Updating input–output matrices: assessing alternatives through simulation

Abstract

A problem that frequently arises in economics, demography, statistics, transportation planning and stochastic modelling is how to adjust the entries of a matrix to fulfil row and column aggregation constraints. Biproportional methods in general and the so-called RAS algorithm in particular, have been used for decades to find solutions to this type of problem. Although alternatives exist, the RAS algorithm and its extensions are still the most popular. Apart from some interesting empirical and theoretical properties, tradition, simplicity and very low computational costs are among the reasons behind the great success of RAS. Nowadays computer hardware and software have made alternative procedures equally attractive. This work analyses, through simulation, the performance of RAS and some minimands when matrix coefficients vary following different schemes of change. Results suggest RAS algorithm as the best option when variations in coefficients are proportional to their size, while the method based on minimizing squared differences is seen to be the best alternative when the standard deviations of variations are either constant, variable, or an inverse function of matrix entries.