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The short-run dynamics of optimal growth models with delays

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Abstract

Differential equations with advanced and delayed time arguments may arise in the optimality conditions of simple growth models with delays. Models with investment gestation lags (time-to-build), consumption gestation lags (habit formation) or learning by using lie in this category. In this paper, we propose a shooting method to deal with leads and lags in the Euler system associated to dynamic general equilibrium models in continuous time. We introduce the discussion describing the dynamics that emerge under various assumptions on learning by using and gestation lags. Then, we implement the numerical method we propose to solve for the short run dynamics of a neoclassical growth model with a simple time to-build-lag.

Suggested Citation

  • Fabrice Collard & Omar Licandro & Luis A. Puch, 2003. "The short-run dynamics of optimal growth models with delays," Documentos de Trabajo del ICAE 0311, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    • Handle: RePEc:ucm:doicae:0311
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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.
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    4. 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.
    5. Raouf Boucekkine & David de la Croix & Omar Licandro, 2006. "Vintage Capital," Economics Working Papers ECO2006/8, European University Institute.
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    7. 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.
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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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).
    6. 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.
    7. 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.
    8. 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.
    9. Mauro Bambi, 2006. "Endogenous growth and time to build: the AK case," Computing in Economics and Finance 2006 77, Society for Computational Economics.
    10. 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.
    11. 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.
    12. 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.
    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. José A. Herce, "undated". "Could this ever happen in Spain? Economic and policy aspects of a SARS-like episode," Working Papers 2004-09, FEDEA.
    15. 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.
    16. Hwan C. Lin, 2018. "Computing Transitional Cycles for a Deterministic Time-to-Build Growth Model," Computational Economics, Springer;Society for Computational Economics, vol. 51(3), pages 677-696, March.
    17. Bambi, Mauro, 2015. "Time-to-build and the capital structure," Economics Letters, Elsevier, vol. 137(C), pages 222-225.

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    More about this item

    Keywords

    Time-to-build; Shooting method; DDEs.;
    All these keywords.

    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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