As generative AI enables the creation and dissemination of information at massive scale and speed, it is increasingly important to understand how people perceive AI-generated content. One prominent policy proposal requires explicitly labeling AI-generated content to increase transparency and encourage critical thinking about the information, but prior research has not yet tested the effects of such labels. To address this gap, we conducted a survey experiment (N = 1,601) on a diverse sample of Americans, presenting participants with an AI-generated message about several public policies (e.g., allowing colleges to pay student-athletes), randomly assigning whether participants were told the message was generated by (i) an expert AI model, (ii) a human policy expert, or (iii) no label. We found that messages were generally persuasive, influencing participants’ views of the policies by 9.74 percentage points on average. However, while 92.0% of participants assigned to the AI and human label conditions believed the authorship labels, labels had no significant effects on participants’ attitude change toward the policies, judgments of message accuracy, nor intentions to share the message with others. These patterns were robust across a variety of participant characteristics, including prior knowledge of the policy, prior experience with AI, political party, education level, and age. Given current levels of trust in AI content, these results imply that, while authorship labels would likely enhance transparency, they are unlikely to substantially affect the persuasiveness of the labeled content, highlighting the need for alternative strategies to address challenges posed by AI-generated information.