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Modelling vintage structures with DDEs : principles and applications

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  • Raouf, BOUCEKKINE

    (UNIVERSITE CATHOLIQUE DE LOUVAIN, Institut de Recherches Economiques et Sociales (IRES) and UNIVERSITE CATHOLIQUE DE LOUVAIN, Center for Operations Research and Econometrics (CORE))

  • David de la Croix

    (UNIVERSITE CATHOLIQUE DE LOUVAIN, Institut de Recherches Economiques et Sociales (IRES) and CORE and FNRS Belgium and UNIVERSITE CATHOLIQUE DE LOUVAIN, Center for Operations Research and Econometrics (CORE))

  • Omar Lidandro

    (European University Institute, Firenze, and FEDEA, Madrid)

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 the 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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Bibliographic Info

Paper provided by Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES) in its series Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) with number 2004004.

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Date of creation: 01 Mar 2004
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Handle: RePEc:ctl:louvir:2004004

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Keywords: Demography; Economic growth; Vintage structures; Optimal control; Differential-difference equations; State-dependence;

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References

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  1. BOUCEKKINE, Raouf & POMMERET, Aude, . "Energy saving technical progress and optimal capital stock: the role of embodiment," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -1703, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Boucekkine, Raouf & Germain, Marc & Licandro, Omar, 1997. "Replacement Echoes in the Vintage Capital Growth Model," Journal of Economic Theory, Elsevier, Elsevier, vol. 74(2), pages 333-348, June.
  3. Raouf BOUCEKKINE & Omar LICANDRO & Luis A. PUCH & Fernando DEL RIO, 2002. "Vintage Capital And the Dynamics of the AK Model," Economics Working Papers, European University Institute ECO2002/07, European University Institute.
  4. Benhabib, Jess & Rustichini, Aldo, 1990. "Vintage Capital, Investment And Growth," Working Papers, C.V. Starr Center for Applied Economics, New York University 90-22, C.V. Starr Center for Applied Economics, New York University.
  5. Fabrice Collard & Omar Licandro & Luis A. Puch, . "The short-run dynamics of optimal growth models with delays," Working Papers 2004-05, FEDEA.
  6. R. Boucekkine & M. Germain & O. Licandro & A. Magnus, . "Creative destruction, investment volatility, and the average age of capital," Working Papers 97-08, FEDEA.
  7. Boucekkine, Raouf & Germain, Marc & Licandro, Omar & Magnus, Alphonse, 2001. "Numerical solution by iterative methods of a class of vintage capital models," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 25(5), pages 655-669, May.
  8. Galor, Oded & Weil, David, 1999. "From Malthusian Stagnation to Modern Growth," CEPR Discussion Papers, C.E.P.R. Discussion Papers 2082, C.E.P.R. Discussion Papers.
  9. Raouf BOUCEKKINE & David de la Croix & Omar LICANDRO, 2002. "Early mortality declines at the dawn of modern growth," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales), Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES) 2002014, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  10. Raouf Boucekkine & Fernando del Río & Omar Licandro, . "Endogenous vs Exogenously Driven Fluctuations in Vintage Capital Models," Working Papers 98-19, FEDEA.
  11. Raouf Boucekkine & Omar Licandro & Luis A. Puch & Fernando del Rio, . "Vintage capital and the dynamics of the AK model," Working Papers 2000-01, FEDEA.
  12. Boucekkine, Raouf & del Rio, Fernando & Licandro, Omar, 1999. "Endogenous vs Exogenously Driven Fluctuations in Vintage Capital Models," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales), Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES) 1999007, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  13. Boucekkine, Raouf & de la Croix, David & Licandro, Omar, 2002. "Vintage Human Capital, Demographic Trends, and Endogenous Growth," Journal of Economic Theory, Elsevier, Elsevier, vol. 104(2), pages 340-375, June.
  14. de la Croix, David & Licandro, Omar, 1999. "Life expectancy and endogenous growth," Economics Letters, Elsevier, Elsevier, vol. 65(2), pages 255-263, November.
  15. Michel, P., 1980. "On the Transversality Condition in Infinite Horizon Optimal Problems," Cahiers de recherche, Universite de Montreal, Departement de sciences economiques 8024, Universite de Montreal, Departement de sciences economiques.
  16. Malcomson, James M., 1975. "Replacement and the rental value of capital equipment subject to obsolescence," Journal of Economic Theory, Elsevier, Elsevier, vol. 10(1), pages 24-41, February.
  17. Collard, Fabrice & Licandro, Omar & Puch, Luis, 2005. "The Short-Run Dynamics of Optimal Growth Models with Delays," CEPR Discussion Papers, C.E.P.R. Discussion Papers 5414, C.E.P.R. Discussion Papers.
  18. Raouf Boucekkine & David de la Croix & Omar Licandro, . "vintage human capital, demographic trends and endogenous growth," Working Papers 2000-02, FEDEA.
  19. Emilio Barucci & Fausto Gozzi, 2001. "Technology adoption and accumulation in a vintage-capital model," Journal of Economics, Springer, Springer, vol. 74(1), pages 1-38, February.
  20. Raouf Boucekkine & Marc Germain & Omar Licandro & Alphonse Magnus, . "Numerical solution by iterative methods of a class on vintage capital models," Working Papers 97-26, FEDEA.
  21. Timothy Cogley & James M. Nason, 1993. "Output dynamics in real business cycle models," Working Papers in Applied Economic Theory, Federal Reserve Bank of San Francisco 93-10, Federal Reserve Bank of San Francisco.
  22. BOUCEKKINE, Raouf & GERMAIN, Marc & LICANDRO, Omar & MAGNUS, Alphonse, . "Creative destruction, investment volatility, and the average age of capital," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -1376, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  23. Raouf Boucekkine & Marc Germain & Omar Licandro, . "Replacement echoes in the vintage capital growth model," Working Papers 96-16, FEDEA.
  24. Raouf Boucekkine & Omar Licandro & Christopher Paul, . "Differential-Difference Equations in Economics: On the Numerical Solution of Vintage Capital Growth Models," Computing in Economics and Finance 1996, Society for Computational Economics _036, Society for Computational Economics.
  25. Raouf Boucekkine & Marc Germain & Omar Licandro & Alphonse Magnus, . "Numerical solution by iterative methods of a class of vintage capital models," Working Papers 98-20, FEDEA.
  26. David de la Croix & Omar Licandro, . "Life expectancy and endogenous growth," Working Papers 97-23, FEDEA.
  27. Kelley, Allen C. & Schmidt, Robert M., 1995. "Aggregate Population and Economic Growth Correlations: The Role of the Components of Demographic Change," Working Papers, Duke University, Department of Economics 95-37, Duke University, Department of Economics.
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