The consumption basket we call "housing"
The other day, my Mercatus colleague Salim Furth tweeted:
Prices are set by the 'marginal buyer' (or renter). In a diverse world, that's impossible to pin down, but we can think about extreme cases.
a) You and almost everyone else care about subway access
b) You care about living near your grandma
Since the marginal buyer cares about (a), you're going to have to pay for it. But (b) will be free. So far so good?
Now suppose we have something else that people care about *in different amounts* (which, on reflection, is going to be everything). Let's say bike lanes.
OK, so bike lanes: Let's say that the marginal renter is willing to pay $20/mo for a good bike lane. But I'm a low-wage worker, I don't bike much, and I only value it at $5/mo. Do I want it to get built?
No! It would benefit me by $5/mo and raise my rent $20/mo: not worth it.
This is an explanation for why people in expensive cities sometimes oppose public amenities.
Sometimes, these positions are a facet of my maxim that “Closed Access makes all good things bad.” With artificial scarcity, everything goes to the highest bidder. All the consumer surplus that makes us a wealthy society gets bid away. For a lot of urban Americans, nice things are a threat. Amenities mean displacement when they are bundled with scarce housing. This leads to an odd situation where locals object to improvements in their neighborhoods or their cities.
After seeing Salim’s comments, I thought this might be an interesting way to talk through what happens as a city turns from 2002 Phoenix into 2023 Los Angeles.
It may be helpful to think of housing demand in 4 categories.
Shelter
Price settles at cost, variable across metro
Neighborhood Amenities
Price determined by income, variable across metro
Metropolitan Area Scarcity
Price determined by income, uniform across metro
Endowments
Idiosyncratic, determines inter-metro migration
Figure 1 shows Price/income ratios across ZIP codes as a guide for thinking about these elements.
Shelter
This is the most equitable source of housing demand. First, a 2x4 is a 2x4, and the Home Depot in your neighborhood isn’t going to raise the price of 2x4’s just because your neighbors are more able to afford them. The price of a 2x4, over time, is roughly the cost of creating a new 2x4.
So, to a first approximation, every household lives in a house that has the quantity and quality of 2x4’s (and shingles, and countertops, and toilets, etc.) that they can afford.
But, that’s not even the half of it. Once a house is built, it depreciates. Some of that depreciation requires maintenance (hot water heaters, air conditioners, etc.), some of it is discretionary (bathroom fixtures, furniture, countertops, etc.), and some of it will mostly just keep on keepin’ on well after it has justified its original cost (walls, foundation, joists, etc.)
In Figure 1, in an affordable city like Phoenix in 2002, the poorest families and the richest families all typically live in homes that reflect their incomes proportionately. In January 2002 in Phoenix, that was about 3x annual income, whether that income was $30,000 or $100,000.
Only a small portion of that distribution is determined by the cost of new homes today. As indicated by the horizontal red arrows for factor 1 in Figure 1, households distribute themselves widely across a metropolitan area. For most of the life of any given house, it is well into its depreciated state. Most of that distribution is a distribution of households through the existing, aging stock of homes.
The natural state of housing, where new building is broadly legal, is for existing homes to depreciate - to filter down. Over time, the new residents who replace the original residents tend to have lower incomes than the original residents had. If homes are filtering down effectively enough, then the existing stock of homes becomes a blank slate for the current population to maintain and update in a way that is appropriate for its current distribution of incomes.
This is why most cities used to look like Phoenix in Figure 1. When homes are filtering down effectively, they eventually become depreciated enough and affordable enough that they will be upgraded, or not upgraded, to match the expectations and budget constraints of the families that currently live in them.
The way I would put it is that in a functional housing market, each household’s income determines the cost of their house. That is why the price/income ratio across all of Phoenix in 2002 approximated 3x. Households in the aggregate upgrade existing homes to a comfortable cost level from the bottom up instead of making compromises downward to meet their budget constraints from above. Phoenix in 2002 in Figure 1 is the picture of a healthy free society. It is the picture of consumption largely driven by discretion.
Neighborhood Amenities
Another factor that determines the distribution of families over time across the existing stock of homes in a city are neighborhood amenities. This is basically what Salim’s tweets were about.
