And in six of the most affected states — Michigan, Minnesota, Montana, North Carolina, Ohio and Tennessee — the probability that a Republican would be elected to a state legislative seat increased by 10 percentage points or more.

In five other states — Colorado, Iowa, Texas, Wisconsin and Wyoming — Republican candidates were seven percentage points more likely to win.

“Citizens United has given corporations and labor unions new means of influencing political elections,” researchers Tilman Klumpp of the University of Alberta, Hugo Mialon of Emory University and Michael Williams of Competition Economics wrote in their paper, “The Business of American Democracy: Citizens United, Independent Spending and Elections.”

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Before the ruling, labor unions were more freely able to spend on campaigns and elections. But by freeing corporations to spend their own money, the study found, “Citizens United has, on balance, increased the political influence of corporations relative to that of unions.”

The study focused on 22 states where bans on independent expenditures by corporations and labor unions were overturned by the Supreme Court’s ruling. The remaining 28 states, which never had bans on independent expenditures, serve as control states.

In the 22 states where independent expenditures were suddenly allowed, Republicans took advantage. The Republican State Leadership Committee raised about $30 million in 2010 through its RedMap program, targeting states such as Colorado, Michigan, North Carolina, Ohio, Pennsylvania, Texas and Wisconsin. The RSLC spent about $1 million each in Michigan, Ohio and Pennsylvania, all of which swung to Republican control after 2010.

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Other conservative groups, organized under section 527 of the Internal Revenue Code, spent heavily in North Carolina, Montana, Colorado and Tennessee, all states where Republicans made gains. The bulk of those groups raised funds from corporations and other politically active groups, such as the U.S. Chamber of Commerce.

The researchers also found evidence that the ruling led to an increase in the number of Republicans who ran for reelection, and a decrease in the number of Democrats who ran for office, especially in state House races. One Democratic candidate dropped out of about every 10th race in states affected by Citizens United, the researchers found.

Spending by outside groups, dubbed “super PACs” in the wake of the Citizens United decision, exploded between 2010, when those PACs were created, and 2012, when they established themselves near the top of the political hierarchy. Business contributions to the 10 largest super PACs multiplied from about $35 million in 2010 to more than $345 million in 2012, the researchers found.