We analyze a purely dynamic model of public debt stabilization under ambiguity. We assume that the debt to GDP ratio is described by a random variable, and thus it can be characterized by investigating the evolution of its density function through iteration function systems on mappings. Ambiguity is associated with parameter uncertainty which requires policymakers to respond to such an additional layer of uncertainty according to their ambiguity attitude. We describe ambiguity attitude through a simple heuristic rule in which policymakers adjust the available vague information (captured by the empirical distribution of the debt ratio) with a measure of their ignorance (captured by the uniform distribution). We show that such a model generates fractal-type objects that can be characterized as fixed-point solutions of iterated function systems on mappings. Ambiguity is a source of unpredictability in the long run outcome since it introduces some singularity features in the steady state distribution of the debt ratio. However, the presence of some ambiguity aversion removes such unpredictability by smoothing out the singularities in the steady state distribution.

Public debt dynamics under ambiguity by means of iterated function systems on density functions / D. La Torre, S. Marsiglio, F. Mendivil, F. Privileggi. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B.. - ISSN 1531-3492. - 26:11(2021), pp. 5873-5903. [10.3934/DCDSB.2021070]

Public debt dynamics under ambiguity by means of iterated function systems on density functions

D. La Torre
Primo
;
2021

Abstract

We analyze a purely dynamic model of public debt stabilization under ambiguity. We assume that the debt to GDP ratio is described by a random variable, and thus it can be characterized by investigating the evolution of its density function through iteration function systems on mappings. Ambiguity is associated with parameter uncertainty which requires policymakers to respond to such an additional layer of uncertainty according to their ambiguity attitude. We describe ambiguity attitude through a simple heuristic rule in which policymakers adjust the available vague information (captured by the empirical distribution of the debt ratio) with a measure of their ignorance (captured by the uniform distribution). We show that such a model generates fractal-type objects that can be characterized as fixed-point solutions of iterated function systems on mappings. Ambiguity is a source of unpredictability in the long run outcome since it introduces some singularity features in the steady state distribution of the debt ratio. However, the presence of some ambiguity aversion removes such unpredictability by smoothing out the singularities in the steady state distribution.
Ambiguity; Dynamical systems; Fixed point equation; Generalized fractal transform; Global attractor; Iterated function systems on density functions; Public debt
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
2021
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/963720
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