INPUT-OUTPUT CROSS ANALYSIS - A THEORETICAL ACCOUNT

In this paper we deal with extractions of one sector (region) or a num ber of sectors (regions) from an (interregional) input-output system. When a certain number of sectors is taken out of the input-output matr ix one obtains a cross. It is shown that the Leontief-inverse for a cr oss can be decomposed into the product of three matrices, OUTINTRA*IN , where INTRA represents all intracross economic interactions, IN repr esents all effects from the rest of economy upon the cross, and OUT re presents all effects from the cross upon the rest of economy. Furtherm ore, we present a general scheme of additive as well as multiplicative decompositions of the Leontief-inverse, reflecting the hierarchical d ecomposition of the matrix of input coefficients into the sum;of cross es. These decompositions provide us with the means to find new insight s into efficient aggregation, importance of regions, and issues of ind ustrial complexes in inter alia input-output analysis.