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...

Biproportional methods are used to update matrices: the projection of a matrix Z to give it the column and row sums of another matrix is R Z S, where R and S are diagonal and secure the constraints of the problem (R and S have no signification at all because they are not identified). However,...

Biproportional methods project a matrix <Emphasis Type="Bold">A to give it the column and row sums of another matrix; the result is <Emphasis Type="Bold">R A S, where <Emphasis Type="Bold">R and <Emphasis Type="Bold">S are diagonal matrices. As <Emphasis Type="Bold">R and <Emphasis Type="Bold">S are not identified, one must normalize them, even after computing, that is, ex post. This article starts from the idea developed in...</emphasis></emphasis></emphasis></emphasis></emphasis></emphasis>

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...

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...

Most national accounting systems are based on the Make-Use model. Two hypotheses are traditionally made featuring either industry-based (IBT) or commodity-based (CBT) technologies. IBT corresponds to a consistent demand-driven model: its solution can be explained as a circuit or in probabilistic...

(VA)Pressure to change the academic reviewing system is growing. We discuss two groups of proposals that introducing market mechanisms. First, Prüfer and Zetland (2009), based on Havrilesky (1975), create an auction system: manuscripts are submitted and auctioned to editors in “academic...

The overall value of the Ghosh model is appraised. Its treatment of quantities and prices is scrutinized by examining the variant with data in quantities and prices, and the variant with data in value and price indexes. The methodology involves returning to the accounting equations and shows...

Bradburd and Ross have proposed a measure of multidimensional inequality based on a quadratic-loss criterion: one matrix is compared to another even if they have not the same margins. This is reconsidered. One removes the effect of size variation between the analyzed distribution and the...