Rick Hasen mentioned a paper on his Election Law listserv (http://electionlawblog.org/archives/006819.html) but the link is broken.
Go to http://www.allacademic.com and search on this string: ” Protecting the Franchise, or Restricting it? The Effects of Voter Identification Requirements on Turnout” and you will find the paper by Timothy Vercollitti and David Andersen of Rutgers University.
The key finding is presented on page 11:
In each model, three of the voter identification requirements exert a statistically significant, negative effect on whether survey respondents said they had voted in 2004. In other words, compared to states that require voters only to state their names, the requirements to sign one’s name, provide a non-photo identification, or photo identification in the maximum requirements or affidavit in the minimum requirements exert a negative influence on turnout.
Of the other state-level factors, only the competitiveness of the presidential race had a significant effect on turnout. In terms of demographic influences, African-American voters were more likely than white voters or other voters to say they had cast a ballot, while Asian-Americans were less likely than white or other voters to say they had turned out. Hispanic voters were not statistically different from white or other voters in terms of reported turnout. Consistent with previous research, education, income, and marital status all were positive predictors of voting. Women also were more likely to say they voted than men. Among the age categories, those ages 45 to 64 and 65 and older were more likely than those ages 18 to 24 to say they voted. Respondents who had earned a high school diploma, attended some college, graduated from college or attended graduate school were all more likely to say they voted than those who had not finished high school. Respondents who had moved within six months before the interview were less likely to say they had voted.