38th Congress of the European Regional Science Association: "Europe Quo Vadis? - Regional Questions at the Turn of the Century", 28 August - 1 September 1998, Vienna, Austria
In a number of recent papers Sonis, Hewings and coworkers have extended spacial path analysis to a block structural context capable of analysing the relationship between direct blocks of influence, such as intra and interregional trade coefficients or demographic-economic interactions, and full model multipliers. The approach makes use of a definition of the direct coefficients block partitioned matrix in terms of simpler matrices each of which is made up of null blocks except for one block column. In the current paper, the underlying technique is extended by making use of an even simpler matrix construction - an "almost null" matrix, defined as null in all partitioned blocks except one. An arbitrary n x n block partitioned direct coefficients matrix can be represented as a sum of n-squared almost null matrices. Properties of almost null matrices are exploited to enable analytically manageable expressions for the Leontief inverse to be written entirely in terms of the almost null matrices making up the direct coefficients matrix. Additive and multiplicative representations in terms of groupings of almost null matrices are provided.