Abstract
In this paper, we consider the discrete version of the Sargent & Wallace (Econometrica 41:1043–1048, 1973) model with perfect foresight. We assume a piecewise linear money demand function, decreasing over a “normal range” \((-a_{R},a_{L})\) and constant when the expected inflation rate is beyond these bounds. In this way, we obtain that the monetary dynamics are described by a one-dimensional map having two kink points. We show that when the slope of the money demand function (\(\mu \)) is sufficiently large in absolute value and the speed of adjustment of the price to the market disequilibrium (\(\alpha \)) is smaller than 1 either cycles of any period or chaotic dynamics may be generated by the model. The description of the bifurcation structure of the \((\alpha ,\mu )\) parameter plane is given.
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Notes
- 1.
We can add that even mathematical justification for such jumps can not be found.
- 2.
Border collision at which two fixed points (one attracting and one repelling, or both repelling) simultaneously collide with the border point (from its opposite sides) and disappear after the collision is called fold BCB. It is worth to emphasise that a fold BCB is not associated with an eigenvalue passing through \(1\).
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Agliari, A., Gardini, L., Sushko, I. (2014). Bifurcation Structure in a Model of Monetary Dynamics with Two Kink Points. In: Dieci, R., He, XZ., Hommes, C. (eds) Nonlinear Economic Dynamics and Financial Modelling. Springer, Cham. https://doi.org/10.1007/978-3-319-07470-2_6
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DOI: https://doi.org/10.1007/978-3-319-07470-2_6
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