Analysts often are interested in learning how much an exchange system has changed over time or how two different exchange systems differ. Identifying structural difference in exchange matrices can be performed using either 'directed' or 'undirected' methods. Directed methods are based on the...

This paper introduces the rest of this issue of Economic Systems Research, which is dedicated to the contributions of Sir Richard Stone, Michael Bacharach, and Philip Israilevich. It starts out with a brief history of biproportional techniques and related matrix balancing algorithms. We then...