Depth and breadth relevance in citation metrics

The Euclidean length of a citation list is “depth relevant”: the metric increases when citations are transferred from less to more cited papers. We introduce “breadth relevance,” which favors consistent achievers over one-hit wonders. The exponent of the CES aggregator then is less than unity rather than greater than unity, as for depth relevance. Using two datasets on citations of economists for the top 50 US and global universities, simply counting citations maximizes the correlation between the citation metrics of researchers and the peer-reviewed rank of their department. However, citation depth may explain the allocation of researchers across lower-ranked departments.