To get at this a little more clearly, I have replaced Phoenix and LA in 2002 with Chicago and Washington DC in 2002. Price/income ratios weren’t quite as flat across the city as they were in Phoenix, but they’re pretty close.
Washington, DC and Chicago both have relatively dense, bustling urban cores, with functional mass transit systems. The distribution of households across the stock of homes is not just a matter of 2x4’s and depreciation. Neighborhood amenities are a big factor - access to transit or ability to walk to various important places, crime, aesthetics, etc.
So, two households in Chicago with $60,000 in annual income might have both lived in a $240,000 unit. But one might be in a 1,600 square foot home on a big lot in Aurora while the other is in a 1,000 square foot condo in the Loop.
Some of the difference between those two units is the cost of building up. Some of the difference is the cost and/or value of neighborhood amenities.
Trading off amenities and shelter can be one more way for households to paint their discretionary expenses on the blank slate of a city’s housing stock. If a household needs 1,600 square feet, they can get it for a lot less in Aurora than they can downtown. But, households don’t seem to sort in that way very much. Poorer families in the densest cities tend to live in the densest neighborhoods and pay a price premium to do it.
There are at least two reasons why neighborhood amenities affect prices differently than the cost of shelter does. One reason is that they are uniform across the neighborhood. You can’t opt out of the bike lane or the subway stop. The second reason is that neighborhoods can have negative amenities, like crime.
This creates social conflict. The decisions of other households can affect the cost of your housing. Changes in either the local infrastructure or the socio-economic status of the families that want to live near you (either higher or lower) change your housing expenditures. Category 1 was a utopia of personal control. Category 2 is not.
Change in either direction can happen in any type of city, as geographic patterns emerge and change. But, they do tend to have a direction based on the broader metropolitan area direction of filtering. In cities that allow ample building, the conflict usually arises as the socio-economic status of a neighborhood declines. This is the sort of thing that motivates zoning rules. In cities that don’t allow ample building (because of things like zoning), the conflict is usually related to rising local amenities, status, and cost.
The change and conflict come in either case. In an affordable city, you might have to move a couple miles from where you started, and neighborhood crime is a harsher compromise than outdated Formica. But the displacement (which could mean moving up-market to escape crime or moving down-market to lower costs) is local, and so it isn’t necessarily that disruptive. We aren’t in utopia anymore, but this version of demand does not preclude the availability of affordable housing.
A Digression on Prices and Amenities
One pattern that I have found in my studies about the housing market, which I touch on frequently here is that price/rent ratios are positively correlated with rents, incomes, and prices. All three of those variables are highly correlated, so the reasons for their correlation with price/rent ratios are a bit of a tangle. I have speculated on them in a place or two. Price/rent ratios in ZIP codes with various incomes in Phoenix in 2015 are shown in Figure 3.
One likely reason for the correlation is that non-structural price factors probably have a lower discount rate (and thus, a higher price multiple). As mentioned above, shelter depreciates and requires maintenance. So, net rental income is lower than gross rental income. The price/gross rent ratio has to be lower in order to account for those costs. But, good schools, bike lanes, subway stations, and parks don’t depreciate for the homeowner. So, when those factors increase rental value, the price/gross rent ratio will rise.
In other words, it might cost $500 each month to maintain a $1,000 rental property. But if an identical house across the street rents for $1,200 because it is in a better school district, then its net rental income is likely close to $700 per month. A 20% higher gross rent provides 40% more income to the landlord.
School performance and crime are correlated with incomes for complicated reasons. The home in the better school district may not have higher school taxes. The home in the neighborhood with less crime may not have higher taxes for police.
So, some of this is probably just pure self-segregation. This is one reason that the price of amenities is correlated with incomes. High home prices and rich neighbors are an effective way to maintain good schools and low crime rates in a neighborhood. The causation goes in both directions. The income segregation itself creates amenity effects.
I have not fully appreciated this aspect in my previous speculation about what causes price/rent to be positively correlated with incomes. One reason for the correlation might be that neighbors with higher incomes are a meta-amenity, and neighborhood amenities naturally settle at higher price/rent ratios. A correlation between income and price/rent ratios may be basically mechanical.
