Daniel Biggers and Michael Hanmer have written this article (forthcoming American Politics Research). Here is the abstract:

Recently, many states have reversed the decades-long trend of facilitating ballot access by enacting a wave of laws requesting or requiring identification from registrants before they vote. Identification laws, however, are not an entirely new phenomenon. We offer new theoretical insights regarding how changes in political power influence the adoption of identification laws. In the most extensive analysis to date, we use event history analysis to examine why states adopted a range of identification laws over the past several decades. We consistently find that the propensity to adopt is greatest when control of the governor’s office and legislature switches to Republicans (relationships not previously identified), and that this likelihood increases further as the size of black and Latino populations in the state expands. We also find that federal legislation in the form of the Help America Vote Act seems to enhance the effects of switches in partisan control.

This looks to be important work confirming what many of us have been suspecting.