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Modelling vintage structures with DDEs: principles and applications

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  • BOUCEKKINE, Raouf
  • DE LA CROIX, David
  • LICANDRO, Omar

Abstract

A comprehensive study of the linkages between demographic and economic variables should not only account for vintage specificity but also incorporate the relevant economic and demographic decisions in a complete optimal control set-up. In this paper, a methodological set-up allowing to reach these objectives is described. In this framework, time is continuous but agents take discrete timing decisions. The mixture of continuous and discrete time yields differential-difference equations (DDEs). This paper shows clearly that the approach allows for a relatively complete and rigorous analytical exploration in some special cases (mainly linear or quasi linear models), and for an easy computational appraisal in the general case.
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Suggested Citation

  • BOUCEKKINE, Raouf & DE LA CROIX, David & LICANDRO, Omar, 2004. "Modelling vintage structures with DDEs: principles and applications," LIDAM Reprints CORE 1758, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:1758
    DOI: 10.1080/08898480890513580
    Note: In : Mathematical Population Studies, 11, 151-179, 2004
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    1. Suresh P. Sethi, 2021. "Optimal Control Theory," Springer Texts in Business and Economics, Springer, edition 4, number 978-3-030-91745-6, October.
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    5. 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.
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    7. Feichtinger, Gustav & Hartl, Richard F. & Kort, Peter M. & Veliov, Vladimir M., 2006. "Capital accumulation under technological progress and learning: A vintage capital approach," European Journal of Operational Research, Elsevier, vol. 172(1), pages 293-310, July.
    8. 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.
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    13. Boucekkine, Raouf & del Rio, Fernando & Licandro, Omar, 1999. "Endogenous vs Exogenously Driven Fluctuations in Vintage Capital Models," Journal of Economic Theory, Elsevier, vol. 88(1), pages 161-187, September.
    14. 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.
    15. David N. Weil & Oded Galor, 1999. "From Malthusian Stagnation to Modern Growth," American Economic Review, American Economic Association, vol. 89(2), pages 150-154, May.
    16. Boucekkine, Raouf & de la Croix, David & Licandro, Omar, 2002. "Vintage Human Capital, Demographic Trends, and Endogenous Growth," Journal of Economic Theory, Elsevier, vol. 104(2), pages 340-375, June.
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    21. Emilio Barucci & Fausto Gozzi, 2001. "Technology adoption and accumulation in a vintage-capital model," Journal of Economics, Springer, vol. 74(1), pages 1-38, February.
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    Cited by:

    1. Augeraud-Véron, Emmanuelle & D'Albis, Hippolyte, 2009. "Continuous-Time Overlapping Generations Models," TSE Working Papers 09-047, Toulouse School of Economics (TSE).
    2. Boucekkine, Raouf & Laffargue, Jean-Pierre, 2010. "On the distributional consequences of epidemics," Journal of Economic Dynamics and Control, Elsevier, vol. 34(2), pages 231-245, February.
    3. 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.
    4. Bonneuil Noël, 2013. "Viability Theory in Population Economics," Mathematical Economics Letters, De Gruyter, vol. 1(1), pages 17-24, October.
    5. Raouf Boucekkine & David De la Croix & Omar Licandro, 2011. "Vintage Capital Growth Theory: Three Breakthroughs," Working Papers 565, Barcelona School of Economics.
    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. Hippolyte d'Albis & Jean-Pierre Drugeon, 2020. "On Investment and Cycles in Explicitely Solved Vintage Capital Models," PSE Working Papers halshs-02570648, HAL.
    8. d'Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Hupkes, Hermen Jan, 2014. "Bounded interest rate feedback rules in continuous-time," Journal of Economic Dynamics and Control, Elsevier, vol. 39(C), pages 227-236.
    9. Bonneuil, Noël & Boucekkine, Raouf, 2017. "Longevity, age-structure, and optimal schooling," Journal of Economic Behavior & Organization, Elsevier, vol. 136(C), pages 63-75.
    10. Goetz, Renan-Ulrich & Hritonenko, Natali & Yatsenko, Yuri, 2008. "The optimal economic lifetime of vintage capital in the presence of operating costs, technological progress, and learning," Journal of Economic Dynamics and Control, Elsevier, vol. 32(9), pages 3032-3053, September.
    11. Hippolyte D'Albis & Emmanuelle Augeraud-Veron, 2008. "Endogenous Retirement and Monetary Cycles," Mathematical Population Studies, Taylor & Francis Journals, vol. 15(4), pages 214-229.
    12. d'Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Schubert, Katheline, 2010. "Demographic-economic equilibria when the age at motherhood is endogenous," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1211-1221, November.
    13. Théophile T. Azomahou & Raouf Boucekkine & Bity Diene, 2009. "A closer look at the relationship between life expectancy and economic growth," International Journal of Economic Theory, The International Society for Economic Theory, vol. 5(2), pages 201-244, June.
    14. Fabbri, Giorgio, 2006. "Viscosity solutions approach to economic models governed by DDEs," MPRA Paper 2826, University Library of Munich, Germany.
    15. 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.
    16. Hippolyte d'Albis & Emmanuelle Augeraud-Véron & Hermen Jan Hupkes, 2012. "Backward- versus Forward-Looking Feedback Interest Rate Rules," Post-Print halshs-00721289, HAL.
    17. Jean-François Mercure, 2015. "An age structured demographic theory of technological change," Journal of Evolutionary Economics, Springer, vol. 25(4), pages 787-820, September.
    18. 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.
    19. Bonneuil, Noël, 2010. "Family regulation as a moving target in the demographic transition," Mathematical Social Sciences, Elsevier, vol. 59(2), pages 239-248, March.
    20. José A. Herce, "undated". "Could this ever happen in Spain? Economic and policy aspects of a SARS-like episode," Working Papers 2004-09, FEDEA.
    21. Fabbri, Giorgio & Gozzi, Fausto, 2006. "Vintage Capital in the AK growth model: a Dynamic Programming approach. Extended version," MPRA Paper 7334, University Library of Munich, Germany.
    22. Cagri Saglam & Vladimir M. Veliov, 2008. "Role of Endogenous Vintage Specific Depreciation in the Optimal Behavior of Firms," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(3), pages 381-410, September.
    23. Raouf Boucekkine & Bity Diene & Theophile Azomahou, 2008. "Growth Economics of Epidemics: A Review of the Theory," Mathematical Population Studies, Taylor & Francis Journals, vol. 15(1), pages 1-26.
    24. Fabbri, Giorgio & Faggian, Silvia & Gozzi, Fausto, 2006. "On the Dynamic Programming approach to economic models governed by DDE's," MPRA Paper 2825, University Library of Munich, Germany.

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    More about this item

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
    • E2 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment
    • D9 - Microeconomics - - Micro-Based Behavioral Economics

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