The S&P/Case-Shiller 20-city home price index increased 4.9 percent in April, and new homes sales rose in June to the highest level since 2008. So all's well in the housing market, right?

Not exactly. "Bidding wars, a hallmark of last decade’s housing boom, are making a comeback in a number of metro areas across the U.S.," writes Wall Street Journal reporter Kris Hudson. That includes thriving cities like San Francisco, Seattle and Denver.

"While the earlier wars reflected enthusiasm fueled by easy-money mortgages, the current froth stems from a market short of homes for sale," he says.

The inventory of homes for sale totaled 2.3 million as of May 31, which would last for 5.1 months at the current sales rate. In a healthy market, the figure would be six to seven months, according to the National Association of Realtors.

The problems include sluggish home-building and the reluctance of many homeowners to sell their abodes, Hudson explains. Their fear stems from worries that they won't qualify for a new mortgage, they can’t afford sales costs and that they'll lose out in the bidding war for their next home.

Former Federal Reserve Chairman Alan Greenspan has worries of his own about the housing market. He notes that the pace for new construction of both homes and commercial properties hasn't returned to the lofty levels that prevailed before the 2008 financial crisis.

"We haven't come out of the bottom," Greenspan told CNNMoney. "We are in the position now of secular stagnation" for real estate.

Before the 2007-09 Great Recession construction of homes and buildings expected to last for 20-plus years accounted for 8 percent of GDP. Now it's only 4 percent, Greenspan notes.

And that's bad news for the overall economy, because real estate construction played a key role in each of the 10 rebounds from recession since World War II, Greenspan explained.

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