Home foreclosures are still high, but they’re falling and falling fast. That’s potentially good news for the economy.

Real estate research firm CoreLogic reported on Wednesday that a total  of 45,000 homes were foreclosed on in December, down 14% from December 2012 and 4.1% from November 2013. For the year overall.

For the year, 620,111 homes were foreclosed on, down 24.4% from 2012 and the lowest level since 2007.

Falling foreclosure levels help support home prices. They also reflect a far more stable jobs market nationally than in the depths of the Great Recession.

The national unemployment rate was 6.7% in December, down from a  10% peak in October 2009. Some 7.6 million jobs have been added to the economy since payroll employment bottomed in February 2010.

CoreLogic said the inventory of foreclosed home nationally fell to  837,000, or 2.1% of all homes, from 1.2 million homes, or 3% of homes in December 2012. That’s a decline of 30.5% and the 26th consecutive month of year-over-year declines. But there were pockets of weakness, including New York, New Jersey and New York. Their foreclosure inventories were above 4% of all homes.

All 50 states saw their foreclosed inventories drop in 2013. States with the largest drops in foreclosed inventory were California (down 54.6%), Arizona (down 46.8%) and Colorado (45.7%).

For CoreLogic, the data suggest the national housing market has started  a recovery after basically collapsing between 2008 and 2011. While the  company sees the recovery continuing in 2014, CEO Anand Nallathambi  warned “we expect progress to remain very slow.”

After big price increases in 2013 in most markets, most real estate  economists see price gains dropping to around 5%.

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