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The short-run Dynamics of Optimal Growth Model with Delays

Author

Listed:
  • Fabrice Collard
  • Omar Licandro
  • Luis A. Puch

Abstract

Differential equations with advanced and delayed arguments arise in the optimality conditions of continuous time growth models with delays. In this paper, we use optimal control theory with delays, and we propose a shooting method to numerically deal with this class of models. We find that for a large delay the economy converges to steady state by oscillations, but consumption smoothing mitigates the induced echo effects through an advanced Euler-type differential equation.

Suggested Citation

  • 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.
  • Handle: RePEc:adr:anecst:y:2008:i:90:p:127-143
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    References listed on IDEAS

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    1. Jody Overland & Christopher D. Carroll & David N. Weil, 2000. "Saving and Growth with Habit Formation," American Economic Review, American Economic Association, vol. 90(3), pages 341-355, 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. Benhabib, Jess & Rustichini, Aldo, 1991. "Vintage capital, investment, and growth," Journal of Economic Theory, Elsevier, vol. 55(2), pages 323-339, December.
    4. Boucekkine, Raouf & Germain, Marc & Licandro, Omar, 1997. "Replacement Echoes in the Vintage Capital Growth Model," Journal of Economic Theory, Elsevier, vol. 74(2), pages 333-348, June.
    5. Boucekkine, Raouf & Licandro, Omar & Paul, Christopher, 1997. "Differential-difference equations in economics: On the numerical solution of vintage capital growth models," Journal of Economic Dynamics and Control, Elsevier, vol. 21(2-3), pages 347-362.
    6. Boucekkine, Raouf & Licandro, Omar & Puch, Luis A. & del Rio, Fernando, 2005. "Vintage capital and the dynamics of the AK model," Journal of Economic Theory, Elsevier, vol. 120(1), pages 39-72, January.
    7. BOUCEKKINE, Raouf & DE LA CROIX, David & LICANDRO, Omar, 2006. "Vintage capital," CORE Discussion Papers 2006024, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, January.
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    Citations

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    Cited by:

    1. Raouf Boucekkine & David De La Croix & Omar Licandro, 2004. "MODELLING VINTAGE STRUCTURES WITH DDEs: PRINCIPLES AND APPLICATIONS," Mathematical Population Studies, Taylor & Francis Journals, vol. 11(3-4), pages 151-179.
    2. 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.
    3. Francesco Ricci, 2007. "Environmental policy and growth when inputs are differentiated in pollution intensity," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 38(3), pages 285-310, November.
    4. Simon Sosvilla-Rivero & Pedro Rodriguez, 2010. "Linkages in international stock markets: evidence from a classification procedure," Applied Economics, Taylor & Francis Journals, vol. 42(16), pages 2081-2089.
    5. Raouf Boucekkine & Giorgio Fabbri & Patrick-Antoine Pintus, 2011. "On the optimal control of a linear neutral differential equation arising in economics," Working Papers halshs-00576770, HAL.
    6. 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;Society for Computational Economics, vol. 31(2), pages 181-206, March.
    7. repec:kap:compec:v:51:y:2018:i:1:d:10.1007_s10614-016-9597-9 is not listed on IDEAS
    8. Mauro Bambi, 2006. "Endogenous Growth and Time-to-Build: the AK Case," Economics Working Papers ECO2006/17, European University Institute.
    9. M. Bambi & G. Fabbri & F. Gozzi, 2012. "Optimal policy and consumption smoothing effects in the time-to-build AK model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(3), pages 635-669, August.
    10. José A. Herce, "undated". "Could this ever happen in Spain? Economic and policy aspects of a SARS-like episode," Working Papers 2004-09, FEDEA.
    11. repec:kap:compec:v:51:y:2018:i:3:d:10.1007_s10614-016-9633-9 is not listed on IDEAS

    More about this item

    JEL classification:

    • O40 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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