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Continuous vs Discrete Time Modelling in Growth and Business Cycle Theory

Author

Listed:
  • Omar Licandro

    (University of Nottingham and Barcelona GSE .)

  • Luis A. Puch

    (Universidad Complutense de Madrid and ICAE.)

  • Jesús Ruiz

    ( Universidad Complutense de Madrid and ICAE.)

Abstract

Economists model time as continuous or discrete. For long, either alternative has brought about relevant economic issues, from the implementation of the basic Solow and Ramsey models of growth and the business cycle, towards the issue of equilibrium indeterminacy and endogenous cycles. In this paper, we introduce to some of those relevant issues in economic dynamics. First, we describe a baseline continuous vs discrete time modelling setting relevant for questions in growth and business cycle theory. Then we turn to the issue of local indeterminacy in a canonical model of economic growth with a pollution externality whose size is related to the model period. Finally, we propose a growth model with delays to show that a discrete time representation implicitly imposes a particular form of time–to–build to the continuous time representation. Our approach suggests that the recent literature on continuous time models with delays should help to bridge the gap between continuous and discrete time representations in economic dynamics.

Suggested Citation

  • Omar Licandro & Luis A. Puch & Jesús Ruiz, 2018. "Continuous vs Discrete Time Modelling in Growth and Business Cycle Theory," Documentos de Trabajo del ICAE 2018-28, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    • Handle: RePEc:ucm:doicae:1828
    as

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    File URL: https://eprints.ucm.es/id/eprint/50175/1/1828.pdf
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    References listed on IDEAS

    as
    1. Benhabib Jess & Farmer Roger E. A., 1994. "Indeterminacy and Increasing Returns," Journal of Economic Theory, Elsevier, vol. 63(1), pages 19-41, June.
    2. Asea, Patrick K. & Zak, Paul J., 1999. "Time-to-build and cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 23(8), pages 1155-1175, August.
    3. Fabrice Collard & Omar Licandro & Luis A. Puch, 2008. "The short-run Dynamics of Optimal Growth Model with Delays," Annals of Economics and Statistics, GENES, issue 90, pages 127-143.
    4. Fernández, Esther & Pérez, Rafaela & Ruiz, Jesús, 2012. "The environmental Kuznets curve and equilibrium indeterminacy," Journal of Economic Dynamics and Control, Elsevier, vol. 36(11), pages 1700-1717.
    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. Bambi, Mauro & Gozzi, Fausto & Licandro, Omar, 2014. "Endogenous growth and wave-like business fluctuations," Journal of Economic Theory, Elsevier, vol. 154(C), pages 68-111.
    7. repec:adr:anecst:y:2008:i:90:p:05 is not listed on IDEAS
    8. Omar Licandro & Luis Puch & Antonio Sampayo, 2008. "A Vintage Model of Trade in Secondhand Markets and the Lifetime of Durable Goods," Mathematical Population Studies, Taylor & Francis Journals, vol. 15(4), pages 249-266.
    9. Hansen, Gary D., 1985. "Indivisible labor and the business cycle," Journal of Monetary Economics, Elsevier, vol. 16(3), pages 309-327, November.
    10. Jovanovic, Boyan, 1982. "Selection and the Evolution of Industry," Econometrica, Econometric Society, vol. 50(3), pages 649-670, May.
    11. Benhabib, Jess, 2004. "Interest Rate Policy in Continuous Time with Discrete Delays," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 36(1), pages 1-15, February.
    12. Burmeister, Edwin & Turnovsky, Stephen J, 1977. "Price Expectations and Stability in a Short-Run Multi-Asset Macro Model," American Economic Review, American Economic Association, vol. 67(1), pages 213-218, February.
    13. Hintermaier, Thomas, 2003. "On the minimum degree of returns to scale in sunspot models of the business cycle," Journal of Economic Theory, Elsevier, vol. 110(2), pages 400-409, June.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Discrete Time; Continuous Time; Solow model; Ramsey model; Indeterminacy; Time–to–Build; Delay Differential Equations.;
    All these keywords.

    JEL classification:

    • O40 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General
    • Q50 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - General
    • E10 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - General
    • E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Investment; Capital; Intangible Capital; Capacity

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