Automated influence, delivered by digital targeting technologies such as targeted advertising, digital nudges, and recommender systems, has attracted significant interest from both empirical researchers, on one hand, and critical scholars and policymakers on the other. In this paper, we argue for closer integration of these efforts. Critical scholars and policymakers, who focus primarily on the social, ethical, and political effects of these technologies, need empirical evidence to substantiate and motivate their concerns. However, existing empirical research investigating the effectiveness of these technologies (or lack thereof), neglects other morally relevant effects-which can be felt regardless of whether or not the technologies "work" in the sense of fulfilling the promises of their designers. Drawing from the ethics and policy literature, we enumerate a range of questions begging for empirical analysis-the outline of a research agenda bridging these fields-and issue a call to action for more empirical research that takes these urgent ethics and policy questions as their starting point. CCS CONCEPTS• Security and privacy → Social aspects of security and privacy; • Human-centered computing → HCI design and evaluation methods.