Vladimir Kogan has posted this draft on SSRN.  Here is the abstract:

Direct democracy is sometimes described as a “gun behind the door” that influences state policy outcomes, but little is known about how legislators react when voters actually pull the trigger. Leveraging the high-profile referendum defeat in November 2011 of a controversial law passed by the Ohio legislature, I examine the legislative response to voter disaffection. Using interest groups to “bridge” roll call votes immediately before and after the election, I show that the measure’s defeat induced substantial moderation on the part of the Republican legislative majority responsible for the unpopular law, while leaving the voting behavior of opposition Democratic legislators largely unchanged. The results suggest that direct democracy has the potential to restrain legislative excesses and alleviate — albeit not eliminate — the problem of leapfrog representation that characterizes modern day policymaking in polarized state legislatures.