Ray La Raja and Brian Schaffner have uploaded this important draft paper.  Here is the abstract:

This paper seeks to understand the effect of campaign finance laws on electoral and policy Spurred by the recent Supreme Court decision, Citizens United v. FEC (2010), which bans on corporate and union political spending, the study focuses on whether such bans generate consequences notably different from an electoral system that lacks such bans. We observe three key outcomes: partisan control of government, incumbent reelection rates and corporate tax burdens. Using historical data on regulations in 49 American states between 1935 and 2009 we test alternative models for evaluating the impact of corporate and union spending bans put in place during this period. The results indicate that spending bans appear to have limited, if any, effect on these outcomes.

I very much look forward to reading this paper!  Note that the paper attempts to measure the effects of spending on electoral outcomes, not legislative outcomes (and the latter in my view is a bigger problem).