The causative-matrix method to analyze temporal change assumes that a matrix transforms one Markovian transition matrix into another by a left multiplication of the first matrix; the method is demand-driven when applied to input-output economics. An extension is presented without assuming the...

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...

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>

Net multipliers, as introduced by Oosterhaven and Stelder (2002) accept outputs as entries instead of final demand. They are found by multiplying ordinary multipliers by the final demand ratio over the sector's output. This pragmatic solution suffers from ratio instability over time. The...

The Make-Use Model serves as a basis for most national accounting systems as the System of National Accounts (SNA) and is acknowledged as the most suitable model for interregional analysis. Two hypotheses are traditionally made featuring either industry-based technologies (IBT) or...

An example in Miernyk (1977) presented a rather counterintuitive result, namely, that introducing accurate exogenous information into an RAS matrix estimating procedure could lead to an estimate that was worse than one generated by RAS using no exogenous information at all. This became an...

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...