Anchoring has been shown to influence numeric judgments in various domains, including preferential judgment tasks. Whereas many studies and a recent Many Labs project have shown robust effects in classic anchoring tasks, studies of anchoring effects on preferential judgments have had inconsistent results. In this paper, we investigate the replicability and robustness of anchoring on willingness-to-pay, which is a widely used measure for consumer preference. We employ a combination of approaches, aggregating data from previous studies and also contributing additional replication studies designed to reconcile inconsistent previous results. We examine the effect of differing experimental procedures used in prior studies, and test whether publication bias could contribute to the inconsistent findings. We find that different experimental procedures used in previous studies do not explain the divergent results, and that anchoring effects are generally robust to differences in procedures, participant populations, and experimental settings.