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The dynamics of the NAIRU model with two switching regimes

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  • Tramontana, F.
  • Gardini, L.
  • Ferri, P.

Abstract

We consider a model of inflation and unemployment proposed in Ferri et al. (JEBO, 2001), in which the dynamics are described by a discontinuous piecewise linear map, made up of two branches. We shall show that the bounded dynamics may be classified in two cases: we may have either regular dynamics with stable cycles of any period or quasiperiodic trajectories, or only chaotic dynamics (pure chaos in which a unique absolutely continuous invariant ergodic measure exists, and structurally stable), in a rich variety of cyclical chaotic intervals. The main results are the analytical formulation of the border collision bifurcation curves, through which we give a complete picture of the possible outcomes of the model.

Suggested Citation

  • Tramontana, F. & Gardini, L. & Ferri, P., 2010. "The dynamics of the NAIRU model with two switching regimes," Journal of Economic Dynamics and Control, Elsevier, vol. 34(4), pages 681-695, April.
    • Handle: RePEc:eee:dyncon:v:34:y:2010:i:4:p:681-695
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    1. Tramontana, Fabio & Westerhoff, Frank & Gardini, Laura, 2010. "On the complicated price dynamics of a simple one-dimensional discontinuous financial market model with heterogeneous interacting traders," Journal of Economic Behavior & Organization, Elsevier, vol. 74(3), pages 187-205, June.
    2. Piero Ferri, 2013. "Income distribution and debts in a fragile economy: market processes and macro constraints," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 8(2), pages 219-230, October.
    3. Annalisa Cristini & Piero Ferri, 2021. "Nonlinear models of the Phillips curve," Journal of Evolutionary Economics, Springer, vol. 31(4), pages 1129-1155, September.
    4. Gardini, Laura & Tramontana, Fabio, 2012. "Structurally unstable regular dynamics in 1D piecewise smooth maps, and circle maps," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1328-1342.
    5. Kiminori Matsuyama & Iryna Sushko & Laura Gardini, 2018. "A piecewise linear model of credit traps and credit cycles: a complete characterization," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 119-143, November.
    6. Piero Ferri, 2011. "Macroeconomics of Growth Cycles and Financial Instability," Books, Edward Elgar Publishing, number 14260.
    7. Olmedo, Elena, 2011. "Is there chaos in the Spanish labour market?," Chaos, Solitons & Fractals, Elsevier, vol. 44(12), pages 1045-1053.
    8. Ferri, Piero & Cristini, Annalisa & Tramontana, Fabio, 2023. "Meta-models of the Phillips curve and income distribution," Journal of Economic Behavior & Organization, Elsevier, vol. 213(C), pages 215-232.
    9. Roya Makrooni & Laura Gardini, 2015. "Bifurcation structures in a family of one-dimensional linear-power discontinuous maps," Gecomplexity Discussion Paper Series 7, Action IS1104 "The EU in the new complex geography of economic systems: models, tools and policy evaluation", revised Jan 2015.
    10. Piero Ferri & Fabio Tramontana, 2018. "Debt Persistence in a Deflationary Environment: A Regime-Switching Model," Computational Economics, Springer;Society for Computational Economics, vol. 52(2), pages 421-442, August.
    11. Elena Olmedo, 2014. "Forecasting Spanish Unemployment Using Near Neighbour and Neural Net Techniques," Computational Economics, Springer;Society for Computational Economics, vol. 43(2), pages 183-197, February.
    12. Ingrid Kubin & Laura Gardini, 2022. "On the significance of borders: the emergence of endogenous dynamics," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 17(1), pages 41-62, January.

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    More about this item

    Keywords

    Phillips curve Regime switching NAIRU Nonlinearities Discontinuous maps;

    JEL classification:

    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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