NEW YORK ( TheStreet) -- There is some good news on the housing front with two reports indicating the long-stagnant U.S. real estate market is climbing to its feet and growing more stable. The first indicator comes from CoreLogic, which says the nation's current "shadow inventory" of homes is in decline, a healthy sign more houses are moving off the "for sale" market. According to CoreLogic, shadow inventory fell 10% from July 2011 to July 2012, from 2.6 million to 2.3 million units. That's about the same level in March 2009, when the U.S. housing market was sinking fast. "Broadly speaking, the shadow inventory continued to shrink in July," says Anand Nallathambi, president and CEO of CoreLogic. "The reduction is being driven by a variety of resolution approaches. This is yet another hopeful sign that the housing market is slowly healing." As more for-sale homes leave the market, existing real estate prices rise too. Fewer homes on the market leaves buyers fewer options, making the real estate market more competitive and thus more expensive for buyers. That's good news for Americans looking to sell. The second piece of good news for the U.S. housing market comes from the U.S. Department of Housing and Urban Development. The agency's September Housing Scorecard, an index the federal government calls a "comprehensive report on the nation's housing market," reports that existing total U.S. home equity has risen a whopping $860 billion since the end of 2011. In addition, August saw the highest level of existing home sales in two years. "As the September housing scorecard indicates, our housing market is showing important signs of recovery -- with homeowner equity at a four-year high and summer sales of existing homes at the strongest pace in two years," HUD Acting Assistant Secretary Erika Poethig says in a press release. HUD reports that total U.S. homeowner equity rose by $406 billion in the second quarter of 2012 and has grown by 13% since the end of 2011. In addition, the number of U.S. homeowners who are underwater on their mortgages (where the mortgage balance owed exceeds the value of their home) has fallen by 11% since 2011, a healthy sign for homeowners and the U.S. real estate market.