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Time, bifurcations and economic applications

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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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  • Stefano Bosi & Lionel Ragot, 2009. "Time, bifurcations and economic applications," Documents de travail du Centre d'Economie de la Sorbonne 09028, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:09028
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    1. Mercenier, j. & michel, p., 1991. "Discrete Time Finite Horizon Approximation of Optimal Growth With Steady State Invariance," Cahiers de recherche 9122, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    2. Mercenier, Jean & Michel, Philippe, 1994. "Discrete-Time Finite Horizon Appromixation of Infinite Horizon Optimization Problems with Steady-State Invariance," Econometrica, Econometric Society, vol. 62(3), pages 635-656, May.
    3. Hintermaier, Thomas, 2005. "A sunspot paradox," Economics Letters, Elsevier, vol. 87(2), pages 285-290, May.
    4. Bergstrom, A.R., 1984. "Continuous time stochastic models and issues of aggregation over time," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 20, pages 1145-1212, Elsevier.
    5. Robert M. Solow, 1956. "A Contribution to the Theory of Economic Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 70(1), pages 65-94.
    6. W. W. Chang & D. J. Smyth, 1971. "The Existence and Persistence of Cycles in a Non-linear Model: Kaldor's 1940 Model Re-examined," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(1), pages 37-44.
    7. Barro, Robert J, 1990. "Government Spending in a Simple Model of Endogenous Growth," Journal of Political Economy, University of Chicago Press, vol. 98(5), pages 103-126, October.
    8. David Cass, 1965. "Optimum Growth in an Aggregative Model of Capital Accumulation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(3), pages 233-240.
    9. Luis A. Puch & Omar Licandro, 2006. "Is Discrete Time a Good Representation of Continuous Time?," Working Papers 2006-20, FEDEA.
    10. Siu Fai Leung, 1995. "A distinction between continuous-time and discrete-time models of uncertain lifetime," Economics Letters, Elsevier, vol. 47(3-4), pages 291-296, March.
    11. Chryssi Giannitsarou & Alexia Anagnostopoulos, 2005. "Modeling Time and Macroeconomic Dynamics," Money Macro and Finance (MMF) Research Group Conference 2005 60, Money Macro and Finance Research Group.
    12. Zhang, Junxi, 2000. "Public services, increasing returns, and equilibrium dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 24(2), pages 227-246, February.
    13. Carlstrom, Charles T. & Fuerst, Timothy S., 2005. "Investment and interest rate policy: a discrete time analysis," Journal of Economic Theory, Elsevier, vol. 123(1), pages 4-20, July.
    14. Kazuo Mino & Kazuo Nishimura & Koji Shimomura & Ping Wang, 2008. "Equilibrium dynamics in discrete-time endogenous growth models with social constant returns," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 34(1), pages 1-23, January.
    15. Dornbusch, Rudiger, 1976. "Expectations and Exchange Rate Dynamics," Journal of Political Economy, University of Chicago Press, vol. 84(6), pages 1161-1176, December.
    16. Bambi, Mauro & Gori, Franco, 2014. "Unifying Time-To-Build Theory," Macroeconomic Dynamics, Cambridge University Press, vol. 18(8), pages 1713-1725, December.
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    Cited by:

    1. Antoine Le Riche & Francesco Magris, 2016. "Decreasing Transaction Costs and Endogenous Fluctuations in a Monetary Model," Economics Bulletin, AccessEcon, vol. 36(4), pages 2381-2393.
    2. Magris, Francesco, 2012. "Indeterminacy and multiple steady states with sector-specific externalities," Economic Modelling, Elsevier, vol. 29(6), pages 2664-2672.
    3. Borissov, Kirill & Dubey, Ram Sewak, 2020. "Growth with many agents and wages paid ex ante," Economic Modelling, Elsevier, vol. 89(C), pages 101-107.
    4. Kirill Borissov, 2011. "On Equilibrium Dynamics with Many Agents and Wages Paid ex ante," EUSP Department of Economics Working Paper Series 2011/05, European University at St. Petersburg, Department of Economics, revised 28 Apr 2011.

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    More about this item

    Keywords

    Discetizations; bifurcations; growth models;
    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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