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A week later, Labor releases the raw data on its website. Many academics use the data, which is stripped of all identifying information, for their own research.

The commissioner is the BLS’ only political appointee. And even he or she operates independently of the presidential administration. The Obama administration has selected a new commissioner: Erica Groshen, a vice president at the New York Federal Reserve. She has yet to be approved by the Senate.

On Friday, Romney refrained from discrediting the government data. But plenty of conservatives did that work for him.

Conn Carroll, an editorial writer at the Washington Examiner, tweeted: ‘‘I don’t think BLS cooked numbers. I think a bunch of Dems lied about getting jobs. That would have same effect.’’

Rick Manning, communications director of Americans for Limited Government and a former public affairs chief of staff at the Labor Department, said ‘‘anyone who takes this unemployment report serious is either naive or a paid Obama campaign adviser.’’

Rep. Paul Broun, a Georgia Republican, weighed in with a statement saying the report ‘‘raises questions for me, and frankly it should be raising eyebrows for people across the country.’’

Conspiracy theories are nothing new for Obama. He has been dogged by discredited claims that he wasn’t born in this country and that he is Muslim.

On Friday, one leading Republican sided with Obama’s team in rejecting the latest accusations.

‘‘Stop with the dumb conspiracy theories. Good grief,’’ Tony Fratto, a strategist who was a top communications official in the Bush White House, tweeted.

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Mayerowitz reported from New York.

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Scott Mayerowitz can be reached at http://twitter.com/GlobeTrotScott . Christopher S. Rugaber can be reached at: http://twitter.com/ChrisRugaber .