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“The results were unusual, but not unprecedented,” he said, adding that chances are the discrepancy will be resolved by some of the drop in unemployment being reversed in the months ahead.

Becoming self-employed

Other economists point out that the department’s household survey is broader than the business survey in that it captures increases in employment by people who get part-time jobs, are self-employed, work on farms or take positions with very small firms that are not included in the department’s business survey. Thus, the household survey may be signaling strength in those sectors.

Lawrence Mishel, president of the labor-backed Economic Policy Institute, said that rather than cry foul, conservatives should be pleased with the evidence that more people struck out on their own last month and started their own businesses or otherwise found jobs in the informal sectors of the economy.

“One could argue, tongue in cheek, that the household employment growth in September captured a surge in ‘job creators’ — self-employment — and agricultural employment in the ‘real America’ that the payroll survey missed because those employment sectors are not in the scope of the payroll survey,” he said. Conservatives have heralded such self-employment gains in the past.

“But this controversy is not funny at all,” Mr. Mishel said. The department’s staff “has been inundated with calls from people attacking them, the predictable consequence of these conspiracy charges. They should not be facing this type of harassment.”

David Kelly, chief global strategist with J.P. Morgan Funds, called the hoopla a case of partisans on one side “blaming the refs” when the numbers didn’t come out in support of their team.

“Americans are passionate about sports,” and “it is amazing how many fans shout themselves hoarse maligning the refs,” he said. “We saw a similar spectacle involving politics and economics.”

The drop in joblessness was “heartening for the economy” and “useful for the president,” but there was no evidence that the government was “somehow fixing the numbers,” he said. “As someone who has worked with analysts from the Commerce Department for many years, I have never had reason to question their integrity, and it is very unfair for political commentators to do so.”

Still, Mr. Kelly said he could understand why the report raised some eyebrows. “Quite possibly quirky seasonal factors played a role in the huge household survey gain, and it would not be a surprise to see some of it reversed in the far-more-important jobs report due out on the Friday before the election,” he said.