, Volume 13, Issue 1-2, pp 121-129

A further procedure for ordering an input-output matrix: some empirical evidence

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In a recent paper Ghosh and Sarkar [5] have developed a model of input-output systems as spatial configurations. Roy has proposed a more efficient solution method; but computation time still increases factorially which rules out its use for large matrices. [15] This note shows that the problem they have formulated belongs to a class of discrete programming problems known as placement or assignment problems. Several natural extensions are briefly discussed. More importantly, an efficient algorithm for the quadratic assignment problem is used to compute the optimal ordering of five comparable input-output matrices (US, Norway, Japan, Italy, India). These preliminary empirical results do show rather stable assignment patterns for the industries; and certain clusters of industries are shown to emerge as hypothesized by Ghosh and Sarkar.

The author wishes to thank an anonymous referee for some important clarifying remarks on a preliminary version of this paper.