Time, bifurcations and economic applications

Stefano Bosi () and Lionel Ragot ()
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Stefano Bosi: EQUIPPE - Université de Lille 1

Documents de travail du Centre d'Economie de la Sorbonne from Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne

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

Keywords: Discetizations; bifurcations; growth models (search for similar items in EconPapers)
JEL-codes: C02 C61 C62 O41 (search for similar items in EconPapers)
Pages: 63 pages
Date: 2009-04
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Citations: View citations in EconPapers (1)

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ftp://mse.univ-paris1.fr/pub/mse/CES2009/09028.pdf (application/pdf)

Related works:
Working Paper: Time, Bifurcations and Economic Applications (2010)
Working Paper: Time, bifurcations and economic applications (2009)
Working Paper: Time, bifurcations and economic applications (2009)
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Persistent link: https://EconPapers.repec.org/RePEc:mse:cesdoc:09028

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