The US economy's 5.7 percent growth last quarter — the fastest pace since 2003 — was a step toward shrinking the nation's 10 percent unemployment rate.

There's just one problem: Growth would have to equal five percent for all of 2010 just to lower the average jobless rate for the year by one percentage point.

And economists don't think that's possible.

Most analysts say economic activity will slow to 2.5 percent or three percent growth for the current quarter as the benefits fade from government stimulus efforts and from companies drawing down less of their stockpiles.

That's why the Federal Reserve and outside economists think it will take until around the middle of the decade to lower the double-digit jobless rate to a more normal five or six percent.

Another way of looking at it: A net total of about three million jobs would have to be created this year to lower the average unemployment rate by one percentage point for 2010, economists estimate. Yet even optimists think the creation of one million net jobs is probably out of reach this year.

High unemployment poses a risk to the unfolding recovery because it leads consumers to spend less, keeping economic growth weak. A sharp pullback in spending might even push the economy back into recession. Joblessness also represents a danger for President Barack Obama's Democratic Party in this fall's congressional elections.

The National Association for Business Economics and the International Monetary Fund think gross domestic product will rise just under three percent for all of this year. GDP, the best gauge of economic activity, measures the value of all goods and services produced in the United States.

To get a sense of just how deep a dent the worst recession since the 1930s has made in the economy, consider this: The economy shrank 2.4 percent for all of 2009 — the sharpest drop since 1946. It was also the first annual decline since 1991.

Mark Zandi, chief economist at Economy.com, and Bill Cheney, chief economist at John Hancock, agree that the economy would have to grow roughly five percent for all of 2010 just to ratchet down the average unemployment rate for the year by one percentage point — to a still-high nine percent.

Their mathematics is based on Okun's law, named for economist Arthur Okun. In 1962, Okun produced a formula for the connection he saw between unemployment and economic activity.

Exactly how much GDP growth is needed to lower the unemployment rate for a given period varies. That's because the formula involves several factors besides GDP growth. It also considers, for example, businesses' productivity growth.

When the economy was recovering from the 2001 recession, it took two years to reduce the unemployment rate by nearly a full percentage point: It fell from sixpercent in 2003 to 5.1 percent in 2005. GDP growth averaged just over three percent.

Economists say the formula hasn't always held up perfectly in recent decades. Rather, it's relied upon as a rough rule of thumb for determining how much growth will be needed to lower unemployment.

But a near-textbook case occurred in 1976, when the economy expanded at a 5.4 percent pace. As Okun would have predicted, that growth drove down the unemployment rate by nearly a full percentage point: from 8.5 percent in 1975 to 7.7 percent.

***

Hopes that America's factories will help drive the economic recovery gained support yesterday from news that manufacturing activity grew in January to its strongest point since 2004.

Other data, though, offered a reminder that the recovery remains fragile. Construction spending sank in December to its lowest level in more than six years. And gains in personal income and spending were too modest in December to suggest that consumers can fuel a strong rebound.

"Right now we're getting a recovery," said Michael Gregory of BMO Capital Markets. "But you have to be skeptical. This kind of performance cannot be sustained unless we get those other areas that are still weak in the economy to contribute to growth — housing, construction, real consumer spending."

Manufacturing activity has become a pocket of strength, though some of it flows from temporary factors such as customers needing to add to depleted stockpiles of goods.

The Institute for Supply Management said its manufacturing index read 58.4 in January, compared with 54.9 in December. It was the sixth straight month of expansion. Analysts polled by Thomson Reuters had expected a level of 55.5. A reading above 50 indicates growth.

New orders, a sign of future growth, jumped in January to its highest level since 2004. So did current production. Order backlogs grew, along with prices companies paid. Thirteen of 18 industries said they were expanding, led by the apparel, textile mills and machinery sectors.

China's manufacturing also expanded in January, and the outlook was positive despite government efforts to cool inflation by tightening control over bank lending, two surveys showed Monday.

US manufacturers have been pumping up production to feed their customers' depleted stockpiles. The ISM said manufacturers' inventories contracted at a slower rate in January. Still, their customers' stockpiles fell to an all-time low.

As their customers try to restock their shelves, manufacturers need to ramp up production to match their demands. That could mean hiring more workers, which would help invigorate the economic rebound. ISM's employment measure grew last month.

"Production growth is finally beginning to tax existing work forces to the point where companies need to expand employment, and, critically, have enough confidence to do so," said Pierre Ellis of Decision Economics.

Companies aren't hiring at a rate anywhere near enough to replace the more than seven million jobs lost during the recession. The manufacturing sector has lost 2.1 million jobs.