Those data points were cross-referenced with the votes cast for Mr. Obama in various polling precincts. The results showed a correlation between magazine sales and the vote share obtained by Mr. Obama, and extrapolated an effect of 1,015,559 votes.

Image Oprah Winfrey and Senator Barack Obama at a rally in Manchester, N.H., in December as the primary election neared. Credit... Elise Amendola/Associated Press

“We think people take political information from all sorts of sources in their daily life,” Mr. Moore said in an e-mail message, “and for some people Oprah is clearly one of them.”

In their as-yet-unpublished research paper on the topic, the economists trace celebrity endorsements back to the 1920 campaign of Warren Harding (who had Al Jolson, Lillian Russell and Douglas Fairbanks in his corner), and call Ms. Winfrey “a celebrity of nearly unparalleled influence.”

The economists did not, however, look at how Ms. Winfrey’s endorsement of Mr. Obama may have affected her own popularity. A number of people  women in particular  were angry that Ms. Winfrey threw her first-ever political endorsement to a man rather than his female opponent.

The research did not try to measure the influence of other stars’ endorsements; for instance, no similar measures were available for Obama supporters like the actress Jessica Alba or Pete Wentz of the band Fall Out Boy. “If a celebrity endorsement is ever going to have an empirically identifiable audience, then it is likely to be hers,” the researchers said of Ms. Winfrey. Sorry, Chuck Norris.