The Reduction of Dimension in the Study of Economic Growth Models
AbstractWe examine the dimension reduction method and prove that it could be isleading if we try to get some insight tinto the dynamics of the original system from the dynamics of the transformed system alone. The reduced system seemingly may give rise to a continuum multiplicity of steady states when, actually, it does exist a unique and isolated steady state or even it does not exist a steady state at all. We show how the dynamics for the primary variables that is recovered from the solution to the reduced system may be refuted by solving the original one. In our opinion there is no alternative because nothing can be regarded as a close substitute for the study of the original system. Although this method has been extensively used in studying different versions of the Lucas-Uzawa two-sector model, we will focus on one-sector models for checking its validity in the simplest way.
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