
doi: 10.1007/bf00347047
In input-output research comparatively little work has been done on the ordering of sectors. As the sectors can be ordered more or less arbitrarily, this has been left generally to the prevalent systems of national accounts and other economic data. The traditional data systems thus rather than any specific lcgic seems to have determined such procedures. One of the authors, 1 in an earlier note showed that certain ordering of sectors reveal an interesting clustering property in input-output matrices which have certain advantages both in understanding the economy as also in computational work. The present note discusses certain other aspects of the problem of ordering. The flows in an input-output matrix looks in certain ways rather similar to the flows from origin to destination in a transportation model. Viewed from this angle, one can look at the sector ordering as analogous to fixing the location of both the centres of origin and the ultimate destination of a group of commodities. The important difference of course is that unlike a transportation problem, here the origins and destinations can be moved about, subject to certain rules. In this sense, therefore, we can look at the flow matrices under different ordering as alternative spatial configurations under certain sets of rules. The ordering problem is then to some extent transformed into a spatial location problem and the ordering index becomes associated with notions of distance. It will be shown that if this approach is taken in the ordering of sectors we are enabled to develop the following useful properties with respect to input-output matrices: i) An ordering of the sectors in an input-output matrix which is in some meaningful sense optimal; ii) A measure of sectoral interdependence of an economy; iii) An optimal ordering of location for units of an industrial complex visualised as a whole.
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