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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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    Cited by:

    1. Raouf Boucekkine & David 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. Akio Matsumoto & Ferenc Szidarovszky, 2024. "Nonlinear Kaldor model augmented with retardation and anticipation," Annals of Operations Research, Springer, vol. 337(3), pages 937-958, June.
    3. d’Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Hupkes, Hermen Jan, 2014. "Stability and determinacy conditions for mixed-type functional differential equations," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 119-129.
    4. Hwan C. Lin & L. F. Shampine, 2018. "R&D-based Calibrated Growth Models with Finite-Length Patents: A Novel Relaxation Algorithm for Solving an Autonomous FDE System of Mixed Type," Computational Economics, Springer;Society for Computational Economics, vol. 51(1), pages 123-158, January.
    5. 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.
    6. 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.
    7. Mauro Bambi, 2006. "Endogenous growth and time to build: the AK case," Computing in Economics and Finance 2006 77, Society for Computational Economics.
    8. 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.
    9. 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.
    10. 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.
    11. Mauro Bambi & Omar Licandro, "undated". "Endogenous Growth and Wave-Like Business Fluctuation," Working Papers 533, Barcelona School of Economics.
    12. 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.
    13. 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.
    14. BOUCEKKINE, Raouf & FABBRI, Giorgio & PINTUS, Patrick, 2012. "On the optimal control of a linear neutral differential equation arising in economics," LIDAM Reprints CORE 2449, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    15. Lin, Hwan C. & Shampine, L.F., 2014. "Finite-length Patents and Functional Differential Equations in a Non-scale R&D-based Growth Model," MPRA Paper 61603, University Library of Munich, Germany.
    16. José A. Herce, "undated". "Could this ever happen in Spain? Economic and policy aspects of a SARS-like episode," Working Papers 2004-09, FEDEA.
    17. Hwan C. Lin, 2018. "Erratum to: Computing Transitional Cycles for a Deterministic Time-to-Build Growth Model," Computational Economics, Springer;Society for Computational Economics, vol. 51(3), pages 697-697, March.
    18. Martina BOBALOVA & Veronika NOVOTNA, 2021. "Modeling Of Time Delayed Processes In Business Economics," Proceedings of the INTERNATIONAL MANAGEMENT CONFERENCE, Faculty of Management, Academy of Economic Studies, Bucharest, Romania, vol. 15(1), pages 79-89, November.
    19. Bambi, Mauro, 2015. "Time-to-build and the capital structure," Economics Letters, Elsevier, vol. 137(C), pages 222-225.

    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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