MATRIX SENSITIVITY, ERROR ANALYSIS AND INTERNAL EXTERNAL MULTIREGIONAL MULTIPLIERS

Sherman and Morrison (1949, 1950) provided essential insights into the properties of sensitivity and error analysis in input-output systems through procedures for specifying the effects of changes in one coeffi cient or changes in one row or column on the rest of the system. Sonis and Hewings (1989, 1992) extended this work and generalized it to inc lude a whole range of changes in direct inputs using the concept of a field of influence. The present paper considers the matricial changes in which sub-matric:es of the matrix of direct coefficients change sim ultaneously; these sub-matrices may be considered to reflect different economic substructures. In this way, the block-generalization of the Sherman-Morrison and Sonis-Hewings formulae are possible through the d evelopment and extension of Miyazawa's (1976) notion of internal and e xternal multi-region multipliers. In this way, the matricial decomposi tions of the matrix of fields of influence can be established.