More broadly, politicians and investors are placing a great deal of weight on a crude and rough estimate that has never been particularly reliable.

“People want the best information that we have right now. But people need to understand that the best information that we have right now isn’t necessarily very informative,” said Tara M. Sinclair, an assistant professor of economics and international affairs at George Washington University. “It’s just the best information that we have.”

The growth rate that the government announces roughly one month after the end of each quarter — news much anticipated in Washington and on Wall Street — has been off the mark over the period from 1983 to 2009 by an average of 1.3 percentage points, compared with more fully analyzed figures released years later, according to federal data.

The second and third estimates, announced at subsequent one-month intervals, are no more reliable. The first quarter this year offers a typical example. The government estimated the annual growth rate at 1.8 percent in May and 1.9 percent in June before issuing its most recent estimate of 0.4 percent.

Perhaps more important, the government underestimated the depth of the recession by a wide margin, initially calculating that the economy contracted by an annual rate of 3.8 percent in the last quarter of 2008. It now estimates the contraction rate at 8.9 percent. Instead of an annual growth rate of 0.2 percent from the fourth quarter of 2007 through the first quarter of 2011, the government now estimates that the economy contracted at an annual rate of 0.2 percent during that period.