Lorraine C. Minnite, a Rutgers University political scientist and a senior fellow at Demos, a liberal think tank, looked for a turnout effect in a 2009 paper she co-authored with Columbia University political scientist Robert S. Erikson. They didn't turn up definitive evidence, concluding, "our data and tools are not up to the task of making a compelling statistical argument for an effect."
Whether the inability to find an effect means there is no effect is contentious. To Prof. Minnite, it means the tools aren't sharp enough, not that ID laws don't curb voting.
Prof. Larocca, though, argues that it is possible the laws really don't suppress turnout. For one thing, even before the laws were passed, many states had laws requiring photo ID for some people wishing to register—so those could already have screened out people without IDs. Also, many of the people without photo ID are in groups that have low turnout rates to begin with.