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Time, Bifurcations and Economic Applications

Author

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  • Bosi Stefano

    (THEMA, Universite de Cergy-Pontoise)

  • Ragot Lionel

    (EQUIPPE, Universite de Lille 1)

Abstract

In this paper,we show how to recover discrete-time models from their continuous-time versions through Euler discretizations. In the first part, we introduce general polynomial discretizations in backward and forward looking and we study the preservation of stability properties and local bifurcations under different discretizations. In the second part, we apply these results to popular growth models. We show how to reconcile the traditional Solow models in discrete and continuous time through a backward-looking discretization. Discrete-time models of endogenous saving, suchas Ramsey(1928), need hybrid discretizations of the continuous-time model because of the forward-looking nature of the Euler equation. The introduction of externalities allows us to illustrate the preservation of stability properties and local bifurcations.

Suggested Citation

  • Bosi Stefano & Ragot Lionel, 2010. "Time, Bifurcations and Economic Applications," THEMA Working Papers 2010-01, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    • Handle: RePEc:ema:worpap:2010-01
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    3. Magris, Francesco, 2012. "Indeterminacy and multiple steady states with sector-specific externalities," Economic Modelling, Elsevier, vol. 29(6), pages 2664-2672.
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    More about this item

    Keywords

    discretizations; bifurcations; growthmodels;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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