inelastic conditions because hysteresis in the sector after the post-2008 collapse is still keeping national capacity below sustainable rates of construction.

What the authors found is empirically true. They are misinterpreting it. But, the facts are accurate. Supply conditions have been relatively similar across the country and migration is how housing markets are equilibrating. The problem is that the academy doesn’t have the interpretive tools to address the authors’ misinterpretation. You have to know about the mortgage crackdown and its effect on capacity to know where the authors went wrong. Nobody in the academy knows those things. They all stipulate that the true but currently unimportant spatial equilibrium model should be the focus of housing explanations, so their replies to this paper will be handicapped.

Figure 4 is from the paper. They show that average home price trends across metro areas are correlated with income trends. As they show it, maybe a bit more than 1:1.

Figure 4

In markets with some supply elasticity, home prices will rise in proportion with incomes. In markets with inelastic supply, home prices will rise, on average, a bit more than incomes, but trends in home prices aren’t symmetrical. Wherever economists post analysis that has a conclusion pushing against the importance of supply, it is very likely that you’ll find they used metro area averages. You can’t understand the effect of inelastic supply using metro area averages.

Figure 5 compares Cincinnati, Phoenix, and Los Angeles in January 2002 and June 2025. In 2002 (left panel), in both Phoenix and Cincinnati, new home supply wasn’t completely inelastic, so the price of homes relative to incomes was uniform across time and cross-sectionally across incomes. Where new homes of some form aren’t outlawed, incomes and home prices trend in parallel over time. Cincinnati and Phoenix are both on the horizontal portion of Figure 3. Supply was basically perfectly elastic in both. More demand had little price effect. It was all quantity. Phoenix had higher demand. Phoenix built more. They were equally affordable.

Over decades, that chart looked like that in both Cincinnati and Phoenix. In earlier decades, it might have been associated with an average 1,200 square foot home. In recent years, it might have been associated with 1,800 square foot homes. In the interim, the real size and quality of homes in Phoenix and Cincinnati changed so that after families traded around within the stock of homes that had been created, their nominal value would be around 3x nominal incomes, with little variation across the market. If the average home is 1,800 square feet it is because the cost of building an 1,800 square foot home on a lot with marginal locational amenity values takes about 3 years’ worth of the average family’s income.

In a market like Los Angeles, supply conditions are so bad that the real condition of the homes doesn’t matter. The marginal price of homes in Los Angeles is based on the inflated premium a lot carries for being associated with the legal right to contain a home in a deeply undersupplied context.

Spatial equilibrium is less important the more a city’s housing market looks like Los Angeles’ in 2025, and the more families are paying for non-tradeable idiosyncrasies and endowments.

Los Angeles is at the top left of Figure 3. In Los Angeles in 2002, demand for homes crossed a vertical supply curve. In the richest neighborhoods, that meant that prices still roughly tracked incomes. In the poorest neighborhoods, prices far outpaced incomes. Figure 4 from the Fed’s letter is for averages. That scatterplot wouldn’t look the same for homes and households at the tops and bottoms of the income distribution.

Figure 5

The right panel of Figure 5 shows current conditions. The supply problem is worse everywhere, because of the 2008 mortgage crackdown and the completely inelastic supply conditions for multi-family housing. So, prices are higher in poorer neighborhoods than they used to be. Phoenix and Cincinnati are later to the shortage party than Los Angeles is, so they have been slowly becoming more asymmetrically unaffordable, like Los Angeles.

This gets at one of the authors’ empirical problems. If I am reading their econo-speak correctly, they are saying that in cities with higher average incomes, the amenities of the cities are more aligned with high-income households, so low-income households move away to other regions that are more aligned with their preferences. But, prices tell a different story. Poorer residents who do live in the cities with rising average incomes are systematically paying more to live there. If prices are a signal of preferences, then poor residents of San Francisco must especially like living there, even as their relative incomes after housing expenses stagnate or decline.

A paper they cite, “The Determinants and Welfare Implications of U.S. Workers’ Diverging Location Choices by Skill: 1980–2000.” by Rebecca Diamond, makes these assertions pretty directly. In its conclusion, the author writes:

The divergence in the location choices of high and low skill workers from 1980 to 2000 was fundamentally caused by a divergence in high and low skill productivity across space. By estimating a structural spatial equilibrium model of local labor demand, housing supply, labor supply to cities, and amenity supply I quantify the ways through which local productivity changes led to a re-sorting of workers across cities. The estimates show that cities which became disproportionately productive for high skill workers attracted a larger share of skilled workers. The rise in these cities college shares caused increases in local productivity, boosting all workers wages, and improved the local amenities. The combination of desirable wage and amenity growth caused large amounts of in-migration, driving up local rents. However, low skill workers were less willing to pay the price of a lower real wage to live in high amenity cities, leading them to prefer more affordable, low amenity locations.

