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Modelling vintage structures with DDEs: principles and applications

  • David DE LA CROIX

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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Paper provided by European University Institute in its series Economics Working Papers with number ECO2004/06.

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Date of creation: 2004
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Handle: RePEc:eui:euiwps:eco2004/06
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  2. David de la Croix & Omar Licandro, . "Life expectancy and endogenous growth," Working Papers 97-23, FEDEA.
  3. 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.
  4. Malcomson, James M., 1975. "Replacement and the rental value of capital equipment subject to obsolescence," Journal of Economic Theory, Elsevier, vol. 10(1), pages 24-41, February.
  5. 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, vol. 25(5), pages 655-669, May.
  6. 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.
  7. Boucekkine, Raouf & Del Rio, Fernando & Licandro, Omar, 1999. "Endogenous vs exogenously driven fluctuations in vintage capital models," CEPREMAP Working Papers (Couverture Orange) 9901, CEPREMAP.
  8. Boucekkine, Raouf & Licandro, Omar & Puch, Luis A. & del Rio, Fernando, 1999. "Vintage Capital and the Dynamics of the AK Model," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2000009, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  9. Boucekkine, Raouf, et al, 1998. "Creative Destruction, Investment Volatility, and the Average Age of Capital," Journal of Economic Growth, Springer, vol. 3(4), pages 361-84, December.
  10. Boucekkine, Raouf & Pommeret, Aude, 2004. "Energy saving technical progress and optimal capital stock: the role of embodiment," Economic Modelling, Elsevier, vol. 21(3), pages 429-444, May.
  11. Boucekkine, Raouf & de la Croix, David & Licandro, Omar, 2000. "Vintage Human Capital, Demographic Trends and Endogenous Growth," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2000007, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  12. Cogley, Timothy & Nason, James M, 1995. "Output Dynamics in Real-Business-Cycle Models," American Economic Review, American Economic Association, vol. 85(3), pages 492-511, June.
  13. 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) 2002014, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  14. 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.
  15. Kelley, Allen C. & Schmidt, Robert M., 1995. "Aggregate Population and Economic Growth Correlations: The Role of the Components of Demographic Change," Working Papers 95-37, Duke University, Department of Economics.
  16. Michel, P., 1980. "On the Transversality Condition in Infinite Horizon Optimal Problems," Cahiers de recherche 8024, Universite de Montreal, Departement de sciences economiques.
  17. Benhabib, Jess & Rustichini, Aldo, 1990. "Vintage Capital, Investment And Growth," Working Papers 90-22, C.V. Starr Center for Applied Economics, New York University.
  18. 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.
  19. 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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