New Nonlinear approaches for the adjustment and updating of a SAM

Abstract

Many structural relationships should be taken into account in any reasonable adjustment and updating process. These structural relationships are mainly represented by ratios of different types, such as technical coefficients or the proportion of the cell value in relation to its row or column total. We believe that in many cases ( either because of lack of information or when the time elapsed for the estimation of a social accounting matrix is not long enough to allow for any significant structural change) the updating process should try to minimize the relative deviation of the new coefficients from the initial ones in a homogeneous way. This homogeneity would mean that the magnitude of this relative deviation is similar among the elements of each row or column, therefore avoiding the concentration of the changes in particular cells of the SAM. In this work, we propose some new adjustment criteria in order to obtain a more homogeneous relative adjustment of the structural coefficients. These criteria combine the adjustment method proposed by Matuszewski et al. (1964) with other deviation functions. Each of the adjustment criteria proposed leads to a nonlinear optimization problem which is reformulated as a linear program. We test the usefulness of this proposal by comparing its results with the ones obtained by more standard approaches and we are able to show that these approaches tend to produce a less homogeneous pattern of coefficient adjustment, under certain circumstances, than the ones we put forward.