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Optimal policy and consumption smoothing effects in the time-to-build AK model

Author

Listed:
  • M. Bambi
  • G. Fabbri
  • F. Gozzi

    (Dipartimento di Scienze Economiche ed Aziendali - LUISS - Libera Università Internazionale degli Studi Sociali Guido Carli [Roma])

Abstract

In this paper, the dynamic programming approach is exploited in order to identify the closed loop policy function, and the consumption smoothing mechanism in an endogenous growth model with time to build, linear technology and irreversibility constraint in investment. Moreover, the link among the time to build parameter, the real interest rate, and the magnitude of the smoothing effect is deeply investigated and compared with what happens in a vintage capital model characterized by the same technology and utility function. Finally, we have analyzed the effect of time to build on the speed of convergence of the main aggregate variables.

Suggested Citation

  • M. Bambi & G. Fabbri & F. Gozzi, 2012. "Optimal policy and consumption smoothing effects in the time-to-build AK model," Post-Print hal-01615440, HAL.
    • Handle: RePEc:hal:journl:hal-01615440
    DOI: 10.1007/s00199-010-0577-3
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    References listed on IDEAS

    as
    1. Hippolyte d’Albis & Emmanuelle Augeraud-Véron, 2007. "Balanced cycles in an OLG model with a continuum of finitely-lived individuals," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 30(1), pages 181-186, January.
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    4. Mauro Bambi, 2006. "Endogenous Growth and Time-to-Build: the AK Case," Economics Working Papers ECO2006/17, European University Institute.
    5. Faggian, Silvia & Gozzi, Fausto, 2010. "Optimal investment models with vintage capital: Dynamic programming approach," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 416-437, July.
    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.
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    9. Ortigueira, Salvador & Santos, Manuel S, 1997. "On the Speed of Convergence in Endogenous Growth Models," American Economic Review, American Economic Association, vol. 87(3), pages 383-399, June.
    10. Fabbri, Giorgio & Gozzi, Fausto, 2008. "Solving optimal growth models with vintage capital: The dynamic programming approach," Journal of Economic Theory, Elsevier, vol. 143(1), pages 331-373, November.
    11. Bambi, Mauro & Gori, Franco, 2014. "Unifying Time-To-Build Theory," Macroeconomic Dynamics, Cambridge University Press, vol. 18(8), pages 1713-1725, December.
    12. Akiomi Kitagawa & Akihisa Shibata, 2005. "Endogenous growth cycles in an overlapping generations model with investment gestation lags," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(3), pages 751-762, April.
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    Cited by:

    1. Emmanuelle Augeraud-Veron & Mauro Bambi, 2012. "Does habit formation always increase the agents' desire to smooth consumption?," Discussion Papers 12/12, Department of Economics, University of York.
    2. Hippolyte d'Albis & Jean-Pierre Drugeon, 2020. "On Investment and Cycles in Explicitely Solved Vintage Capital Models," PSE Working Papers halshs-02570648, HAL.
    3. Fabbri Giorgio & Federico Salvatore, 2014. "On the Infinite-Dimensional Representation of Stochastic Controlled Systems with Delayed Control in the Diffusion Term," Mathematical Economics Letters, De Gruyter, vol. 2(3-4), pages 33-43, November.
    4. Mauro Bambi & Cristina Girolami & Salvatore Federico & Fausto Gozzi, 2017. "Generically distributed investments on flexible projects and endogenous growth," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(2), pages 521-558, February.
    5. Cristiano Ricci, 2023. "A non-invariance result for the spatial AK model," Papers 2311.06811, arXiv.org.
    6. 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.
    7. William Lefebvre & Enzo Miller, 2021. "Linear-quadratic stochastic delayed control and deep learning resolution," Working Papers hal-03145949, HAL.
    8. 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.
    9. Faggian, Silvia & Gozzi, Fausto & Kort, Peter M., 2021. "Optimal investment with vintage capital: Equilibrium distributions," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    10. Emmanuelle Augeraud-Veron & Mauro Bambi & Fausto Gozzi, 2017. "Solving Internal Habit Formation Models Through Dynamic Programming in Infinite Dimension," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 584-611, May.
    11. d’Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Hupkes, Hermen Jan, 2014. "Multiple solutions in systems of functional differential equations," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 50-56.
    12. Caulkins, Jonathan P. & Hartl, Richard F. & Kort, Peter M., 2010. "Delay equivalence in capital accumulation models," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1243-1246, November.
    13. Filippo de Feo & Salvatore Federico & Andrzej 'Swik{e}ch, 2023. "Optimal control of stochastic delay differential equations and applications to path-dependent financial and economic models," Papers 2302.08809, arXiv.org.
    14. William Lefebvre & Enzo Miller, 2021. "Linear-quadratic stochastic delayed control and deep learning resolution," Papers 2102.09851, arXiv.org, revised Feb 2021.
    15. Mauro Bambi & Cristina Di Girolami & Salvatore Federico & Fausto Gozzi, 2014. "On the Consequences of Generically Distributed Investments on Flexible Projects in an Endogenous Growth Model," Discussion Papers 14/15, Department of Economics, University of York.
    16. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.
    17. 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).
    18. Frédéric Zumer & Jacques Le Cacheux & Marc Flandreau, 1998. "Stability without a pact? Lessons from the European Gold Standard, 1880-1913," Sciences Po publications n°98-01, Sciences Po.
    19. Augeraud-Veron, Emmanuelle & Bambi, Mauro, 2015. "Endogenous growth with addictive habits," Journal of Mathematical Economics, Elsevier, vol. 56(C), pages 15-25.
    20. Kuangyuan Zhang & Richard Olawoyin & Antonio Nieto & Andrew N. Kleit, 2018. "Risk of commodity price, production cost and time to build in resource economics," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 20(6), pages 2521-2544, December.
    21. 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.
    22. William Lefebvre & Enzo Miller, 2021. "Linear-Quadratic Stochastic Delayed Control and Deep Learning Resolution," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 134-168, October.
    23. William Lefebvre & Enzo Miller, 2021. "Linear-quadratic stochastic delayed control and deep learning resolution," Post-Print hal-03145949, HAL.
    24. 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; AK model; Dynamic programming; Optimal strategies; Closed loop policy;
    All these keywords.

    JEL classification:

    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Investment; Capital; Intangible Capital; Capacity
    • O40 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General

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