Doug Spencer and Abby Wood have posted this draft on SSRN.  Here is the abstract:

What were the effects of Citizens United v. FEC? In this Article, the first to systematically examine the effects of the decision, we use a variety of empirical methods to show an increase in independent expenditures in states where the decision deregulated campaign finance laws. In those states, independent spending increased by around $19 million over what it would have been in the absence of the decision. However, the effect was not uniform across states. We attempt to use detailed data to evaluate whether the sources of expenditures de-regulated by the opinion, corporations and unions, responded directly, explaining why the existing disclosure framework prevents anyone from knowing the ultimate source of some independent expenditures. Finally, we address the distributional effects of Citizens United. We find that the distributional effects were not as dramatic as many scholars and commentators predicted in the wake of the opinion.