The deeply depressed housing sector finally seems to have found its bottom — and may even be starting to bounce back.

A wide range of housing indicators — construction, home sales, prices — have stabilized in the past few months, although they remain at historically very low levels. And it looks as if construction activity in particular will pick up in 2012.

The latest evidence of the momentum — new-housing starts for November — was released Tuesday. The surprising 9.3 percent gain bumped the rate of new-housing construction to its highest level in 19 months, to a rate of 685,000 new units a year. The number of building permits issued for new houses and apartments also rose, to 5.7 percent in November.

“The good news is that housing has switched from being a drag on overall growth, to modest positive contributions,” said Brian Bethune, chief economist of Alpha Macroeconomic Foresights.

Behind this improvement was a combination of powerful demographic trends, differences in the job and housing markets in various local economies, and the half-decade in which very few homes were built or renovated.

In normal times, about 1.2 million new households are created in the United States each year, because of rising population. That number falls during bad economic times as more young adults live with their parents, retirees move in with their children and immigration declines. But it doesn’t fall as dramatically as has home construction amid the housing bust and recession.

Housing starts peaked in January 2006, and for the past five years the United States has been building considerably fewer new houses each year than demographics would seem to demand — 554,000 units were started in 2009, for example, and 587,000 in 2010.

Part of that gap is attributable to the excess built during the housing bubble, when more houses went up than demographics would support. More than 2 million units were started in 2005 alone. With so many homes to fill, there has been little need for more.

But the construction boom was not uniform. While far too many houses were built in markets such as Miami, Las Vegas and Phoenix, other regions experienced only a moderate oversupply. And many of those other markets have seen improved job growth this year.

A house in Las Vegas isn’t much use for someone who has a new job in Dallas or Washington. So even as the housing-bubble cities are still hobbled with a glut of vacant homes, building activity is rising rapidly in some of the stronger local economies.

In the first 10 months of 2011, the number of permits for new-housing units rose 36 percent in the Los Angeles metropolitan area over the corresponding period in 2010. The gain was 31 percent in Dallas, 32 percent in Washington and 35 percent in San Francisco.

In some of the housing-bubble markets such as Phoenix and Riverside, Calif., there was little or no increase.

The strongest gains in housing activity in November, as in recent months, were in apartments and other buildings that contain more than five units. That reflects a shift away from home ownership toward renting.

Even after a 50 percent rise in multi-family housing starts this year, “we expect a similar pace of growth next year,” Bank of America-Merrill Lynch senior economist Michelle Meyer said in a research note. It has its roots in a shift toward renting among Americans buffeted by foreclosures, a weak job market and tight credit.

The rising demand for apartments has driven up rent prices. Nationwide, there was a 3.4 percent gain in rents over the past 12 months, according to Labor Department data, compared with a 2.4 percent rise in all consumer prices. Some individual markets saw much larger gains. And those higher rents are coaxing developers to see opportunity.

“We have been and expect to continue to be very active in all aspects of our investment activity,” Bryce Blair, chief executive of AvalonBay Communities, said in a conference call with analysts last month. The Arlington-based company owns about 50,000 housing units across the country and has $1 billion worth of development underway. Blair noted rising rents and the dearth of new-building projects.

It’s hard to know how much of that shift is by choice — people avoiding the risk of buying a house that could decline in value — and how much is driven by the difficulty in getting a mortgage loan. But the reasons don’t matter much for the broader U.S. economy. If the gains in new permits and housing starts keep up, they could put construction workers back on the job.