Metropolitan Area Scarcity
So far, the first two types of demand have determined how housing is distributed within the population of a metropolitan area. But, the defining problem of our time is that some metropolitan areas have such harsh political limits on new housing production that the entire metropolitan area goes into a state of deprivation. This creates many notable symptoms. Chief among them is a persistent domestic outmigration of families with lower incomes because of rising housing costs. This problem in cities that block housing has been documented by many researchers.
As with neighborhood amenities, this is a uniform factor out of the control of individual households. So, the effect on home prices is not determined by individual preferences. The price is determined by the preference of the marginal household who would choose it, and that is largely a product of income. The more wealth or income you have, the more you can pay for the amenity called “Los Angeles”. When there is plenty of housing, the cost of your housing is a reflection of your income. When there is a lack of adequate housing, the cost of your housing is a reflection of other households' incomes.
Since neighborhood amenities vary across a metro area, households can change neighborhoods to find a match. But, metro scarcity applies to the entire region, because it is caused by the unwillingness of the entire metro area to approve new homes. Households can only sort themselves by paying the higher price or moving out of the region entirely.
This increases prices across the metropolitan area. Viewing the market on a price/income basis, as shown in Figures 1 and 2, makes clear how the relative value of the metro area systematically presses affordability constraints on households with lower incomes, who are unable to pay the price.
It is easy to confuse this category of demand for the competition for neighborhood amenities. In practice, when a metro area lacks adequate housing supply so that there is a metro area premium, demand must express itself as a competition for existing neighborhoods.
Households with higher incomes must trade down into neighborhoods that would otherwise be claimed by households with lower incomes. Sometimes, something like that happens in the category of demand for neighborhood amenities. The difference is easy to see in Figures 1 and 2. Demand for neighborhood amenities causes some households to change neighborhoods in order to maintain a good match between their preferences, their needs, and their budgets, after their previous neighborhood has changed. Displaced households can generally relocate to a location with an appropriate cost level.
When the source of the dislocation is metro area scarcity, the displaced households generally must accept higher costs. Anti-gentrification activists frequently fail to make this distinction. If you had to move to a nearby affordable neighborhood because rents rose after a new condo building, bike lanes, and a Whole Foods moved in, then gentrification could be called the cause of your displacement. If the nearby neighborhoods have all become more expensive or you had to move out of the region entirely, then the apparent gentrification was a symptom of metro area housing deprivation. The greater the displacement, the less causal the gentrification was. In a nutshell, this is why being anti-gentrification misses the point and is unlikely to be broadly helpful in maintaining an affordable and functional city. If a study shows that gentrification raises local rents substantially, it might be evidence that gentrification (competition for amenities) isn’t the root cause of the displacement in that case.
If demand for amenities was the extent of it, home prices in LA in Figures 1 and 2 would look similar to home prices in Phoenix, DC, and Chicago. Competition for neighborhood amenities causes some neighborhoods to be somewhat more expensive than others. Since it comes bundled with a lot of resources like accessible public transportation, the average household in the condo in the Loop spends more on housing than the average household in Aurora spends. But, mostly, households sort geographically into neighborhoods that match their socioeconomic status.
Competition for Metro Area amenities works the same, but the personal cost of regional displacement is so much higher than the personal cost of neighborhood displacement that avoiding regional displacement forms an entirely different category of housing demand. We can infer that regional displacement is much more painful than neighborhood displacement because we can see its much greater influence on home price trends.
Endowments
The endowment effect is idiosyncratic and highly variable. In Salim’s tweet, “living near grandma” is one facet of it. It could be access to a type of job, access to certain public support resources, friends, local knowledge, occupational licenses, etc. Some people live in a place that doesn’t have any endowment value for them, and they do move regionally just like some people move neighborhoods.
You can see the idiosyncratic nature of this category of demand in public discourse about the housing problem. Sometimes locals will complain about the cosmopolitan class who just moves from city to city, with no deep local connection - no care for local institutions and culture - and displaces the real locals whose values made the place what it is. Complaints about tech workers in San Francisco or finance professionals in New York City can take this form.
And, that really is a specific description of what is happening. The reason there is tension is that the category of demand that the cosmopolitans are acting on is Metro Area Scarcity, and their demand is expressed as a portion of their incomes. Since their incomes are high, they can outbid locals for Metro Area Scarcity.
