Aggregation in Multisector Models: Using the Perron Vector
Titel:
Aggregation in Multisector Models: Using the Perron Vector
Auteur:
Dietzenbacher, Erik
Verschenen in:
Economic systems research
Paginering:
Jaargang 4 (1992) nr. 1 pagina's 3-24
Jaar:
1992
Inhoud:
The present paper investigates the effects of aggregation on the Perron vector, i.e. the eigenvector corresponding to the dominant eigenvalue. First, necessary and sufficient conditions are given for the aggregation to be consistent with respect to the Perron vector. That is, the Perron vector of the aggregated matrix is equal to the aggregated Perron vector of the original matrix, while the dominant eigenvalue remains the same. Secondly, upper and lower bounds are derived for the dominant eigenvalue and for the elements, of the Perron vector, which correspond to the sectors that are not aggregated. Thirdly, the results are applied to the traditional aggregation problem in input-output analysis, using the Perron vector as an artificial tool. It is indicated how the effects of aggregation on the input-output multipliers may be analyzed in a similar way.
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