Internal and External Matrix Multipliers in the Input-Output Model

Abstract

There are many useful applications in which the n industries of an input-output table are divided into two or more strategic industry groups and the interaction among these groups traced through. To mention some examples, we have the interactions between the goods-producing sectors and service sectors, between the primary growth sectors and the supplementary or derived growth sectors, and between two regions which have structurally different characters. Another example is found in the necessity of distinguishing industries subject to capacity limitations from those which have ample capacity. Examples of this sort might be given by the hundreds.

This and the next chapter are revised and integrated versions of articles which were originally published, under the same titles, in Hitotsbashi Journal of Economics Vol. 7 No. 1, June 1966, and in the same Journal, Vol. 12 No. 1, June 1971. The mathematical part of this chapter is a summarized version of Chap. 4 and Appendix C in the author’s The Structural Interdependence Analysis of an Economy (in Japanese), 1963, and the empirical applications are from the author’s article (in Japanese): “An Interregional Input-Output Model and its Application”, Monthly Survey of Japan Industrial Structure Institute, No. 52, Jan. 1965. I have introduced some improvements in this rewriting.