Nour Abdul-Razzak, Carlo Prato and Stéphane Wolton in the Monkey Cage:

Our research focuses on state legislative elections because we can more easily isolate the effect of Citizens United compared with other factors that influence election outcomes at various levels (such as the popularity of the president). Before 2010, 23 states had bans on corporations and union funding of outside spending. As a result of the court’s ruling, these states had to change their campaign laws. We can then compare the changes before and after Citizens United in these 23 states with the same changes in the 27 states whose laws did not change. The effect of the court’s ruling is then simply the differences between these two before-and-after comparisons.

We find that Citizens United increased the GOP’s average seat share in the state legislature by five percentage points. That is a large effect — large enough that, were it applied to the past twelve Congresses, partisan control of the House would have switched eight times. In line with a previous study, we also find that the vote share of Republican candidates increased three to four points, on average.

We also uncovered evidence that these results stem from the influence of corporations and unions. In states where union membership is relatively high and corporations relatively weak, Citizens United did not have a discernible effect on the partisan balance of the state legislature. But in states with weak unions and strong corporations, the decision appeared to increase Republican seat share by as much as 12 points.