Local Bifurcation Theory Applied to OLG Models
In Section 1 a brief overview is given of the standard overlapping generations model as presented in Blanchard and Fischer (1989). The first step in all sections below is to develop the model structure with a minimum of functional hypotheses, followed by results under explicit forms for utility and/or production. In Section 2 the basic model is then extended to include a pay-as-you-go pension scheme and forward dynamics are determined from the backward equation of motion. In Section 3 the basic model is extended to allow for the accumulation of capital, leading to a second order relation for which fold bifurcations exist. In Section 4 a brief overview is given of a well-known OLG model in two dimensions, following Medio (1992) for which Neimark-Sacker bifurcations exist. In Section 5 an extension is given for the case of an environmental externality leading to a three dimensional system for which both fold and Neimark-Sacker bifurcations exist.
KeywordsCapital Stock Positive Steady State Invariant Circle Fold Bifurcation Forward Dynamic
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