An analysis of corporate PAC contributions to almost 19,000 races for Senate, House, governor and state legislatures from 1980 to 2010 finds zero evidence to “support the jeremiads of pundits and reformers” who claim our political system is hopelessly corrupted by these contributions.

Corporate money is alleged to “alter election results in favor of pro-business candidates and away from the preferences of the public.” The winners of these elections then make policy decisions that benefit their contributors, which can be measured by an increase in the firm’s value. That’s the theory, anyway.

But researchers from the University of Chicago and Northwestern, whose work covers over 2,800 corporations and is published in the Journal of Politics, conclude that if there are any such increases, they would be “so small that we are not able to statistically detect them.”

In fact, it would be difficult to figure out — much less predict — how a quid pro quo could be arranged in a system as complicated as ours. For such an arrangement to work, “campaign contributions need to buy access, access has to change the behavior of elected officials [and] that behavior has to translate into policy” that then benefits the firm. That’s asking a lot of $10,000 per election cycle.

Although there is “limited data” in the study from the post-Citizens United period, the researchers still found no evidence in those races that firms benefited when candidates they supported won. The landmark Supreme Court case made no difference.

Previous research cited in this study throws still more light on the supposedly corrupting influence of corporate money on the American political system. Get-out-the-vote studies show that each additional vote in a given race costs between $100 and $200 to “create” through campaign strategies, which means influencing the outcome of most large elections would be mighty pricey.

Take the 2014 gubernatorial race in Illinois, which was considered extremely competitive. Bruce Rauner, the Republican, won by more than 142,000 votes.

If a group or company had wanted to tip the scale in favor of Rauner’s opponent, Democrat Pat Quinn, “they would have had to spend at least $14 million, even if there was no equilibrium response from contributors on the other side,” the researchers write. But most campaign contributions “are three or four orders of magnitude smaller and go to candidates in less competitive races.” That means tilting a race with a PAC contribution would be difficult, if not outright impossible.