House for rent. Attributed to waltarrrrr.
House for rent. Attributed to waltarrrrr.

Some cities are more expensive to live in than others. Many writers and researchers have attempted to quantify the difference. One commonly used metric is the ratio of median home selling price to median household income. This makes intuitive sense; if home prices are higher, then people will spend more on housing, right? Unfortunately, this metric is deeply flawed. As an example, Detroit consistently ranks among the cities with the lowest price-to-income ratio, which would seem to suggest that it’s an affordable place to live. But an alternate measure—the ratio of median rent to median household income—shows that Detroit is among the least affordable cities. This metric isn’t perfect either (as the rest of the article will demonstrate), but it’s a lot more accurate than the first one.

How can these two measures be so different? Why is the incorrect measure so widely reported? And can this mistake teach us anything about how we should plan and build our cities?

Broadly speaking, there are four reasons that house prices do not, by themselves, tell us much about affordability.

Selling price is not cost of ownership

The selling price of a for-sale home is only loosely related to the monthly costs of living in that home. Here is a short sample of costs that are not included in the selling price:

  • Mortgage interest, and possibly mortgage insurance.
  • Property insurance.
  • Property taxes.
  • Utilities.
  • Homeowners’ association dues (or the equivalents for condos or co-ops).
  • Maintenance and repair expenses.

Some of these costs are roughly correlated with selling price. Others may be completely unrelated, or even inversely correlated. For example, if two properties are otherwise identical, but one of them has higher taxes or HOA dues, then it will sell for a lower price than the property with lower taxes or dues.

More generally, the fact that a city has cheap homes for sale does not tell us whether those homes are in habitable condition. If one city is full of homes in excellent condition, and another city is full of fixer-uppers in disrepair, then of course the first city’s homes will sell for a higher price, but that does not actually mean that residents will pay more (once you factor in repair costs).

Property is an income-producing asset

There are many ways that people can earn income. They can work at a job, and receive regular wages. They can own a business. They can work on a freelance or contract basis. They can own financial assets, like stocks and bonds. They can own real estate, and receive rental income.

Most of the time, income takes the form of money. Maybe you get a paycheck, or you get a rent check from your tenant. But income can take other forms. For example, suppose that a friend asks you to house-sit while they go on vacation for six months, in exchange for free rent. You’re doing a job (taking care of their house), and you’re being paid (a free place to live).

In the case of housing, there’s a very important class of non-monetary income. If you own a home outright, and you live in it, then you don’t have to pay rent.

Let’s say that Alice and Bob live in identical side-by-side houses. Alice owns hers outright; Bob rents his. All else equal, Alice is in a better financial situation than Bob. But why, exactly? We could say that Alice’s housing expenses are lower than Bob’s, and in a sense, that’s true. But in another sense, Alice and Bob are both consuming the same amount of house. The real difference is income. Alice owns an asset (her house) that pays her a “coupon” for free rent each month. If she rented her home to a tenant, then she would receive a rent check; instead, she effectively pays rent to herself.

In economics, this “coupon” is called imputed rent. Roughly speaking, imputed rent is the rent that the occupant of a home would have paid the owner of a home, if the owner and occupant weren’t the same person. You can think of it as the hypothetical fair market rent of an owner-occupied home.

When we factor in imputed rental income, we can see that high home prices are not as bad for affordability as they might seem. Yes, you still need to have enough money for the down payment, and for the monthly payments afterwards. But people who buy homes in these markets are already richer than people who don’t. Their reported income is artificially depressed, because it does not include their imputed rental income. So when we divide median selling price by median reported income, we unfairly penalize cities where selling prices are high.

This leads to the next point:

Renters matter

There are some places where just about everyone owns their home. By and large, these places are not cities.

There are many reasons that someone would choose to rent a home. They might be planning on moving in a short time. They might like the freedom of not having to worry about repairs. They might want to live in a dense urban neighborhood where it’s hard to find any condos for sale at all. But as a rule, renters have a lower income than homeowners.

The median household income is an inclusive group. It includes both owners and renters. But, by definition, the median selling price of for-sale homes does not include rentals.

Consider a city where 50% of residents rent, and 50% own. These numbers are pretty typical for a moderately-dense city like Seattle. In this city, the bottom half of the housing market is rentals, and the top half is for-sale. That is, the nicest rental is not as nice (or as expensive) as the cheapest for-sale home. In addition, the lower-income half of residents rent, and the upper-income half own their home.

In this city, we’re effectively comparing the median household income with the 75% percentile home. We exclude rental homes from consideration, but we do not exclude renters.

We can take this to an extreme. In New York City, a full 2/3 of residents rent. Using the simplifying assumptions above, this means that we’re comparing the median household income with the 83% percentile home. It’s not surprising that a home at the top of the housing market would be unaffordable to a family with a median income. It’s also not useful, if we’re interested in understanding the affordability of a housing market in general.

Transportation costs

Most people live in one place, but they travel to many others. They will use some form of transportation to get to and from work, school, medical appointments, errands, and leisure activities.

It would be nice if transportation were free. And if you walk everywhere, it is. But once a vehicle is involved, the costs add up. Bicyclists must buy and maintain a bike and equipment, or maybe participate in a bike-share program. Transit services generally have fares. Cars are very expensive to purchase, and then you have to buy gas, and otherwise keep them in good shape. Taxis and other hired-ride services cost money each time you ride.

Unsurprisingly, where you live plays a huge role in how much you spend on transportation. Some of the lowest transportation costs in the country are found in Manhattan, where about 80% of households do not own a car. In Manhattan, you can easily get anywhere you need to go by walking, biking, riding the subway, or taking a taxi. At the other extreme, some people in Sun Belt exurbs must drive over 50 miles each way to get to and from their jobs.

The high cost of transportation in outlying areas isn’t due to bad planning or government inaction. It’s a fundamental law of geometry. If you live far away from everyone else, then you will have to travel a long distance to get anywhere. And if the places you’re going are popular, you can expect a lot of congestion along the way.

In short, it’s misleading to measure housing costs without considering transportation costs, just like it would be misleading to consider the cost of purchasing a car without considering insurance and gas.

An alternative

Given all these problems, is there a better metric we can use?

In fact, there is. For each owner-occupied property, we can calculate the imputed rent. This tells us how much the occupant would be paying in rent if they didn’t own their property.

Using this data, we can calculate the median rent in a city, including both imputed rents for owner-occupied properties, and observed (actual) rents for rental properties. Because imputed rents take into account all of the costs of owning, this allows us to fairly compare the cost of all housing in a region.

We can also add imputed rent to household income (adjusting for the costs of acquiring that income, e.g. mortgage payments, property taxes, etc.), as a way of recognizing that households with a lot of home equity are richer than households without it.

Finally, we can compute the expected transportation cost for each census tract in a region. We can add those costs to the housing costs, to come up with a estimated annual expenditure for housing and transportation.

The resulting quotient, of median household imputed/actual income divided by median household imputed/actual rent+transportation cost, would give us a meaningful number that truly reflects the affordability of living in a region.

In a future post, I will attempt to compute these numbers for a handful of major cities in the US.

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3 COMMENTS

  1. Absolutely brilliant! This discussion formalizes a lot of things I previously grasped intuitively, but could never state so clearly. Looking forward to your attempts to build a better cost of housing formula.

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