Biproportional Techniques in Input-Output Analysis: Table Updating and Structural Analysis

This paper 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 discuss the RAS algorithm developed by Sir Richard Stone and others. We follow that by evaluating the interpretability of the product of the adjustment parameters, generally known as R and S. We then move on to discuss the various formal formulations of other biproportional approaches and discuss what defines an algorithm as “biproportionalâ€. After mentioning a number of competing optimization algorithms that cannot fall under the rubric of being biproportional, we reflect upon how some of their features have been included into the biproportional setting (the ability to fix the value of interior cells of the matrix being adjusted and of incorporating data reliability into the algorithm). We wind up the paper by pointing out some areas that could use further investigation.