During the 2000s, as U.S. manufacturing was transformed by devastating job losses, prominent economists and presidential advisers offered comforting words.

The paring of the manufacturing workforce, which shrank by a third over the decade, actually represented good news, they said. It meant that U.S. workers and factories had become more efficient and that, as a result, manufacturing companies needed fewer people.

“What happened to manufacturing? In two words, higher productivity,” Robert Reich, who served as labor secretary in the Clinton administration, wrote in 2009.

“The decline in U.S. manufacturing employment is explained by rapid growth in manufacturing productivity over the past 50 years,” said Glenn Hubbard, chairman of the Council of Economic Advisers (CEA) under President George W. Bush.

But a handful of economists are challenging that explanation, chipping away at the long-offered assurances that the state of U.S. manufacturing is not as bad as employment numbers make it look.

Instead, they say, it’s significantly worse.

What caused the job losses, in their view, is less the efficiency of U.S. factories than the failure of those factories to hold their own amid global competition and rising imports. The apparent productivity gains reflected in the official U.S. statistics have been miscalculated and misrepresented, they say, a position that has been at least partially validated by recent research.

“I bought into this idea for a long time that it was superior labor productivity that caused most manufacturing job losses,” said Rob Atkinson of the Information Technology and Innovation Foundation, a nonpartisan think tank. “Then I began to dig into the numbers.”

The arguments, which get a fresh airing in a report to be issued this week by the think tank, are being mounted as economists and politicians on the presidential campaign trial debate what, if anything, to do to help the nation’s manufacturers. Among the options are tax incentives, trade assistance and education credits.

“These numbers have been tossed about to say, ‘Look how productive U.S. factories have been,’ ” said Susan Houseman, senior economist at the W.E. Upjohn Institute, co-author with three Federal Reserve economists of a paper that raises questions about the accuracy of the productivity numbers. “The reality is a lot more complex and not as flattering.”

As calculated by federal statisticians, the productivity growth of U.S. factories has seemed quite impressive. Between 1991 and 2011, productivity more than doubled, meaning that a single worker today produces what two did 20 years ago, according to Bureau of Labor Statistics figures.

Looking at this number, many economists have concluded that the loss of manufacturing work could be considered a success story. Just as farming became more efficient over the previous century and fewer Americans found jobs on farms, U.S. manufacturing is simply becoming more efficient, as economists such as N. Gregory Mankiw, CEA chairman under Bush, and Austan Goolsbee, a recent CEA chief under President Obama, have argued.

“It is exactly the same process that agriculture went through,” Goolsbee said in a 2006 speech.

While many Americans blamed free trade for much of the unemployment in the Rust Belt, the idea that productivity was the culprit amounted to orthodoxy among many mainstream economists.

But as Houseman, Atkinson and others have pointed out, that view may mask a far more complex reality.

For starters, the reported productivity gains may be overstated because the statistics the government collects do not adequately reflect the changes that have come with globalization, as Houseman and Federal Reserve colleagues Christopher Kurz, Paul Lengermann and Benjamin Mandel have shown.

Calculating labor productivity depends on determining the value of U.S. manufacturing output and dividing it by the number of manufacturing-worker hours.

But in a time when factories increasingly have turned to outsourcing, it can be difficult to determine what is U.S. manufacturing output and what should be properly counted as output from a foreign factory.

Critically, Houseman and others have shown that the price savings that U.S. factories have realized from outsourcing have incorrectly shown up as gains in U.S. output and productivity.

This bias may have accounted for as much as half of the growth of U.S. manufacturing output from 1997 to 2007, excluding computers and electronics manufacturing, Houseman and her co-authors have estimated.

For example, suppose a U.S. factory decides to offshore the production of a part for which it used to pay $1. With the switch to an overseas supplier, it might pay 50 cents for the part. If U.S. statistics do not capture this drop in price, the savings by the U.S. factory can show up as a gain in output and productivity.

The federal statistical agencies, which have helped fund Houseman’s work, agree that the bias exists, though they say there might be other problems that are off­setting.

“Figuring out where the productivity gains actually happened can be difficult,” said Brent Moul­ton, associate director for national economic accounts at the Bureau of Economic Analysis, which generates the output figures used in calculating commonly used measures of labor productivity.

On the agency’s Web site, a new message says the bias could account for overestimating the nation’s gross domestic product and productivity by one-tenth or two-tenths of a percentage point.

But there may be another, broader problem with the manufacturing output and productivity figures.

Those numbers lump all manufacturing together when there are actually two very different trends afoot.

Between 2000 and 2010, manufacturing output of computer and electronic products rose at a remarkable rate of almost 18 percent per year.

Over the same period, output in the rest of U.S. manufacturing remained roughly flat, according to Bureau of Economic Analysis figures tallied by Houseman. That’s a dismal showing for a decade.

It is only when computer and electronic products are included that overall manufacturing output registers the impressive increases. Though it represents 15 percent or less of manufacturing output, the sector’s strong growth makes the rest of U.S. manufacturing seem much more robust than it really is.

Moreover, as the critics point out, there are reasons to question what the remarkable growth in computer and electronics production really means.

For one thing, much of the nation’s production of computers and electronics has moved overseas. The number of consumer electronics shipped from U.S. factories dipped about 70 percent between 2000 and 2010, according to the Census Bureau’s Current Industrial Report.

Moreover, at least some of the productivity gains shown in U.S. computer manufacturing reflect the increasing power and decreasing prices that come with innovation. When a computer chip doubles in efficiency, that can turn up in a doubling of output and productivity in computer manufacturing. But that is not what is ordinarily thought of as manufacturing efficiency.

“It is innovation that makes it look like they’re manufacturing a whole lot more in the U.S. than they really are,” Atkinson said.

Finally, the critics note that high productivity should not necessarily lead to job losses. During the 1990s, for example, when reported U.S. productivity was also high, the job losses in manufacturing were slight compared with the drama of the past decade, when employment in the sector dropped from 17.2 million to 11.6 million, according to Bureau of Labor Statistics figures.

When pressed, economists on both sides of the debate about the health of U.S. manufacturing acknowledge that it amounts to a matter of emphasis. But the differences between the two camps are large enough to alter how one should view the future of U.S. manufacturing.

Atkinson and other critics of the productivity story concede that indeed, some of the job loss was caused by increasing productivity. Many factories are filled with automated machines that are far more efficient, after all, so one worker can account for far more output. But he thinks the primary cause of the job loss was that U.S. manufacturers lost their edge amid increasing world competition. Based on that view, he favors changes to government policy that he says could return millions of manufacturing jobs to the United States.

Similarly, Goolsbee says there are many reasons manufacturing has shed so many jobs. And Reich, now at the University of California at Berkeley, says that while he has recently focused on productivity as an explanation of the job losses, “I don’t think there’s any question that outsourcing has played an important role. The question is, what role?”

Regardless of what caused the job loss, Reich said, “it’s difficult to see a huge number of jobs coming back in manufacturing.”