A housing comeback is now underway; that much is clear. Adding to a steady drumbeat of positive data for the sector, new data on Tuesday showed a surprising 3.6 percent gain in housing starts in October, which came on the back of a 15.1 percent rise in September.

The question now is how strong it will be and where it will take place. And to answer those questions it helps to look into the fundamentals of the major U.S. housing markets. These numbers suggest the future for housing is looking bright in the Atlanta, New York, and Chicago metro areas. But that’s getting ahead of things.

Housing construction is on the rise, but analyzing prices and rents gives hints of where. Lenny Ignelzi/AP

A good way to look at which housing markets are potentially overvalued and which are undervalued—and where the market seems to be begging for new home construction and where there is still a surplus of unneeded houses—is to look at the relationship between rents and home prices. Over long periods of time, the price to rent a given house should rise at about the same rate as the price to buy one.

But over shorter periods of time, the two can diverge. And when they do, it is usually a sign that something curious is up in that market. For example, from 2000 to 2005, prices in the Miami metro area rose by 136 percentage points more than did rents, a sure sign that it was one of the nation’s most bubbly housing markets.

(Those numbers, like all in this piece, come from comparing changes in the
S&P Case-Shiller home price index for different major metro areas compared with the Labor Department’s consumer price index measure of “Owner’s Equivalent Rent,” for those same areas. Owner’s equivalent rent is a measure of what it would cost to rent the housing stock that people in that city own. Because there are some metro areas for which Case-Shiller data is available and BLS data is not, and vice verse, only 12 major markets are included in this analysis).

Sure enough, in Miami, in the four years starting in 2005, rents kept rising, up 23 percent, while home prices fell 38 percent. Essentially, the imbalance reversed itself.

Few places have experienced booms and busts quite that dramatic, but the same analytical tools can help explain what cities are poised for a rise in prices and construction in the future. When rents are rising faster than home prices, it is a sign that purchasing a home is becoming relatively more affordable, and so it will behoove people to seriously think about buying. That in turn should create upward pressure on prices in the future and so coax builders into the market.  These things can move in slow waves, so it’s not necessarily proof that the markets flashing green lights for improvement will get better next year. But over time, this is a solid indicator of where new construction ought to occur.

As alluded to above, the biggest divide between rents and prices, both over the last year and the last three years, has been in Atlanta. It was a city that experienced far less of a housing bubble during the 2000 to 2005 years, with price increases outstripping rent increases only 22 percent percentage points (recall that in Miami that was 136 percent). But despite having missed the excesses of the boom, the Atlanta metro area housing market still saw a steep price drop during the housing bust, falling 16 percent drop from 2005 to 2009. Prices have continued falling in the last three years, even as equivalent rents in Atlanta have been rising slightly. All that adds up to a market that would seem primed for improvement; at this point, Atlanta would seem to be the most undervalued of the 12 major markets examined here.

In the last year alone, prices fell another 6.1 percent while equivalent rents rose 1.3 percent.

A similar, if less dramatic, story is evident in New York and Chicago. Both markets similarly avoided the worst excesses of the bubble, but have had a steady drop in prices since then at a time rents in those places kept rising. Over the last year, New York saw a 1.4 percent rise in rents and a 2.3 percent decline in prices, while Chicago experienced a 1.7 percent rise in rents paired with a 1.6 percent drop in prices. Both point to a rebound in home prices and construction activity in the future.

What markets are showing the opposite trend, with prices rising much faster than rents? The good news is that there are no markets showing numbers that are dramatically out of whack. The two with the largest spread between prices and rents are those that were so distorted by the housing boom and bust that it is hard to know how to read their numbers. In Miami, home prices rose 4 percentage points more than rents over the past year, and in Detroit that was almost 6 percent. But over a longer time horizon, going back to 2000, both Miami and Detroit still show the reverse, so there may be a catch-up effect underway.

The best news out of this analysis, though, may be this: Most of the largest U.S. cities have housing markets that have been in pretty good balance over the last year, with prices rising at about the same rate as rents.  That’s true of the Washington metro area ( where prices are up 4.3 percent, rents up 2.4 percent), and also of San Francisco, Los Angeles, Boston, Dallas, Seattle, and Cleveland.

And that may be the best sign for the housing market of all. After all these years of bubbles and busts, ups and downs, there finally is a measure of stability. And that is a shift that bodes well for the economy.