Time, bifurcations and economic applications

Stefano Bosi () and Lionel Ragot ()
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Stefano Bosi: EQUIPPE - Economie Quantitative, Intégration, Politiques Publiques et Econométrie - Université de Lille, Sciences et Technologies - Université de Lille, Sciences Humaines et Sociales - PRES Université Lille Nord de France - Université de Lille, Droit et Santé

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

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: Discretizations; bifurcations; growth models.; growth models; Discrétisations; modéles de croissance. (search for similar items in EconPapers)
Date: 2009-04
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00384513
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Citations: View citations in EconPapers (3)

Published in 2009

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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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