That paper relies quite a bit on metro area averages. And, I think there are 2 fundamental issues with using this paper as a citation for current conditions. First, is the issue of price and rent appreciation being highly negatively correlated with neighborhood incomes and neighborhood amenities. This paper covers the period 1980 to 2000, and the asymmetrical cost inflation didn’t really start to heat up until the late 1990s. So, metro area averages might be good enough to explain the spatial equilibrium world that paper was looking at. But these conclusions aren’t generalizable to current conditions.

Second, the paper appears to rely on college share of employees as its motivating variable, and assumes that rising share is from increased demand of newcomers. There is some tertiary discussion of in-migration and out-migration, but I don’t think migration directions are differentiated in the model. And, maybe there was a period of time where rising in-migration of college educated workers was the causal driver. But, the Closed Access cities have been growing slowly for decades. During periods where housing has become asymmetrically expensive, they have been the slowest growing cities in the country, frequently even shrinking.

This century, the rate of in-migration and the incomes of the newcomers have been average in the Closed Access cities. Where the Closed Access cities are outliers is that they have unusually high out-migration and the incomes of their leavers are unusually low. Rising college share of local workers is now more a product of who moves away than who is moving in.

Inelastic supply leads existing residents to sort themselves into those who will leave when their real incomes suffer from the housing shortage and those who have reasons to remain there even after paying ransom rents. In fact, that paper notes that less-than-college workers are more likely to prefer to live in the region they were born in. I wonder if there is some sort of more recent survey data that would reflect the self-selection of remainers over time in the Closed Access cities to residents with stronger than average preferences for that.

This points to another problem with the conclusion in the San Francisco Fed letter. Much of the increase in local average incomes comes from that self-selection into displacement. Figure 6 visualizes the effect of the shortage on displacement. In an amply supplied market, prices are symmetrically correlated with incomes, and so are migration patterns both within and into and out of the market.

Figure 6

In undersupplied markets, the premium on lots within the market reflecting the lack of supply in the market creates a relatively uniform premium on lots across the market, which proportionately pushes prices of low-tier homes higher. (A $100,000 premium doubles the price of a $100,000 home but only adds 10% to a $1 million home.) So, the margin of choosing to reduce the amenities and luxuries associated with their housing, choosing to be poorer, or choosing to be regionally displaced pushes harder on poorer residents. Poorer residents are more likely to both pay more and to move away under those conditions. And, as I described above, as supply conditions worsen, supply conditions increasingly determine the selection of which families live in which city. As economists would put it, supply conditions are endogenous to average income.

When families are displaced from Los Angeles to Phoenix, the average income of families that remain in Los Angeles rises while the average income of families in Phoenix declines. Before 2008, there was little relationship between incomes and home prices, cross-sectionally, except for the Closed Access outlier cities. That’s because where housing markets operate like the left panel of Figure 6, migration really does operate like the spatial equilibrium model says it should. Prices and incomes tend not to deviate so much from city to city because families move for utilitarian reasons on amenities with tradeable values. As migration became easier across the 20th century, regional incomes converged, and have remained more uniform across the country. Then, in the cities that enforced vertical housing supply curves, local average incomes moved much higher than in other places because of the asymmetrical costs on poorer residents. Since 2008, every city has a shortage of some scale, and so they all look a bit like the right panel of Figure 6.

Also, as I noted in my recent Mercatus paper, where this asymmetry is dominant, value weighted averages tend to understate the experience of rising housing costs for the average family. So, migration causes the income trends of Closed Access cities to be overstated, and the arithmetic causes costs to be understated. If you picked the average family in the Closed Access cities in 2000 and followed them over those 20 years, they likely had less income growth and more housing cost growth than Figure 4 suggests.

Now, as the country slowly redevelops the capacity to build homes, differences in local demand determine how asymmetrically expensive housing is going to be, and how much self-selection into local and regional displacement poorer residents will have to engage in.

There has been some recognition of the change in supply elasticity. But, since the entire academy doesn’t know about the most important thing that happened in the last 20 years, they fill in the 80% gap with other explanations, like Glaeser and Gyourko pointing to zoning.

Under current zoning conditions, as national capacity to build continues to grow, local differences in single-family elasticities will start to matter more again, though it will require much more investor activity. Let’s hope we get to those conditions before that market is banned.