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Aggregation of Variables in Dynamic Systems
Herbert A. Simon
Albert Ando
Abstract
Previous studies have examined dynamic systems that are decomposable into independent subsystems. This article treats of systems that are nearly decomposable--systems with matrices whose elements, except within certain submatrices along the main diagonal, approach zero in the limit. Such a system can be represented as a superposition of (1) a set of independent subsystems (one for each submatrix on the diagonal) and (2) an aggregate system having one variable for each subsystem. This superposition separates short-run from long-run dynamics and justifies the ignoring of "weak" linkages in partial equilibrium studies.
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