Recent claims that we're already there may be overstated.

Earlier this month, Peter Wallison, a senior fellow at the American Enterprise Institute, wrote a piece in The New York Times warning that another housing bubble was sneaking up on us, and the Internet has been gnawing over his pronouncement since.

Much of the debate has focused on Wallison's long-standing take that government policy caused the last housing bubble. But here is his explanation in the Times for how we'll identify the next one:

Housing bubbles are measured by comparing current prices to a reliable index of housing prices. Fortunately, we have one. The United States Bureau of Labor Statistics has been keeping track of the costs of renting a residence since at least 1983; its index shows a steady rise of about 3 percent a year over this 30-year period. This is as it should be; other things being equal, rentals should track the inflation rate. Home prices should do the same. If prices rise much above the rental rate, families theoretically would begin to rent, not buy.

Housing bubbles, then, become visible — and can legitimately be called bubbles — when housing prices diverge significantly from rents.

Over the last two years, he writes, this has begun to happen again. From 2011 through the third quarter of 2013, housing prices grew by 5.83 percent. Rental costs grew by just 2 percent.

I asked Taz George and Bing Bai at the Urban Institute's Housing Finance Policy Center to plot a graph of what they thought Wallison was talking about (since they've been skeptical of his argument, too). This is it:

Sure enough, home prices and rents closely tracked each other until around the year 2000. Then we get what literally looks like a bubble. And now the light blue line is suspiciously ticking upward again.

Maybe this sounds inconsistent with your own experience in New York, or San Francisco, or Washington, D.C., that rents are at an all-time high. That Rent Index shown above, though, doesn't track median rental rates paid in the U.S. It wouldn't make a lot of sense to directly compare home prices and median rents, because those figures describe two very different stocks of housing. A studio apartment rental isn't comparable to a for-sale single-family home.

Rather, a housing bubble starts to look suspicious when the price of for-sale homes begins to exceed what those same homes are actually worth as, well, shelter. To estimate this, the Bureau of Labor Statistics calculates something called owner's equivalent rent. This metric poses a specific question: If you were to rent the house you own – and the tenant was only interested in the shelter it provided, not some future imagined payoff from selling it – what would it rent for? The cost of shelter is the implicit rent that someone would have to pay to live in your house.

When the price of housing is suddenly a lot higher than this implicit rent, that's one piece of the evidence that people are buying homes based on speculation.

Now, all that said, George and Bai believe that the Home Price Index in the above graph – the Case-Shiller Index that tracks repeat sales over time of the same homes – still leaves something important out of the picture: interests rates. Housing prices alone don't reflect the total cost of owning a home, because the same home will cost more in monthly mortgage payments when interest rates are high than when they're low. And interest rates vary substantially over time.

"For a bubble to occur," George and Bai have written, "the mortgage payment relative to rent must be historically high—a sign that families are continuing to purchase homes even though renting is more economical."

This second chart is similar to the one above, but it compares the Rent Index over time to a Mortgage Payment Index George and Bai created that factors in interest rates (assuming a 15 percent down payment):

Part of what we're looking at in the late 1980s, for example, is the effect of high historic interest rates. Over the last three years, we're seeing a market with historically low interest rates (but with a stricter standard for creditworthiness), where it's actually been more economical to buy homes than to rent them, relative to a typical period. Viewed this way, it doesn't particularly look like a new bubble is forming.

"It looks more like a correction than a bubble," George says.

We can compare the two approaches side-by-side in this last graph. The light blue line shows the ratio of Wallison's Home Price Index to the Rent Index (or, rather, the relationship between them). The dark blue line shows a similar ratio using the Mortgage Payment Index. In the dark blue line, mortgage payments relative to rent aren't historically high at all; they're low, and creeping back to average.

This certainly isn't the final word on the topic. Identifying bubbles is a messy science, and these same graphs would look quite different if we were to drill down to the local level, comparing the markets in, say, Milwaukee and Los Angeles (this is something George and Bai are hoping to do). But after the last housing bubble, we have more reason now than ever to figure out how to identify these things with some precision.

Top image of new townhouses under construction in San Marcos, California: Mike Blake/Reuters.

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