Conor Dowling and Amber Wichowsky have written this article for American Politics Research. Here is the abstract:
Despite the Supreme Court’s acceptance of disclosure requirements, some donors have been able to remain anonymous through a combination of regulatory gaps, complicated financing schemes, and lags in when information is made public. As a first examination of the potential consequences of increased anonymity in political advertising we designed an experiment that varied the amount and format of information about the interests behind an attack ad sponsored by an “unknown” group. We find that participants were more supportive of the attacked candidate after viewing information disclosing donors, suggesting that voters may discount a group-sponsored ad when they have more information about the financial interests behind the message. We also find some evidence that the effect of disclosure depends on how campaign finance information is presented. Our study has implications for how (to this point, failed) congressional efforts to require greater disclosure of campaign finance donors may affect electoral politics.