The boom in Phoenix was founded on a basic truth: it was a place where many people wanted to live. But the market turned irrational. Investors bought homes they did not even bother to rent out. They merely waited a few months until prices rose again so they could flip them.

Ordinary homeowners got caught up, too. “People saw themselves as cashing in on a once-in-a-lifetime opportunity,” Mr. Guntermann said.

Except for the few who managed to get out at the peak, it was a mistake. By now, anyone who bought in Phoenix a decade ago would have lost money after inflation. Many did not get off so easily. Foreclosure notices were filed against one in 40 houses in the metropolitan area in the first quarter, according to RealtyTrac Inc. That was the ninth-highest rate in the country.

The Case-Shiller data show that housing markets across the United States are still suffering. Half of the 20 metropolitan areas in the index posted record year-over-year declines. In all, the 20-city index was down 2.2 percent from January.

From Atlanta to San Francisco to Chicago, not one of the 20 cities posted a gain in home prices from January to February, and values in all but five cities dropped by double digits from a year earlier.

The nearly 51 percent drop in Phoenix is not an isolated plunge. Prices in Las Vegas are down some 48 percent from their peaks. They are down 45 percent in Miami from their highest levels, and down 40 percent in Los Angeles and San Diego.

Economists said housing prices would probably continue to fall as Americans, worried about rising unemployment and the recession, put off big financial decisions like buying a home.