Seth E. Masket, Jonathan Winburn^, and Gerald C. Wright have written this article for PS.  Here is the abstract:

Redistricting received substantial attention in the popular media in 2011, as states redrew state legislative and congressional district boundaries. Many reformers continue to argue for a de-politicization of the redistricting process, claiming that partisan redistricting is responsible for declining electoral competition and increasing legislative polarization. Our analysis of evidence from state legislatures during the last decade suggests that the effects of partisan redistricting on competition and polarization are small, considerably more nuanced than reformers would suggest, and overwhelmed by other aspects of the political environment.