Luke Keele and Ismail White have posted this draft on SSRN.  Here is the abstract:

The 1965 Voting Rights Act has been a central part of Federal efforts to increase minority participation in the U.S. The latest phase of enforcement under the Voting Rights Act has been the creation of majority-minority Congressional districts. To fight vote dilution, these districts are drawn so that a majority of the voting age population are minorities. One open question about minority-majority districts is whether they increase citizen participation in the form of turnout. While much of the empirical literature on this question has produced inconclusive answers, recent studies suggest that residing in one of these districts can significantly increase minority turnout. We argue that much of the variability in these findings can be attributed to the different design choices of previous researchers. In this study we address the weakness of previous research designs and offer a new design that exploits the redistricting process to gain additional leverage on this question. Unlike previous research, our design accounts for possible variation in treatment specification by ensuring that voters who were moved into minority-majority districts through the redistricting process are comparable to voters that remained in existing districts. Our use of the redistricting process also allows us to correctly model the selection process that leads voters to be moved into minority-majority districts. We find little evidence that minority voter turnout increases when minority voters are moved into these districts.