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Existence, Multiplicity and Dynamic Complexity in an OLG Model with Fiscal Policy and Debt

We consider the overlapping generation model formulated in Dioikitopoulos (2018) that tackles the problem of fiscal policy rules for debt sustainability, allowing for the presence of debt bubbles. The author gives conditions for sustainability achievement in terms of debt and capital control channels, taking into account initial conditions. Our mathematical analysis improves his study and reveals a wider spectrum of possible economic outcomes that might sometimes be opposed to the conclusions to which Dioikitopoulos (2018) comes. In detail, we reconsider the role of fiscal policy prescriptions, implemented by means of debt and capital responsiveness parameters, in determining the existence and multiplicity of stationary states. We also deepen the influence of policy parameters on local stability properties, highlighting the possible occurrence of two bifurcation scenarios and the consequent emergence of periodic and complex dynamics. Moreover, we review the role of fiscal policies in changing the fate of incoming economic scenarios and in preventing non sustainable paths from occurring.