From a NYT Op-Ed here:
Kyle Raze, a graduate student in economics at the University of Oregon, studied turnout patterns in the wake of the 2013 Supreme Court ruling in Shelby County v. Holder. The court declared Section 5 of the 1965 Voting Rights Act, which required jurisdictions with a history of discrimination to get preclearance from the Justice Department for any change in election law, unconstitutional. Shelby opened the door to the enactment of voter suppression measures.
Raze, in his February 2021 paper, “Voting Rights and the Resilience of Black Turnout,” writes that
Despite well-founded fears to the contrary, the Shelby decision does not appear to have widened the turnout gap between Black and White voters in previously covered states.
Instead, Raze found
an accumulating body of evidence that suggests that voters mobilize in response to increases in the cost of voting when those increases are perceived as threats to the franchise.