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A different way of measuring what we spend on housing.

Most lists of the least affordable metros in America include San Francisco, New York, Boston, and Washington – four cities that share a notable characteristic beyond their hefty housing prices. They all have solid public transit, an asset that should, in theory, allow residents to devote more of their income to housing than would be typical in, say, car-dependent Kansas City.

Most housing affordability metrics, however, aren't good at capturing these local differences: the willingness of people in some places to spend more on housing than in others, the related costs that make that possible, the relativity of "affordability" itself.

A family with a median income, buying a median home in metro San Francisco, for example, historically devotes more than twice the share of monthly income to housing as a family with a median income, buying a median-priced home, in Atlanta. This is one way of saying that people in San Francisco have to spend a whole lot more to get roughly the same thing as comparable households in Atlanta. But it also suggests, on some level, that San Franciscans are willing to pay more for housing (and maybe less for travel, or transportation, or dining out).

Does that willingness mean, by extension, that more housing is within reach of people in San Francisco than we often think? And would that make the region more affordable than its stereotype, using a hyper-local standard of "affordability" that would never make sense in Atlanta?

The National Association of Realtors measures affordability by comparing median home prices to median incomes in an area. They assume that people spend 28 percent of their pre-tax income on housing costs (mortgage principal, interest, taxes plus insurance). They also assume you'll put down a 20 percent down payment. If a family with a median income can do all of that while affording the median-priced home in an area, that's a big sign that the market is affordable.

In metro San Francisco, though, if most people actually expect to devote something more like 50 percent of their income to housing – and if other infrastructure in the city makes that feasible – the premise behind this calculation doesn't work very well.

Let's frame this in charts, courtesy of the Urban Institute. Here is a ranking of the 37 largest metropolitan statistical areas in the U.S. by housing affordability, using the traditional measure of what that means:

"The Impact of Mortgage Rate Increases on Housing Affordability," by L. Shi and L. Goodman

DTI is the debt-to-income ratio that assumes here that people spend 28 percent of their monthly gross income on housing. In metros above 1, median income is more than what you'd need to buy the median-priced home. In metros below 1, the median-priced home is beyond the reach of someone on a median income. By this measure, San Francisco fares the worst.

Lan Shi and Laurie Goodman of the Urban Institute's Housing Finance Policy Center have made some adjustments to these numbers. "We need a way to measure different willingness to pay for housing across places," they write. And so they tried to measure that willingness by looking at actual debt-to-income ratios in each metro area back in 2000-2003 (that was a period of "relatively rational housing prices" in between the tech bubble and the housing boom).

When you factor in the fact that people in San Francisco typically pay more of their income for housing than people in Detroit, the chart now looks like this:

San Francisco grows considerably more "affordable" (or, perhaps, less unaffordable). Atlanta's position grows worse. We can go one step further and factor in the local differences in how much money people tend to offer as a down payment. The more money you put down, the smaller your subsequent mortgage payments become (expressed in a smaller loan-to-value ratio). In the early 2000s, people in New York were making relatively larger down payments on median homes than people in San Antonio. Factor in those regional differences, and the picture changes a little more:

This regionally adjusted measure essentially looks at whether a family with a median income can afford a median-priced local home – if they do what most people in the region have historically done. Consider affordability that way, and New York and San Francisco fare better. Detroit is still affordable, but not by such a landslide. And Atlanta actually tips into unaffordable territory:

These numbers can't capture exactly what people are doing with the money they don't spend on housing, or even why they might be willing to spend so much in a city like San Francisco. But this last graph suggests, for instance, that people living in metro Atlanta may have higher costs from some other source (perhaps transportation), leading them to spend a smaller share of their income on housing. And if that's the case, the region may be less affordable than its real estate listings alone imply.

This analysis from Shi and Goodman begins to address the criticism that "unaffordable" city rankings unfairly finger dense, transit-rich places where it's possible to live without a car (transportation, after all, is typically a family's second largest budget item). We'd need a lot more data about how people are spending all their income to fully understand these tradeoffs. But this is a useful step toward thinking about "affordability" by its most relevant rubric: a local one.

Top image: Radoslaw Lecyk/Shutterstock.com

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