IDEAS home Printed from https://ideas.repec.org/p/nbr/nberte/0211.html
   My bibliography  Save this paper

Time-to-Build and Cycles

Author

Listed:
  • Patrick K. Asea
  • Paul J. Zak

Abstract

We analyze the dynamics of a simple growth model in which production occurs with a delay while new capital is installed (time-to-build). The time-to-build technology is shown to yield a system of functional (delay) differential equations with a unique steady state. We demonstrate that the steady state, though typically a saddle, may exhibit Hopf cycles on a measurable set of the parameter space. Furthermore, the optimal path to the steady state is oscillatory. A counter-example to the claim that intrinsically oscillatory on the central technical apparatus the mathematics of functional differential equations.

Suggested Citation

  • Patrick K. Asea & Paul J. Zak, 1997. "Time-to-Build and Cycles," NBER Technical Working Papers 0211, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberte:0211
    Note: IFM
    as

    Download full text from publisher

    File URL: http://www.nber.org/papers/t0211.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Boldrin, Michele & Woodford, Michael, 1990. "Equilibrium models displaying endogenous fluctuations and chaos : A survey," Journal of Monetary Economics, Elsevier, vol. 25(2), pages 189-222, March.
    2. Jess Benhabib & Kazuo Nishimura, 2012. "The Hopf Bifurcation and Existence and Stability of Closed Orbits in Multisector Models of Optimal Economic Growth," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 51-73, Springer.
    3. Nishimura Kazuo & Sorger Gerhard, 1996. "Optimal Cycles and Chaos: A Survey," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 1(1), pages 1-20, April.
    4. Ioannides, Yannis M. & Taub, Bart, 1992. "On dynamics with time-to-build investment technology and non-time-separable leisure," Journal of Economic Dynamics and Control, Elsevier, vol. 16(2), pages 225-241, April.
    5. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-1370, November.
    6. Reichlin Pietro, 1997. "Endogenous Cycles in Competitive Models: An Overview," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 1(4), pages 1-13, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Golosov, Mikhail & Menzio, Guido, 2020. "Agency business cycles," Theoretical Economics, Econometric Society, vol. 15(1), January.
    2. Sergio Rebelo, 2005. "Real Business Cycle Models: Past, Present, and Future," NBER Working Papers 11401, National Bureau of Economic Research, Inc.
    3. Sergio Rebelo, 2005. "Real Business Cycle Models: Past, Present and Future," Scandinavian Journal of Economics, Wiley Blackwell, vol. 107(2), pages 217-238, June.
    4. Barnett, William A. & Serletis, Apostolos & Serletis, Demitre, 2015. "Nonlinear And Complex Dynamics In Economics," Macroeconomic Dynamics, Cambridge University Press, vol. 19(8), pages 1749-1779, December.
    5. Guo, Jang-Ting & Lansing, Kevin J., 2002. "Fiscal Policy, Increasing Returns, And Endogenous Fluctuations," Macroeconomic Dynamics, Cambridge University Press, vol. 6(5), pages 633-664, November.
    6. Gomes, Orlando, 2008. "Too much of a good thing: Endogenous business cycles generated by bounded technological progress," Economic Modelling, Elsevier, vol. 25(5), pages 933-945, September.
    7. Tarek Coury & Yi Wen, 2009. "Global indeterminacy in locally determinate real business cycle models," International Journal of Economic Theory, The International Society for Economic Theory, vol. 5(1), pages 49-60, March.
    8. Kitagawa, Akiomi & Shibata, Akihisa, 2001. "Long gestation in an overlapping generations economy: endogenous cycles and indeterminacy of equilibria," Journal of Mathematical Economics, Elsevier, vol. 35(1), pages 99-127, February.
    9. Cui, Dan & Wei, Xiang & Wu, Dianting & Cui, Nana & Nijkamp, Peter, 2019. "Leisure time and labor productivity: A new economic view rooted from sociological perspective," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 13, pages 1-24.
    10. Brock, W.A. & Hommes, C.H., 1997. "Models of Compelxity in Economics and Finance," Working papers 9706, Wisconsin Madison - Social Systems.
    11. Ralph Winkler, 2008. "Optimal compliance with emission constraints: dynamic characteristics and the choice of technique," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 39(4), pages 411-432, April.
    12. Michail E. Rousakis, 2010. "Capitalizing Implementation Cycles," 2010 Meeting Papers 1184, Society for Economic Dynamics.
    13. Alexeeva, Tatyana A. & Kuznetsov, Nikolay V. & Mokaev, Timur N., 2021. "Study of irregular dynamics in an economic model: attractor localization and Lyapunov exponents," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    14. Calvet, Laurent-Emmanuel & Grandmont, Jean-Michel & Lemaire, Isabelle, 2018. "Aggregation of heterogenous beliefs, asset pricing, and risk sharing in complete financial markets," Research in Economics, Elsevier, vol. 72(1), pages 117-146.
    15. Alain Venditti, 2012. "Weak concavity properties of indirect utility functions in multisector optimal growth models," International Journal of Economic Theory, The International Society for Economic Theory, vol. 8(1), pages 13-26, March.
    16. Paul Beaudry & Dana Galizia & Franck Portier, 2015. "Reviving the Limit Cycle View of Macroeconomic Fluctuations," NBER Working Papers 21241, National Bureau of Economic Research, Inc.
    17. Farmer, Roger E.A., 2016. "The Evolution Of Endogenous Business Cycles," Macroeconomic Dynamics, Cambridge University Press, vol. 20(2), pages 544-557, March.
    18. Indrajit, Mallick, 2008. "Finance in the Theory of Business Cycles," MPRA Paper 15472, University Library of Munich, Germany.
    19. Orlando Gomes, 2007. "Routes to chaos in macroeconomic theory," Journal of Economic Studies, Emerald Group Publishing, vol. 33(6), pages 437-468, January.
    20. Bhattacharya, Joydeep & Russell, Steven, 2003. "Two-period cycles in a three-period overlapping generations model," Journal of Economic Theory, Elsevier, vol. 109(2), pages 378-401, April.

    More about this item

    JEL classification:

    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:nbr:nberte:0211. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/nberrus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.