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MODELLING VINTAGE STRUCTURES WITH DDEs: PRINCIPLES AND APPLICATIONS

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  • RAOUF BOUCEKKINE
  • DAVID CROIX
  • OMAR LICANDRO

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. 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). It is clearly shown 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.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:mpopst:v:11:y:2004:i:3-4:p:151-179
    DOI: 10.1080/08898480890513580
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    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 & Germain, Marc & Licandro, Omar & Magnus, Alphonse, 1998. "Creative Destruction, Investment Volatility, and the Average Age of Capital," Journal of Economic Growth, Springer, vol. 3(4), pages 361-384, December.
    8. Feichtinger, Gustav & Hartl, Richard F. & Kort, Peter M. & Veliov, Vladimir M., 2006. "Anticipation effects of technological progress on capital accumulation: a vintage capital approach," Journal of Economic Theory, Elsevier, vol. 126(1), pages 143-164, January.
    9. 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.
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    17. 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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    22. 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.
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    Cited by:

    1. 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.
    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. 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.
    4. 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.
    5. Hippolyte D'Albis & Emmanuelle Augeraud-Veron, 2008. "Endogenous Retirement and Monetary Cycles," Mathematical Population Studies, Taylor & Francis Journals, vol. 15(4), pages 214-229.
    6. 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.
    7. 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.
    8. Raouf Boucekkine & David de la Croix & Omar Licandro, 2011. "Vintage capital growth theory: Three breakthroughs," UFAE and IAE Working Papers 875.11, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    9. 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.
    10. Augeraud-Véron, Emmanuelle & D'Albis, Hippolyte, 2009. "Continuous-Time Overlapping Generations Models," TSE Working Papers 09-047, Toulouse School of Economics (TSE).
    11. 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.
    12. 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.
    13. Bonneuil, Noël & Boucekkine, Raouf, 2017. "Longevity, age-structure, and optimal schooling," Journal of Economic Behavior & Organization, Elsevier, vol. 136(C), pages 63-75.
    14. Jean-François Mercure, 2015. "An age structured demographic theory of technological change," Journal of Evolutionary Economics, Springer, vol. 25(4), pages 787-820, September.
    15. Bonneuil, Noël, 2010. "Family regulation as a moving target in the demographic transition," Mathematical Social Sciences, Elsevier, vol. 59(2), pages 239-248, March.
    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. José A. Herce, "undated". "Could this ever happen in Spain? Economic and policy aspects of a SARS-like episode," Working Papers 2004-09, FEDEA.
    18. 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.
    19. Bonneuil Noël, 2013. "Viability Theory in Population Economics," Mathematical Economics Letters, De Gruyter, vol. 1(1), pages 17-24, October.
    20. 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.
    21. Fabbri, Giorgio, 2006. "Viscosity solutions approach to economic models governed by DDEs," MPRA Paper 2826, University Library of Munich, Germany.
    22. 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.
    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. Raouf Boucekkine & David de la Croix & Omar Licandro, 2011. "Vintage capital growth theory: Three breakthroughs," UFAE and IAE Working Papers 875.11, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    25. 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.

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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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