But the locals can’t just move away, because the metro area has endowment value for them. This is a cost that applies only to them. The family next door might choose to move away at the first sign of rent inflation. The households who truly are connected to the community won’t do that.
A Mix of Motivations
Let’s walk through a hypothetical case of the housing demand of two households in two scenarios.
Scenario A - An amply housed city (20th Century LA)
In a city with enough housing, households trade off shelter and amenities in a process of segregation. In this example, a typical household with $75,000 annual income will choose a home that costs about $300,000 - 4x their income. Here, I assume that cost is mostly in the shelter of the home, with some positive neighborhood amenity value. In reality, the $75,000 household in scenario A could make a different trade-off between amenities and structures, or (in terms of the graph) move their dot up or down, left or right, depending on preferences. What is important is that there is a spot on the graph that is a comfortable baseline from which to express those preferences.
The family that makes $150,000 will likely live in a more valuable house in a nicer neighborhood with more amenities, as described above.
Both households could hold any range of endowment value for their neighborhoods or the region. It doesn’t matter. In an amply supplied market, as Salim said, you don’t have to pay for your idiosyncratic preferences. In both cases, the households pay for the structural and neighborhood preferences they value and no more.
Amply housed cities change. Those dots aren’t stationary. So, it is possible that the $75,000 neighborhood is in a prime location that will become more sought after as the city grows. It is possible that the neighborhood will start moving to the right (attracting households with higher incomes). That will make its amenity value rise. It may become a poor fit for the $75,000 family.
Generally, these changes are slow and of a small scale. But, one can imagine being motivated to oppose the proverbial bike lane if you’re the $75,000 family. In scenario A, at most, the $75,000 family would be motivated to move to a nearby ZIP code that hasn’t shifted right.
Most of the time in a growing city, the ZIP code is transitioning down. Incomes rise over time while homes naturally depreciate. In most places with a growing economy, it is a mixture of changing households and changing houses that creates change. The $75,000 family is likely to slowly become a $100,000 family. If their neighborhood continues to be a $75,000 neighborhood, the family might shift right while the neighborhood shifts left, in relative terms. This is the filtering process, and it happens everywhere that housing is affordable.
Scenario B - An under-housed city (21st Century LA)
When a city obstructs new construction, homes have to become expensive enough to trigger outmigration. This is scenario B. As described above, we can think of the demand for housing in this context in two categories - Metro Area Scarcity (the uniform value of living in the metro area - local industry employment opportunities, etc.) and Endowments (living near family, support services, etc.)
Since there aren’t enough new homes, households have to engage in compromises between the 4 categories of demand. In this hypothetical, Scenario B forces the $150,000 family to compromise down in the structures and amenities they are willing to accept. Now, the $150,000 family is bidding for a home in the $75,000 family’s neighborhood.
Their home had been worth about $300,000 in Scenario A. Now, the $150,000 family is willing to pay the $300,000 for the home, and they are willing to pay more for amenities. Maybe those amenities were free amenities before. Maybe they are the amenities related to having neighbors with higher incomes. Maybe the bike lanes and Whole Foods stores follow the $150,000 family to the neighborhood and increase the amenities. All of these effects on the neighborhood are a different facet of the change, but at their root they all are caused by the lack adequate housing.
Because, if there was enough housing in the metro area, in general, there wouldn’t be a Metro Area Scarcity premium, and the $150,000 family wouldn’t be making compromises in structures and amenities. They would still be buying a home with 4x their income in structural and amenity value. Since there is Metro Area Scarcity, they are buying a home for 5-6x their income which only has structural and amenity value of 3x their income.
For the $75,000 family in the house that should cost $300,000, at first, they probably also are willing to pay some Metro Scarcity premium. Maybe they are willing to live in a $500,000 house because of the uniformly shared preference to live in the city.
But, as demand ratchets up, and the house goes from $500,000 to $600,000, and up, they are faced with a lack of local alternatives, and they must make increasingly difficult trade-offs. Now, since they don’t have local alternatives, they might have to pay for their personal endowments. They might have to pay to live near grandma.
