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Time, bifurcations and economic applications

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  • Stefano Bosi

    ()
    (EQUIPPE - ECONOMIE QUANTITATIVE, INTEGRATION, POLITIQUES PUBLIQUES ET ECONOMETRIE - Université Lille I - Sciences et technologies - Université Lille II - Droit et santé - Université Lille III - Sciences humaines et sociales - PRES Université Lille Nord de France)

  • Lionel Ragot

    (EQUIPPE - ECONOMIE QUANTITATIVE, INTEGRATION, POLITIQUES PUBLIQUES ET ECONOMETRIE - Université Lille I - Sciences et technologies - Université Lille II - Droit et santé - Université Lille III - Sciences humaines et sociales - PRES Université Lille Nord de France, CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne)

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    Abstract

    In this paper, we apply first and higher-order Euler discretizations to compare dynamic systems in discrete and continuous time. In addition, we stress the difference between backward and forward-looking approximations. Focussing on local bifurcations, we find that time representation is neutral and asymptotically neutral for models with saddle-node and Hopf bifurcations, respectively. Conversely, it is far from neutral for models with flip bifurcations (in discrete time), even though these bifurcations disappear under a critical discretization step or under higher-order Euler discretizations. In the second part, we apply the theory to popular economic models. Discrete-time dynamics of capital accumulation, such as Solow (1956), can be recovered under first-roder backward-looking discretizations because of the predetermined nature of capital. Models of capital accumulation with intertemporal optimization, such as Ramsey (1928), need hybrid discretizations because of the forward-looking nature of the Euler equation, where consumption behaves as jumping variable.

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    Bibliographic Info

    Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00384513.

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    Date of creation: Apr 2009
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    Handle: RePEc:hal:cesptp:halshs-00384513

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    Keywords: Discretizations; bifurcations; growth models.;

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