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Time-to-Build and Cycles

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Author Info
Patrick K. Asea
Paul J. Zak

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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.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0211.

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Date of creation: May 1997
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Handle: RePEc:nbr:nberte:0211

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Find related papers by JEL classification:
E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis

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  1. Fabrice Collard & Omar Licandro & Luis A. Puch, 2003. "The short-run dynamics of optimal growth models with delays," Documentos del Instituto Complutense de Análisis Económico 0311, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales. [Downloadable!]
    Other versions:
  2. Ulrich Brandt-Pollmann & Ralph Winkler & Sebastian Sager & Ulf Moslener & Johannes Schlöder, 2008. "Numerical Solution of Optimal Control Problems with Constant Control Delays," Computational Economics, Springer, vol. 31(2), pages 181-206, March. [Downloadable!] (restricted)
    Other versions:
  3. Bambi, Mauro & Fabbri, Giorgio & Gozzi, Fausto, 2009. "Optimal policy and consumption smoothing effects in the time-to-build AK model," MPRA Paper 17128, University Library of Munich, Germany. [Downloadable!]
  4. Omar Licandro & Luis A. Puch, 2006. "Is Discrete Time a Good Representation of Continuous Time?," Economics Working Papers ECO2006/28, European University Institute. [Downloadable!]
    Other versions:
  5. Ralph Winkler, 2008. "Optimal compliance with emission constraints: dynamic characteristics and the choice of technique," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 39(4), pages 411-432, April. [Downloadable!] (restricted)
  6. Mauro BAMBI & Omar LICANDRO, 2004. "(In)determinacy and Time-to-Build," Economics Working Papers ECO2004/17, European University Institute. [Downloadable!]
  7. Mauro Bambi, 2008. "Unifying time-to-build theory," CER-ETH Economics working paper series 08/98, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich. [Downloadable!]
  8. Charles Himmelberg & Alessandra del Boca & Marzio Galeotti & Paola Rota, 2005. "Investment and Time to Plan: A Comparison of Structures vs. Equipment in a Panel of Italian Firms," Working Papers 2005.54, Fondazione Eni Enrico Mattei. [Downloadable!]
  9. Ghassan Dibeh, 2001. "Time Delays and Business Cycles: Hilferding's model revisited," Review of Political Economy, Taylor and Francis Journals, vol. 13(3), pages 329-341, July. [Downloadable!] (restricted)
  10. Ralph Winkler, 2008. "Optimal control of pollutants with delayed stock accumulation," CER-ETH Economics working paper series 08/91, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich. [Downloadable!]
  11. Mauro Bambi, 2006. "Endogenous growth and time to build: the AK case," Computing in Economics and Finance 2006 77, Society for Computational Economics. [Downloadable!]
    Other versions:
  12. Fabbri, Giorgio, 2007. "Viscosity solutions to delay differential equations in demo-economy," MPRA Paper 2826, University Library of Munich, Germany. [Downloadable!]
  13. Winkler, Ralph & Brandt-Pollmann, Ulrich & Moslener, Ulf & Schlöder, Johannes, 2005. "On the Transition from Instantaneous to Time-Lagged Capital Accumilation : The Case of Leontief Type Production Functions," ZEW Discussion Papers 05-30, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research. [Downloadable!]
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