In fact, this is what determines the price of a house in LA. Housing supply is determined by the willingness of locals to be displaced. More housing supply lessens the Metro Area Scarcity premium. So, if nobody had any endowments in LA, then as soon as the Metro Area Scarcity premium increased the home price of the $75,000 family above 4x their income, they would move away and increase the supply of houses for those who have the means to pay for Metro Area Scarcity.
Those two categories of demand are two sides of a coin. If there is endowment value, then the Metro Area Scarcity premium will increase until the next marginal family has to pay so much for their endowments that they can’t any more.
Let’s add a clause to our LA home price determination. The cost of a home in LA is a reflection of richer households' incomes and poorer households’ endowments. It is a product of how much it is worth to have it in general and how much it hurts some individually to give it up.
In this hypothetical, when the price hits about $800,000, it has finally eaten up all the $75,000 family’s endowments - the value of community, family, safety net resources, etc. - and that family determines the marginal level of Metro Area Scarcity premium that LA requires by moving away and making their home available to the family with more resources.
The $75,000 family might try to retain their endowments by trading down like the $150,000 did - go to a poor neighborhood with negative amenities, smaller, older homes, etc., and create a chain of displacement. But, whether it is them or another family at the end of the chain, someone will have to leave the city.
You can think of homeless families with this model. For homeless families, they have compromised the cost of structure all the way to zero. They are deeply into negative amenities. But the endowments of the local area are positive enough to net out to positive.
Housing supply skeptics and “Superstar city” apologists imagine that homeless families move into their cities to capture Metro Area Scarcity premiums (generous welfare benefits, mild weather, etc.), but most homeless are local. They don’t leave because when you have nothing left, familiarity, community, place, and local knowledge are very valuable.
In a way, the housing supply skeptics implicitly use this model to try to solve the local homelessness problem. If we produce enough negative amenities for them and remove metro area advantages, they will all go back to where they came from. But, if local endowments are what keeps homeless families around, then that is the height of cruelty. That is making it painful enough for them to leave family, friends, and personal support networks.
Since housing deprivation creates these intra-metro competitions, it is easy to see how the $75,000 family might vote for a city council that promises to keep away good-paying employers and sabotage the local economy. You can imagine that someone far enough down the socio-economic ladder might be forced to trade off negative amenities and endowments. “If the police and social workers clean up my neighborhood, lower crime, and make its amenity value less negative, then I will have to pay more for the endowment of living close to grandma. That won’t help me. In fact, people who are willing to pay to avoid negative amenities will price me out of living near grandma. Don’t change the character of this neighborhood!”
In general, families with low endowment value will migrate away and families with high endowment value will trade down to a neighborhood in the metro area with negative amenities.
Another Digression on Prices and Amenities
In Figure 4, I have copied Figure 3, showing price/rent ratios in Phoenix in 2015, and I have added the price/rent for the same Phoenix ZIP codes in August 2023. Supply conditions have been poor across the country since the Great Recession, so all cities look more like Los Angeles today. Prices have increased in ZIP codes in Phoenix where incomes are lower, which is a sign of inadequate supply and an increase in “Metro Area Scarcity” and families paying for endowments. Homelessness is also visibly increasing.
As I described above, price/rent ratios tend to always be higher where incomes are higher, because more of the value of those houses comes from neighborhood amenities. Metro Area Scarcity is another form of amenity. So are endowments. When Metro Area Scarcity increases and endowments must be paid for, a larger portion of home values in ZIP codes with low incomes doesn’t require maintenance and upkeep.
The two-sided coin of Endowment effects and Metro Area Scarcity premium increases price/rent ratios, and it increases them the most in the poorest neighborhoods.
In a city with ample housing, the poorest neighborhoods tend to have the oldest homes with negative amenities, which lowers their price/rent ratio. In an undersupplied city, families self-select into those neighborhoods based on who is willing to pay an Endowment premium.
Conclusion
Whenever locals appear to be irrational, it might be helpful to think about their reactions through their trade-offs. They may be trading a negative amenity in order to afford an endowment or they may be bidding with their endowment demand against a household with metro area scarcity demand.
A city must not let the perfect be the enemy of the good. You want to live near grandma without paying for it? Create amenities and structures for others, which they’ll happily pay for.
great article!