WASHINGTON – By most economic measures, the moribund housing sector seems to have turned a corner and is now firmly in recovery. For many homeowners, however, it may still feel like a statistical rebound because an improving housing sector is not the same as a healthy one.

Economists are broadly in agreement that housing is no longer weighing against economic growth and will actually be a positive contributor in 2013.

That’s supported by most measurements of the housing sector, such as starts of new single-family homes, sales of existing homes, rising median home prices or shrinking foreclosures as a percentage of total sales.

“The current forecast is for 5 million existing homes and 500,000 new single-family (housing starts). That’s a pretty healthy growth in existing sales of about 8.5 percent,” said Danielle Hale, director of housing statistics for the National Association of Realtors.

Sounds good, but there is a sobering footnote.

“They’re coming off of extraordinarily low levels,” Hale cautioned. “That’s still a below-trend growth rate. Obviously if the economy improves beyond what’s forecast, then the housing position will be better.”

After several years of false projections that housing had hit bottom, it appears that the sector truly is now in recovery mode.

“I think housing has clearly bottomed. But I think there is clearing skies, not blue skies,” said Mark Vitner, senior economist with Wells Fargo Securities in Charlotte, N.C. “It’s going to be years for housing to get back to what’s considered normal. But we’re going to see improvement along the way. We have a great deal of improvement in virtually every metric that matters to housing.”

Pending home sales, although declining in December, have stayed above year-ago averages for 20 consecutive months, according to data released last week by the National Association of Realtors.

And the group reported earlier in January that housing was at record affordability rates in 2012, for the second straight year. “Distressed” sales, which in 2011 represented 32 percent of all home sales, fell to 24 percent at the end of last year.

“It is robust; we are starting on a recovery; we don’t think there is going to be a second housing market downturn for the whole country,” said Andres Carbacho-Burgos, an economist specializing in housing for forecaster Moody’s Analytics in West Chester, Pa. “We believe that the housing sector is no longer a drag on economic growth. That’s the good news. The bad news, if you can call it that, is that the housing recovery is not going to be spectacular.”

An improving housing market is important for U.S. economic growth. For much of 2005 and 2006, investment in residential housing ranged between 5.5 percent and 6.3 percent of the nation’s gross domestic product, the broadest measure of the sale of goods and services. It plunged during the financial crisis of 2008, dropping to just 2.2 percent of GDP for most of 2011 and climbing to just 2.6 percent of GDP in the final three months of 2012.

Whether it’s a good or a bad market depends on perspective. For the first 11 months of 2012, a housing affordability index compiled by the realtors’ group showed record levels, and that’s great for buyers. The index measures the relationship between median home prices, median family income and average mortgage rates.

And prices are going up, which on the face of it would seem like good news for sellers. The latest read from the closely followed Case-Shiller Indices, which track metropolitan home prices in 10-city and 20-city composites, was positive. Data released last week that span a 12-month period ending Nov. 30 showed that prices rose 4.5 percent on the 10-city index and 5.5 percent on the 20-city index.