Technological Similarity and Aggregation in Input-Output Systems: A Cluster-Analytic Approach

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A4MONG the many problems raised by the X'Wactual construction of empirical input-output tables two key issues are often singled out: (1) what industrial classification scheme should be adopted and (2) how the data should be structured. Actually, these problems of industry definition and data structuring are two facets of a more fundamental problem: Given external constraints on data gathering (availability and format) which make the industry concept mostly unobservable, how can we best group the available data into an input-output table. Ideally, each industry would be defined by a single well-defined product and a separate industry should be used for different, but possibly 6closely related, products.1 A widely accepted notion of best grouping is one which minimizes the bias, i.e., the difference between the gross output forecast obtained with a disaggregated table and the forecast obtained with an aggregated table, for any final demand bill. Historically, a theoretical condition for zero aggregation bias was first derived by Hatanaka (1952).2 Briefly stated, let A denote the (n x n) disaggregated direct coefficient matrix; x denote the n-dimensional column vector of gross outputs; y denote the n-dimensional column vector of final demands; I denote the (n X n) unit matrix; S denote the aggregation operator where S is (M X n) and reads