Aggregation of variables in dynamic systems

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.