Tilman Klumpp, Hugo Mialon and Michael Willaims have posted this draft on SSRN.  Here is the abstract:

In Citizens United v. FEC (2010), the U.S. Supreme Court ruled that restrictions on independent political expenditures by corporations and labor unions are unconstitutional on First Amendment grounds. We analyze the effects of Citizens United on election outcomes. The 50 U.S. states provide an ideal setting for this analysis, as the ruling only affected a subset of the states. We find that Citizens United is associated with an increase of approximately two percentage points in Republican election probabilities in state House races. The increase is estimated to be ten or more percentage points in several states. We link these estimates to qualitative, “on the ground” evidence of significant spending by conservative organizations funded in large part by corporations through channels enabled by Citizens United. However, we find no conclusive evidence that Citizens United has yet reduced candidate entry or direct contributions in state elections. Implications for national elections and possible regulatory responses are discussed.