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Time-to-Build and Cycles

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  • 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
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    1. Reichlin Pietro, 1997. "Endogenous Cycles in Competitive Models: An Overview," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 1(4), pages 1-13, January.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-1370, November.
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    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

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